Digital Electronics 1

Copyright © 2017 Project Lead The Way, Inc. All rights reserved. Student Accessibility In addition to the student accessibility standards inherent in the way we develop PLTW courses, PLTW supports purposeful student accessibility in the following ways: Courses supports standard accessibility practices and techniques including the use of video captions, alternative text descriptions, and compatibility with screen readers. (Note: Features may vary based on course development date.) Some of our newer PLTW course developments feature a Student Accommodation section to help support you in adjusting course activities, projects, or problems to be accessible for your students. A non-digital, PDF version of the student course curriculum is available for use in the following classroom situations: Technology issues. Students who require a text or print version. Another circumstance in which student access to digital course curriculum is not feasible or possible. These course versions are intended to be used only to support student accessibility when access to digital content through Courses is not possible. Important: Due to its non-digital nature, the PDF version of course curriculum will not feature digital interactivity and tools, embedded media, or any updates made available via Courses during the school year.

1. Course Level Resources 1. General Prep and Considerations 1. Course Preface 2. Curriculum Revisions 3. Course Preparation 4. Presentation Download 5. PLTW Engineering Notebook 6. Professional Development Opportunities 7. Community Forums 2. Copyright Notice 1. It is illegal to make copies of this course without the permission of Project Lead The Way, Inc. 2. Unit 1: Foundations in Electronics 1. Introduction to Digital Electronics 1. Welcome to Digital Electronics 1. Welcome to Digital Electronics 2. Curriculum Design 1. Teacher Resources 2. Course Curriculum Frameworks 3. Instructional Timeline 3. Lesson Structure 1. Activities, Projects, and Problems (APBs) 2. Problem-based and Inquiry-based Learning 3. Role of the Teacher 4. Role of the Learner 4. References 2. Lesson 1.1: Introduction to Electronics 1. Lesson 1.1 Teacher Notes 1. Introduction to Digital Electronics 2. Classroom and Laboratory Safety 3. Quiz 1.1.1 General Safety in the Electronics Classroom 4. Activity 1.1.2 Investigating Basic Circuits 5. Investigating Basic Circuits 6. Scientific and Engineering Notation 7. Activity 1.1.3 Scientific and Engineering Notation 8. Introduction to Resistors and Capacitors 9. Activity 1.1.4 Component Identification: Analog 10. Circuit Theory Laws 11. Activity 1.1.5a Circuit Theory: Hand Calculations 12. Activity 1.1.5b Circuit Theory: Simulation 13. The Breadboard (Optional Review) 14. Activity 1.1.5c Circuit Theory: Breadboarding 15. Activity 1.1.6 Component Identification: Digital 16. Introduction to Logic Gates and Integrated Circuits 17. Activity 1.1.7 Introduction to Datasheets 18. Soldering and Desoldering 19. Project 1.1.8 Soldering Practice: Fun Light Project (Optional) 20. Introduction to the Board Game Counter

Copyright © 2017 Project Lead The Way, Inc. All rights reserved. 21. Project 1.1.9 Soldering: Random Number Generator 2. Lesson 1.1 Teacher Resources 1. Preface 2. Day-by-Day Plans 1. Day 1 2. Day 2 3. Day 3 4. Day 4 5. Day 5 6. Day 6 7. Days 7–8 8. Days 9–10 9. Days 10–11 10. Days 12–15 11. Days 16–17 12. Day 18 13. Days 18–20 (Optional) 14. Days 19–20 3. Activity 1.1.1 Answer Key 1. Procedure 4. Activity 1.1.2 DMS Answer Key 1. Procedure 1. Part A: Creating a Circuit and Measuring a Circuit’s Properties 2. Part B: Series and Parallel Circuits 2. Conclusion 1. Going Further 5. Activity 1.1.3 Answer Key 1. Procedure 2. Conclusion 6. Activity 1.1.4 Answer Key 1. Procedure 2. Conclusion 7. Activity 1.1.5a Answer Key 1. Procedure 2. Conclusion 1. Going Further (Optional) 8. Activity 1.1.5b Answer Key 1. Procedure 2. Conclusion 9. Activity 1.1.5c Answer Key 1. Conclusion 10. Activity 1.1.6 Answer Key 1. Procedure 1. Combinational Logic 2. Sequential Logic 3. Clock Signals (The 555 Timer) 2. Conclusion 11. Activity 1.1.7 Answer Key 1. Procedure 2. Conclusion 12. Activity 1.1.8 Answer Key 1. Conclusion

Copyright © 2017 Project Lead The Way, Inc. All rights reserved. 13. Project 1.1.9 Answer Key 1. Conclusion 14. Lesson 1.1 References 3. Lesson 1.2: Introduction to Circuit Design 1. Lesson 1.2 Teacher Notes 1. Circuit Design 2. Activity 1.2.1 Introduction to Combinational Logic Design: Seat Belt Circuit 3. Analog and Digital Signals 4. Activity 1.2.2 Analog and Digital Signals 5. The Binary Number System 6. Activity 1.2.3 Binary Number System 7. Activity 1.2.4 Introduction to Sequential Logic Design: Counters 8. Using a Clock Signal 9. Clock Signals: 555 Timer 10. Activity 1.2.5 Clock Signals: 555 Timer 11. Understanding Analog Design: Random Number Generator 12. Project 1.2.6 Understanding Analog Design: The Random Number Generator 13. Understanding Digital Design: Random Number Generator 14. Project 1.2.7 Understanding Digital Design: Random Number Generator 2. Lesson 1.2 Teacher Resources 1. Preface 2. Day-by-Day Plans 1. Days 1–3 2. Day 4 3. Day 5 4. Days 6–8 5. Days 9–12 6. Days 13–15 7. Days 16–20 3. Activity 1.2.1 Answer Key 1. Procedure 2. Conclusion 1. Going Further (Optional) 4. Activity 1.2.2 Answer Key 1. Procedure 2. Conclusion 5. Activity 1.2.3 Answer Key 1. Procedure 2. Conclusion 1. Going Further (Optional) 6. Activity 1.2.4 DMS Answer Key 1. Procedure 2. Conclusion 7. Activity 1.2.5 Answer Key 1. Procedure 1. Simulation 8. Project 1.2.6 Answer Key 1. Procedure 2. Conclusion 9. Project 1.2.7 Answer Key 1. Procedure 2. Conclusion

Copyright © 2017 Project Lead The Way, Inc. All rights reserved. 10. Lesson 1.2 References 3. Unit 2: Combinational Logic 1. Lesson 2.1: AOI Combinational Logic Circuit Design 1. Lesson 2.1 Teacher Notes 1. Combinational Logic Design Process 2. AOI Design: Truth Tables to Logic Expressions 3. Activity 2.1.1 AOI Design: Truth Tables to Logic Expressions 4. AOI Design: Logic Analysis 5. Activity 2.1.2 AOI Logic Analysis: Circuit to Truth Table to Logic Expressions 6. AOI Logic Implementation 7. Activity 2.1.3 AOI Logic Implementation 8. Circuit Simplification: Boolean Algebra 9. Activity 2.1.4 Circuit Simplification: Boolean Algebra 10. Circuit Simplification: DeMorgan’s Theorems 11. Activity 2.1.5 Circuit Simplification: DeMorgan’s Theorems 12. Digital Electronics Equations and Theorems 13. Project 2.1.6 AOI Logic Design: Majority Vote 2. Lesson 2.1 Teacher Resources 1. Preface 2. Day-by-Day Plans 1. Days 1–2 2. Day 3 3. Days 4–5 4. Days 6–7 5. Days 8–9 6. Days 10–11 3. Activity 2.1.1 Answer Key 1. Procedure 1. Truth Tables to Logic Expressions 2. Logic Expressions to Truth Tables 3. Seat Belt Alarm Circuit 4. Humidity Sensor Circuit 2. Conclusion 1. Going Further (Optional) 4. Activity 2.1.2 Answer Key 1. Procedure 2. Conclusion 5. Activity 2.1.3 Answer Key 1. Procedure 2. Conclusion 6. Activity 2.1.4 Answer Key 1. Procedure 2. Conclusion 7. Activity 2.1.5 Answer Key 1. Procedure 2. Conclusion 8. Project 2.1.6 Answer Key 1. Procedure 9. Lesson 2.1 References 2. Lesson 2.2: Alternative Design: Universal Gates and K-Mapping 1. Lesson 2.2 Teacher Notes 1. Karnaugh Mapping

Copyright © 2017 Project Lead The Way, Inc. All rights reserved. 2. Activity 2.2.1 Circuit Simplification: Karnaugh Mapping 3. Universal Gate - NAND 4. Activity 2.2.2 Universal Gates: NAND Only Logic Design 5. Universal Gate - NOR 6. Activity 2.2.3 Universal Gates: NOR Only Logic Design 7. Activity 2.2.4 Design Tool: Logic Converter 8. Project 2.2.5 Universal Gates and K-Mapping: Fireplace Control Circuit 9. Combinational Logic Design Process 2. Lesson 2.2 Teacher Resources 1. Preface 2. Day-by-Day Plans 1. Days 1–2 2. Days 3–5 3. Days 6–8 4. Day 9 5. Days 10–13 6. Day 14 3. Actvity 2.2.1 Answer Key 1. Procedure 2. Conclusion 1. Going Further (Optional) 4. Actvity 2.2.2 Answer Key 1. Procedure 2. Conclusion 5. Actvity 2.2.3 Answer Key 1. Procedure 2. Conclusion 6. Actvity 2.2.4 Answer Key 1. Procedure 2. Conclusion 7. Project 2.2.5 Answer Key 1. Conclusion 8. Lesson 2.2 References 3. Lesson 2.3: Specific Combinational Logic Designs 1. Lesson 2.3 Teacher Notes 1. Hexadecimal and Octal Number Systems 2. Calculators 3. Activity 2.3.1 Hexadecimal and Octal Number Systems 4. Seven Segment Display Driver 5. Activity 2.3.2 Seven-Segment Displays 6. Multiplexed Signals and Demultiplexed Signals 7. Activity 2.3.3 Multiplexers (MUX) and Demultiplexers (DEMUX) 8. 2’s Complement Arithmetic 9. Activity 2.3.4 Two’s Complement Arithmetic 10. XOR, XNOR, and Binary Adders 11. Activity 2.3.5 Binary Adders: XOR and XNOR 2. Lesson 2.3 Teacher Resources 1. Preface 2. Day-by-Day Plans 1. Day 1 2. Days 2–3 3. Days 4–5

Copyright © 2017 Project Lead The Way, Inc. All rights reserved. 4. Days 6–7 5. Days 8–9 6. Day 10 3. Activity 2.3.1 Answer Key 1. Procedure 2. Conclusion 1. Going Further (Optional) 4. Activity 2.3.2 Answer Key 1. Procedure 1. Seven-Segment Display Drivers 2. Conclusion 5. Activity 2.3.3 Answer Key 1. Procedure 2. Conclusion 6. Activity 2.3.4 Answer Key 1. Procedure 2. Conclusion 7. Activity 2.3.5 Answer Key 1. Procedure 2. Conclusion 1. Going Further 8. Lesson 2.3 References 4. Lesson 2.4: Introduction to Programmable Logical Devices (PLDs) 1. Lesson 2.4 Teacher Notes 1. Combinational Logic Student Design Problem: Date of Birth 2. Problem 2.4.1 Combinational Logic Circuit Design: Date of Birth 3. Combo Logic Design Process 4. Overview of Programmable Logic Devices 5. Activity 2.4.2 Introduction to PLDs Programming Tutorial 6. Project 2.4.3 Combinational Logic Design: Date of Birth with a PLD 2. Lesson 2.4 Teacher Resources 1. Preface 2. Day-by-Day Plans 1. Performance-based Assessment (Optional) 2. Days 1–5 3. Day 6 4. Day 7 3. Problem 2.4.1 Answer Key 1. Conclusion 4. Activity 2.4.2 Answer Key 1. Conclusion 5. Project 2.4.3 Answer Key 1. Procedure 1. Digital MiniSystem (DMS): (Cmod S6 FPGA Module) 2. Digital Logic Board (DLB) 2. Conclusion 6. Lesson 2.4 References 4. Unit 3: Sequential Logic 1. Lesson 3.1: Sequential Logic Circuit Design 1. Lesson 3.1 Teacher Notes 1. Flip-Flops and Latches 2. Activity 3.1.1 Sequential Logic: D Flip-Flops and J/K Flip-Flops

Copyright © 2017 Project Lead The Way, Inc. All rights reserved. 3. Flip-Flop Applications 4. Activity 3.1.2 Flip-Flop Applications: Event Detection 5. Activity 3.1.3 Flip-Flop Applications: Shift Register 2. Lesson 3.1 Teacher Resources 1. Preface 2. Day-by-Day Plans 1. Days 1–2 2. Days 3–4 3. Days 5–6 3. Activity 3.1.1 Answer Key 1. Procedure 2. Conclusion 4. Activity 3.1.2 Answer Key 1. Conclusion 5. Activity 3.1.3 Answer Key 1. Procedure 1. Simulation (Design Mode) 2. Simulation (PLD Mode) 2. Conclusion 6. Lesson 3.1 References 2. Lesson 3.2: Asynchronous Counters 1. Lesson 3.2 Teacher Notes 1. Asynchronous Counter Presentation 2. Activity 3.2.1 Asynchronous Counters: Small-Scale Integration (SSI) Up/Down Counters 3. Activity 3.2.2 Asynchronous Counters: Small-Scale Integration (SSI) Modulus Counters 4. Activity 3.2.3 Asynchronous Counters: Medium-Scale Integration (MSI) Suspend/Reset Counts 5. Problem 3.2.4 Asynchronous Counters: Now Serving Display (DMS) 2. Lesson 3.2 Teacher Resources 1. Preface 2. Day-by-Day Plans 1. Day 1 2. Days 2–5 3. Days 6–8 4. Days 9–14 5. Days 15–25 3. Activity 3.2.1 Answer Key 1. Procedure 1. Simulation (Design Mode) 2. Simulation (PLD Mode) 3. Export to PLD (PLD Mode) 2. Conclusion 4. Activity 3.2.2 PLD Answer Key 1. Procedure 1. Simulation (Design Mode) 2. Digital MiniSytem (DMS) (Disregard if using the DLB) 2. Conclusion 5. Activity 3.2.2 PLD_CLK Answer Key 1. Procedure 1. Simulation (Design Mode)

Copyright © 2017 Project Lead The Way, Inc. All rights reserved. 2. Digital MiniSytem (DMS) (Disregard if using the DLB) 2. Conclusion 6. Activity 3.2.3 Answer Key 1. Procedure 2. Conclusion 7. Problem 3.2.4 DMS Answer Key 1. Conclusion 8. Lesson 3.2 References 3. Lesson 3.3: Synchronous Counters 1. Lesson 3.3 Teacher Notes 1. Synchronous Counters 2. Activity 3.3.1 Synchronous Counters: Small-Scale Integration (SSI) 3. Synchronous Counters with MSI Gates 4. Activity 3.3.2 Synchronous Counters: Medium-Scale Integration (MSI) 74LS163 Up Counter 5. Activity 3.3.3 Synchronous Counters: Medium-Scale Integration (MSI) 74LS193 Up/Down Counter 6. Project 3.3.4 Synchronous Counters: Sixty-Second Timer (DMS) 2. Lesson 3.3 Teacher Resources 1. Preface 2. Day-by-Day Plans 1. Day 1 2. Days 2–5 3. Days 6–10 4. Days 11–15 5. Days 16–25 3. Activity 3.3.1 Answer Key 1. Procedure 2. Conclusion 4. Activity 3.3.2 Answer Key 1. Procedure 1. Simulation (PLD Mode) 2. Conclusion 5. Activity 3.3.3 Answer Key 1. Procedure 1. PLD Mode 2. Conclusion 6. Problem 3.3.4 DMS Answer Key 1. Procedure 1. Simulation: (Design Mode or PLD Mode) 7. Lesson 3.3 References 5. Unit 4: Controlling Real World Systems 1. Lesson 4.1: Introduction to State Machines 1. Lesson 4.1 Teacher Notes 1. Platform and Hardware Options (VEX) 2. Introduction to Sensors and Motors: Copier Jam Dectector VEX/DMS 1. Helpful VEX design notes 2. VEX parts needed for this fixture 3. State Machine Design 1. Helpful design notes 2. VEX parts needed for this fixture 4. Problem 4.1.3 State Machines: Tollbooth (VEX/DMS)

Copyright © 2017 Project Lead The Way, Inc. All rights reserved. 2. Lesson 4.1 Teacher Resources 1. Preface 2. Day-by-Day Plans 1. Days 1–4 2. Days 5–8 3. Days 8–20 3. Project 4.1.1 VEX-DMS Answer Key 1. Conclusion 1. Design Mode – Simplified 2. PLD Mode Design – Simplified 4. Activity 4.1.2 DMS Answer Key 1. Design Mode (Procedure item 8) 2. PLD Mode - DMS (Procedure item 11) 3. Conclusion 1. Going Further (Optional) 5. Problem 4.1.3 VEX-DMS Answer Key 1. State Graph Analysis 2. Tollbooth State Transition Table Analysis 3. Design Equations 4. Tollbooth Test Fixture: Design Mode 5. Conclusion 6. Lesson 4.1 References 2. Lesson 4.2: Introduction to Microcontollers 1. Lesson 4.2 Teacher Notes 1. Microcontrollers, Microcomputers, and Microprocessors 2. Tutorial 4.2.1 Installing Arduino IDE Software 3. Activity 4.2.2 Introduction to Microcontrollers 4. PWM: Pulse Width Modulation Signals 5. Activity 4.2.3 PWM Signals 6. Problem 4.2.4 Microcontrollers: The Tollbooth Revisited 2. Lesson 4.2 Teacher Resources 1. Preface 2. Day-by-Day Plans 1. Day 1 2. Days 2–5 3. Days 5–6 4. Days 7–10 3. Activity 4.2.2 Answer Key 1. Procedures 1. Sketch 2: “AltBlink” 2. Sketch 3: “Pushbutton” 3. Sketch 4: “DigitalReadSerial” 4. Sketch 5: “DigitalReadSerialLED” 5. Sketch 5: “PIRDigitalReadSerial” 6. Sketch 6: “AnalogReadSerial” 7. Sketch 7: “Joystick” 2. Conclusion 4. Activity 4.2.3 Answer Key 1. Sketch 1: “Two Axis Accelerometer” 5. Problem 4.2.4 Answer Key 6. Lesson 4.2 References 6. Additional Resources

Copyright © 2017 Project Lead The Way, Inc. All rights reserved. 1. General Teacher Resources 1. Course Presentations 2. Assessment Resources 1. EoC Assessment Administration Manual 2. Score Interpretation Guide 3. Content Map 4. Sample Multiple-Choice Items 5. Test Blueprint Template 3. Hardware and Software Support 4. Multisim 14 CDS Files 5. Arduino IDE Files 2. Course Resources 1. Digital Electronics Course Outline 2. Digital Electonics Resume 1. Computational and Analytical Skills 2. Digital Electronics Design Experience 3. Practical Application Experience 4. Tools and Software 5. Professional Skills 6. Course Knowledge 1. Foundations in Electronics 2. Combinational Logic 3. Sequential Logic 4. Controlling Real World Systems 3. Frameworks 4. Student Accessibility 7. Appendix 1. Remarks

General Prep and Considerations Course Preface

From smartphones to appliances, digital circuits are all around us. This Digital Electronics (DE) course provides a foundation for students who are interested in electrical engineering, electronics, or circuit design. Students study topics such as combinational and sequential logic and are exposed to circuit design tools used in industry, including logic gates, integrated circuits, and programmable logic devices. Curriculum Revisions

The Digital Electronics curriculum is continuously updated to provide content and instructional resources that are current and based on best practices. Significant revisions to the curriculum implemented since the prior release of DE are documented in the Digital Electronics Curriculum Revisions.

Course Preparation

Verify that you have the equipment and supplies necessary to implement Digital Electronics. To view a list of required equipment and supplies, use the calculator tool on the PLTW.org website.

Equipment & Supplies Calculator | pltw.org

Check the Optional items to make sure you have included equipment and supplies for any optional activities, projects, or problems that you plan to implement in your classroom. Verify that you have the appropriate classroom supplies for the options that you intend to implement.

Extensive instructional guidance is provided in the Teacher Notes and Teacher Resources pages for each unit of the course. Read these resources thoroughly to identify equipment and supplies needed for each day’s activity.

Prior to presenting each lesson, check all internet links (especially in the Student Course) to make sure that they are not blocked by your system and connect properly. Presentation Download

To support your instruction, the Microsoft® PowerPoint® files corresponding to each of the slideshows embedded in the Student Course are available for you to download. You may access the presentations from the Course Presentations page nested under General Teacher Resources.

The PLTW Engineering curriculum requires students to keep a bound PLTW Engineering Notebook. An engineering notebook contains all design work completed for a specific design project. It is a chronological documentation of all tasks completed during a design process.

Students are required to keep a bound engineering notebook for this course. A single engineering notebook to document design work for multiple projects and problems is acceptable. However, each project or problem should have a separate designated section within the notebook that includes only pertinent information for that particular project or problem. You should have a plan in place to make sure each student can obtain an engineering notebook.

Instructional resources related to engineering notebooks are accessible from the General Student Resources page in the Student Course. Note that an engineering notebook is different from a course binder or portfolio. Detailed descriptions of an engineering notebook, portfolio and course binder are provided in the PLTW Engineering Notebook, Portfolio and Course Binder resource.

Students should be advised to keep all of their course work. Design work related to the design process of projects and problems should be documented in an engineering notebook; all other documents and work can be kept in a course binder. When a portfolio is required, each student can then select work from their notebook and binder to place in their portfolio.

You may choose to use other documentation tools, such as a digital notebook, an electronic document to be shared with you, or an online collaboration service (such as Google Drive). Communicate your expectations to your students when facilitating each APB. Professional Development Opportunities

Professional development opportunities are available to you from the Professional Development page of myPLTW.org. To begin learning, visit myPLTW.org and select the Professional Development icon. myPLTW.org

PLTW provides membership to Lynda.com® for all PLTW teachers. Lynda.com is a leading online learning platform that helps users learn or improve professional, software, technology, and creative skills to achieve personal and professional goals. Members have access to the extensive Lynda.com video library of courses taught by recognized industry experts. To log in, visit myPLTW.org, select the Professional Development icon, and then access the Lynda.com link.

Community Forums

The Community tool allows users to create posts, ask questions, and share files within their Community groups. As a PLTW teacher, you will automatically be subscribed to Community groups based on the course(s) for which you are certified.

As a Community group member, you will have the opportunity to post comments, tag posts, bookmark, and follow other members of your group. The Community environment is provided to facilitate a professional learning community among teachers who teach the same course across the country. Use this forum to ask questions, share best practices and lessons learned, and provide Copyright © 2017 Project Lead The Way, Inc. All rights reserved. instructional support to your community of professionals.

To access the Community tool, visit myPLTW.org and select the Community icon. myPLTW.org

It is illegal to make copies of this course without the permission of Project Lead The Way, Inc.

All software, courseware, images and material contained in this course are the property of Project Lead The Way, Inc., unless otherwise provided, and are protected under Federal copyright law. It is illegal to make and/or distribute any of the contents of this course without the permission of Project Lead The Way, Inc. The use of this course and its contents is for the PLTW Program, by its network of educational institutions, schools, teachers and affiliates, in accordance with the terms of their agreements with Project Lead The Way, Inc. Duplication or other use of this file without proper authorization may be against Federal law, and may subject you to monetary and other penalties.

If you have questions about the proper use of PLTW materials or to report copyright violations, please contact:

Project Lead The Way, Inc. 3939 Priority Way South Drive, Suite 400 Indianapolis, IN 46240 Toll Free: 877-335-PLTW (7589) Local: 317-669-0200 Fax: 317-663-8296 Email: [email protected] © 2009–2017 Project Lead The Way, Inc.

Welcome to Digital Electronics

The goal of this course is to introduce high school students to solving engineering design problems through digital circuit design and creation. Students will build fundamental skill sets and understandings that will transfer to designing circuits. The presentation of topics and concepts is meant to align with two historical threads.

Advancements and improvements made to the circuit design process Advancements and improvements in technology from the invention of the transistor, gates, integrated chips, programmable logic devices, and microcontrollers

The curriculum is standards-based, aligned with both Common Core and Next Generation Science Standards, and yet is flexible and customizable so that schools and school districts can meet their curricular needs. Curriculum Design

Teacher Resources

Included in the teacher resource pages are:

A day-by-day lesson plan Answer keys Simulations

For the most up-to-date Standards Alignment, please visit PLTW’s Alignment to Standards.

Course Curriculum Frameworks

Each lesson begins with an overview, which includes a Preface introducing the topic to the student and a listing of the Student Established Goals, Transfers, Essential Questions, Understandings, Knowledge, and Skills for the lesson. The Established Goals, Transfers, and Understandings are the broad learning objectives for the lesson. The intent of the Essential Questions is to create a framework for teachers and students to focus student learning. Course-specific projects can be developed by the students to solve problems posed by these questions. The Goals, Transfers, Understandings and Essential Questions should be communicated to the students at the beginning of every Unit and Lesson to establish the focus of the learning objectives.

Instructional Timeline

Copyright © 2017 Project Lead The Way, Inc. All rights reserved. This curriculum is designed to be taught to high school students within a typical high school schedule. This means that a class which meets each day for 40–45 minutes, 175 days a year should be able to cover the content of this course. Some minor adjustments will need to be made by those schools that teach under a double block system. For the most part, this will simply entail combining two days’ worth of activities into one. Lesson Structure

Each major unit is composed of lessons. Major units are not an indication of topic timelines (example: four units does not imply each is to be nine weeks long). All units are not equal in content or time required to cover.

Activities, Projects, and Problems (APBs)

PLTW’s activities-, project-, and problem-based (APB) learning approach centers on hands-on, real- world projects that help students understand how the information and skills they are learning in the classroom may be applied in everyday life. The APB-based learning approach scaffolds student learning, building the required skill sets to apply toward an open-ended design problem.

What is an Activity?

ACTIVITIES are for the acquisition of skills and knowledge. Activities set the stage for developing the content, skills, and understandings that will help students successfully navigate the design problem.

Examples of activities include:

APBs that introduce or practice knowledge/skills on topics such as simple circuits, using a digital multimeter, or reading resistor color codes. Using research skills that might include reading informational texts on inventions or accessing websites with content information. Building or designing objects by following directions.

What is a Project?

PROJECTS are related to the design challenge/problem and provide opportunities for meaning- making. Projects provide investigations into concepts or skills that will be applied in solving the design challenge for the module.

Examples of projects include:

APBs that create a common challenge that will typically lead all students to land on the same solution.

What is a Problem?

PROBLEMS provide opportunities for students to transfer the new and past knowledge and skills from previous activities or projects in a real-world setting.

Examples of problems include:

APBs that create a common challenge that will typically lead all students to create unique

Copyright © 2017 Project Lead The Way, Inc. All rights reserved. solutions no other student came up with. An attempt to solve a problem that has no clear/best solution currently. There is “no right answer”.

Problem-based and Inquiry-based Learning

Problem-based learning is a learner-focused educational approach in which learners, through self- directed attainment and application of skills and knowledge, solve ill-structured problems. Problem- based learning is generally defined to involve the solution of relevant problems integrating multiple disciplines through free inquiry and collaboration. In addition, reflection, involving both self and peer assessment, is generally associated with problem-based learning.

Another powerful approach to learning is the introduction of fundamental concepts through inquiry- based activities. Inquiry-based activities are structured to “guide” students through a learning event for students to construct their own learning rather than be told what to expect and reproduce the effect. Through inquiry-based learning, students take charge of their own learning and develop new knowledge and skills through discovery.

Role of the Teacher

The role of the teacher is to facilitate learning. In this context, “facilitate” means that the teacher is charged with the responsibility of creating an effective educational environment for learning. This will require a variety of instructional and assessment strategies designed to guide and manage students as they engage in learning events. First, the teacher must have a solid foundation in the related content so that they can explain concepts in a variety of ways. However, the teacher’s role is not to disseminate the content but rather to guide student learning by encouraging student participation in learning activities that are connected to reality and reflect accepted professional (engineering) practices.

Teachers should offer guidance by implementing teaching strategies that are effective in a given situation and constantly adjust those strategies to reflect student needs. Although direct instruction is sometimes useful, in general, teachers should limit direct instruction and input while students problem solve or perform hands-on activities, to promote student learning and self-efficacy. Good questioning skills, listening skills, and formative assessment strategies are especially important to maximize student achievement.

In short, a teacher’s role includes:

Facilitation of learning Modeling and transfer of accepted professional (engineering) practices Informal and formal assessment of learning

Role of the Learner

To achieve their full potential, learners must fully participate in their learning experience. A learner’s role is to:

Utilize curiosity and creativity. Actively engage in learning. Appropriately apply previously learned knowledge and skills or (through self-directed learning) obtain the necessary knowledge and skills.

Copyright © 2017 Project Lead The Way, Inc. All rights reserved. Work cooperatively with educators and peers in achieving learning goals. Reflect on their work and the work of others to improve learning and their educational experience. References

Bybee, R. W. (2013). The Case for Stem Education: Challenges and Opportunities. Arlington, VA: NSTApress.

Dagget, W. R. (2005). Achieving academic excellence through rigor and relevance. Retrieved 9.22.13 from http://www.daggett.com/pdf/Academic_Excellence.pdf

Hmelo-Silver, C. E. (2004). Problem-based learning: What and how do students learn? Educational Psychology Review, 16(3), 235–266.

Holden, T. (2013). Project-based global learning in an era of high-stakes accountability. Education Weekly. Retrieved 9/13/13 from http://blogs.edweek.org/edweek/global_learning/2013/09/project- based_global_learning_in_an_era_of_high-stakes_accountability.html

Krauss, J., & Boss, S. (2013). Thinking Through Project-Based Learning: Guiding Deeper Inquiry. Thousand Oaks, CA: Corwin.

Lambros, A. (2002). Problem-Based Learning in K-8 Classrooms. Thousand Oaks, CA: Corwin.

McTighe, J., & Wiggins, G. (2013). Essential questions: Opening doors to student understanding. Alexandria, VA: ASCD.

McTighe, J., & Wiggins, G. (2005). Understanding by design (2nd ed). Alexandria, VA: ASCD.

McTighe, J., & Wiggins, G. (2011). Understanding by design: Creating High-quality Units. Alexandria, VA: ASCD.

Sanders, M. (2009). STEM, STEM Education, STEMmania. The Technology Teacher, 68(4),20–26. Retrieved 9/20/13 from http://esdstem.pbworks.com/f/TTT+STEM+Article_1.pdf

National Research Council (2011). Successful K-12 STEM education: Identifying effective approaches in science, technology, engineering, and mathematics. Washington, D.C.: National Academies Press. Retrieved 9/24/13 from http://www.stemreports.com/wp- content/uploads/2011/06/NRC_STEM_2.pdf

Lesson 1.1 Introduction to Electronics

Teacher Notes

It is recommended that you present the activities, projects, problems, and presentations in the following sequence. Introduction to Digital Electronics

This presentation will give students an overview of electronics and help instructors guide students through a discussion on how digital electronics impacts their lives. Classroom and Laboratory Safety

This presentation reviews the general safety rules for the classroom and laboratory as well as safety rules specific to possible electrical injuries. These rules are very general; supplement this presentation with any safety regulations that are specific to your school, building, or classroom. This presentation should be covered prior to assigning Quiz 1.1.1 General Safety.

Quiz 1.1.1 General Safety in the Electronics Classroom

This activity is actually a 20-question, multiple-choice quiz on general safety rules. Each student should take this quiz independently, but the results should be reviewed by the class as a whole and used to prompt discussions on the issue of safety. This quiz should not be included as part of the course grade. Activity 1.1.2 Investigating Basic Circuits

This activity is a guided investigation where students are introduced to the equipment, concepts, and skills that are foundations in the study of electronics. While most students have been exposed to these concepts in the Gateway Magic of Electrons unit (Gateway-ME) or the PLTW foundational course Principles of Engineering (POE), this inquiry-based activity assumes that students have no prior knowledge related to electrical circuits, Ohm’s law, digital multimeters (DMM), or common components like resistors and LEDs. The activity can be presented as a new introduction to electronics or as a review for advanced students who are familiar with these concepts and skills. This activity should be treated as a completion grade with no weight placed on the answers provided. Use the answers the students provide to guide a classroom discussion capturing the major concepts, ideas, and skills of the activity. Investigating Basic Circuits

Copyright © 2017 Project Lead The Way, Inc. All rights reserved. This presentation will help the instructor guide the class discussion after completion of Activity 1.1.2 Investigating Basic Circuits. Students will be able to clearly define electrical circuits, voltage, current, resistance, series and parallel circuits, Ohm’s law; know how to use a digital multimeter to measure voltage; and describe what common components like resistors and LEDs do. Scientific and Engineering Notation

This presentation reviews the process of representing the very large and very small numbers frequently encountered in electronics in scientific, engineering, and System International (SI) notation. The examples provided in the presentation are directly related to the exercises in Activity 1.1.3 Scientific and Engineering Notation. Activity 1.1.3 Scientific and Engineering Notation

This activity is designed to give students practice representing numbers in scientific, engineering, and System International (SI) notation, as well as in converting numbers between each representation. Introduction to Resistors and Capacitors

This presentation will introduce students to many of the common components used in electronics, with particular attention being paid to the wide range of resistor and capacitor package styles. Additionally, students will learn how to use the resistor color code to read a resistor’s nominal value. They will learn how to read the nomenclatures used to mark capacitor values. As part of the presentation, the teacher will give a hands-on demonstration on how to use a digital multimeter (DMM) to read resistance values. The examples and demonstration provided in the presentation are directly related to the exercises in Activity 1.1.4 Component Identification. Activity 1.1.4 Component Identification: Analog

In this activity the students will identify and determine the nominal value for a series of resistors and capacitors. Additionally, the students will use a digital multimeter (DMM) to measure the actual resistance of 10 randomly selected resistors. Students will determine whether the measured values are within the accepted tolerance. Each student will work with 10 resistors. This activity contains several color photographs of electronic components that may not reproduce well on black-and-white copiers. It may be helpful to project these photographs for the class to view while completing this activity. Circuit Theory Laws

This presentation introduces students to the basics of electricity/electronics. It will define voltage, current, resistance, Ohm’s Law, and Kirchhoff’s Voltage and Current Laws. These concepts will be applied to simple resistive series and parallel circuits. This presentation should be covered prior to assigning Activity 1.1.5a Circuit Theory – Hand Calculations.

Note: You may download a printable student version of the activity from Lesson 1.1 Teacher Resources page.

In this activity students will gain experience applying Ohm’s Law and Kirchhoff’s Voltage and Current Laws to solve simple series and parallel circuits. The circuits used in this activity will be revisited in later activities on simulation and breadboarding. Activity 1.1.5b Circuit Theory: Simulation

Note: You may download a printable student version of the activity from Lesson 1.1 Teacher Resources page.

In this activity students will gain experience using the Circuit Design Software (CDS) to analyze simple analog circuits. The circuits are some of the same circuits that were analyzed by hand in Activity 1.1.5a. Thus, the theoretical and simulation results can be compared.

Prior to assigning this activity, give a demo on the use of the circuit design software.

Procedure 1: Make your circuit appear as the one pictured. To add a voltmeter, select a voltmeter from the tool bar. (View > Toolbars > Measurement components)

In Activity 1.1.2 students learned to place voltmeters in parallel with components to take a measurement of the voltage across a component. Students will be introduced to the ammeter in simulation to protect DMM fuses in you classroom. Once students have clearly demonstrated their understanding that ammeters must be placed in series with components, you may let them measure active circuits.

Procedure 2: Double-click a meter and uncheck all boxes in the display (Figure 1).

If students do not get a reading on the ammeter, check the wiring to ensure there is not an added wire. If it is wrong (Figure 2), have them delete the extra wire and try again.

Figure 2: Incorrect Wiring on the Ammeter Correct Wiring on the Ammeter The Breadboard (Optional Review)

This presentation reviews the breadboard and general guidelines for properly constructing a circuit on the breadboard. Activity 1.1.5c Circuit Theory: Breadboarding

Note: You may download a printable student version of the activity from Lesson 1.1 Teacher

In this activity students will gain experience using a breadboard to build and test simple analog circuits. The circuits analyzed in this activity are some of the same circuits that were analyzed by hand in Activity 1.1.5a and simulated in Activity 1.1.5.b. This will allow the student to compare the theoretical, simulated, and measured values for the same circuit. Prior to assigning this activity, give a demo on the use of a DMM to measure voltage and current. Activity 1.1.6 Component Identification: Digital

Note: You may download a printable student version of the activity from Lesson 1.1 Teacher Resources page.

In this activity students will investigate the outputs of AOI logic gates, flip-flops, and clock signals. Note: The rate at which a clock signal is displayed is dependent on the processing speed of the computer it is being displayed on. The capacitor values listed in the activity and in the simulation may be too small to see a significant difference. You might use larger values with a fast processor. Introduction to Logic Gates and Integrated Circuits

This presentation introduces and gives students an overview of AOI logic gates, flip-flops, and clock signals. Activity 1.1.7 Introduction to Datasheets

Note: You may download a printable student version of the activity from Lesson 1.1 Teacher Resources page.

In this activity students will learn to locate and interpret data sheets related to common integrated circuits used in digital electronics Soldering and Desoldering

After reviewing the tools used in the hand soldering process, this presentation demonstrates the soldering and desoldering process. This demonstration will include:

1. How to tin a solder iron 2. How to properly solder various components to a printed circuit board 3. How to use a solder sucker and solder wick to remove a component

Additionally, students will identify the characteristics of a good solder connection and classic soldering mistakes. The examples and demonstration provided in the presentation are directly related to the exercises in Activity 1.1.7b Soldering and De-Soldering Practice and 1.1.7a The Board Game Counter. Project 1.1.8 Soldering Practice: Fun Light Project

Note: You may download a printable student version of the activity from Lesson 1.1 Teacher Resources page.

In this project the students will practice their soldering and desoldering skills while constructing a simple electronic project. What the students actually build for this activity is irrelevant; the intent is for students to practice soldering and desoldering. If students happen to destroy the project, and some will, it is of no consequence. The PLTW Store contains an inexpensive kit that can be used for this project, but if you can obtain scrap printed circuit boards from a local manufacturer, they will serve the purpose. Introduction to the Board Game Counter

This presentation will introduce the Random Number Generator, present an introduction of what the circuit does, and detail all of the parts that will be used to create the circuit. This presentation must be shown prior to assigning Project 1.1.8 Soldering: Introduction to the Board Game Counter.

Project 1.1.9 Soldering: Random Number Generator

Note: You may download a printable student version of the activity from Lesson 1.1 Teacher Resources page.

In this project students will follow a set of detailed instructions to assemble, solder, and test their Random Number Generator.

Lesson 1.1 Introduction to Electronics

Teacher Resources

View Student Course Preface

For many students, PLTW Digital Electronics (DE) is the first exposure to digital circuit design in high school. Students may have learned about electricity and circuits in previous courses such as Principles of Engineering or Physics, but this course is unique in that the focus is on circuit design, not just understanding the scientific principles that make a circuit work.

In Unit 1: Foundations in Electronics, students will explore the fundamental components, concepts, equipment, and skill sets associated with circuit design. They will learn an engineering design process that can be used to guide the creation of circuits based on a set of design requirements. Throughout the course, students will learn about advancements in circuits and circuit design that have shaped the world of digital electronics today.

Random Number Generator

In this unit, students will be introduced to a full digital circuit design example named the “Random Number Generator”. This example will show how an analog section, combinational logic section, and sequential logic section can be designed to work together to generate a random output each time an input button is pushed. The presentation of this example is meant to give students an understanding of a complete design. Deeper understanding of the board game counter circuit design will be achieved as students progress through the course.

In Lesson 1.1 Introduction to Electronics, students will learn to distinguish between analog and

Copyright © 2017 Project Lead The Way, Inc. All rights reserved. digital components. They will begin by exploring basic circuits and the measurement tools used to characterize and validate calculations that predict a circuit’s behavior. Students will be able to clearly describe electrical circuits, voltage, current, resistance, series and parallel circuits, Ohm’s law, and how to use a digital multimeter to measure voltage. Students will be introduced to common components such as resistors, capacitors, light emitting diodes (LEDs), seven-segment displays, combinational logic gates, and sequential logic gates.

Established Goals

It is expected that students will…

1. Work safely with electronics.

2. Express numbers in scientific notation, engineering notation, and System International (SI) notation.

3. Use Ohm’s Law, Kirchhoff’s Voltage Law, and Kirchhoff’s Current Law to solve for simple series and parallel circuits.

4. Identify many of the common components used in electronics.

5. Measure voltage, current, and resistance using a digital multimeter (DMM).

6. Determine a resistor’s nominal value by reading its color code.

7. Determine a capacitor’s nominal value by reading its labeled nomenclature.

8. Demonstrate proper soldering/de-soldering techniques to solder and desolder components on printed circuit boards.

9. Understand the significance of the base 2 number system in digital electronics.

Transfer

Students will be able to independently use their learning to …

1. Model safe practices and procedures when working with electronics.

2. Use scientific and engineering notation to represent large/small numbers and read the values of electrical components.

3. Calculate, identify, and accurately measure characteristics of electrical circuits such as voltage, current, and resistance.

4. Predict the characteristics and behavior of a circuit based on the orientation of components in relation to each other (series and parallel).

5. Recognize and understand the function of common components used in electrical circuits and circuit designs.

Essential Questions

Students will keep considering …

1. Why are the safety considerations and best practices associated with working in electronics important?

2. How are calculations and measurement used to design and verify circuit characteristics?

3. What are the functions of the most common analog and digital components used in electronics?

4. What are the technical skills and processes that are utilized throughout electronics?

Understandings

Students will understand that …

1. Safety is an important concept that must be considered at all times. Safety considerations can affect the individual, class, and overall environment of the classroom/laboratory.

2. Electricity, even at the nominal levels used in this curriculum, can cause bodily harm or even death.

3. Engineers and technicians use scientific notation, engineering notation, and Systems International (SI) notation to conveniently write very large or very small numbers frequently encountered when working with electronics.

4. The concepts of voltage, current, and resistance are related to one another and can be calculated using circuit theory laws.

5. The series or parallel arrangement of components in a circuit affects current, voltage, and resistance across the component. These values can be calculated and verified through measurement.

6. Engineers use measurement instrumentation and equipment such as digital multimeters (DMM), oscilloscopes, and function generators to verify designs and the functions of a circuit.

7. Resistors, capacitors, and light emitting diodes (LEDs) are common analog indicators in digital circuits.

8. Seven-segment displays are used to display the digits 0–9, as well as some alpha characters.

9. The two varieties of seven-segment displays are common cathode and common anode.

10. The input and output values of combinational and sequential logic function differently.

12. The flip-flop is the fundamental building block of sequential logic.

13. Logic gates are depicted by their schematic symbol, logic expression, and truth table.

14. Integrated circuits are categorized by their underlying circuitry, scale of integration, and packaging style.

15. Transistor-Transistor Logic (TTL) gates are available in a series of sub-families, each having their own advantages and disadvantages related to speed and power.

16. Soldering is an important skill/process specifically related to working in electronics.

Knowledge

Students will …

1. Recognize safety hazards associated with electrical circuits and know the best practices of working safely in an electronics lab environment.

2. Identify the equipment and know how to effectively use the equipment in an electronics lab.

3. Know scientific notation, engineering notation, and System International (SI) notation.

4. Know formulas for Ohm’s Law, Kirchhoff’s Voltage Law, and Kirchhoff’s Current Law.

5. Know the characteristics of series and parallel sections of a circuit.

6. Identify digital and analog components and recognize the schematic symbol representation.

7. Know resistor color codes for labeling values.

8. Know capacitor labeling codes.

9. Know the characteristics of LEDs and how to locate LED data sheets.

10. Recognize combinational logic gates.

11. Recognize sequential logic gates.

12. Recognize types of integrated circuits and know where to find manufacturer data sheets.

13. Relate schematic symbols to logic gates and logic gates to schematic symbols.

14. Relate truth tables to logic gates and logic gates to truth tables.

15. Know base 2 and base number systems.

16. Know the best practices of soldering and de-soldering components.

Students will …

1. Practice proper safety and best practices while working with electronics.

2. Accurately take measurements with a Digital Multimeter (DMM).

3. Express numbers in scientific notation, engineering notation, and System International (SI) notation.

4. Solve for unknown values within circuits (series, parallel, and combination circuits) using Ohm’s Law, Kirchhoff’s Voltage Law, and Kirchhoff’s Current Laws.

5. Use Circuit Design Software (CDS) and validate hand calculations of analog circuit solutions.

6. Identify and describe the function of common components used in electronics.

7. Demonstrate series and parallel circuits on a breadboard.

8. Identify a resistor’s nominal value by reading its color code.

9. Measure a resistor’s actual value by reading its resistance with a Digital Multimeter (DMM).

10. Identify a capacitor’s nominal value by reading its labeled nomenclature.

11. Identify commonly used electronic components given their part number or schematic symbol.

12. Obtain manufacturer data sheets and extract information for components commonly used in digital electronics.

13. Identify various integrated circuit (IC) package styles.

14. Recognize the fundamental differences between combinational and sequential logic.

15. Identify and describe the function of AND, OR, and INVERTER gates.

16. Convert numbers between the binary and decimal number systems.

17. Count from 0–15 in binary.

18. Demonstrate proper soldering/desoldering techniques to solder and desolder components on a printed circuit board.

19. Properly tin the tip of a soldering iron and distinguish good solder joints from bad solder joints.

Resources

Activity 1.1.1 General Safety Test

Investigating Basic Circuits Post-Activity Discussion

Activity 1.1.5b Circuit Theory: Simulation

Activity 1.1.5c Circuit Theory: Breadboarding

Activity 1.1.6 Component Identification: Digital

Activity 1.1.7 Introduction to Datasheets

Project 1.1.8 Soldering Practice: Fun Light

Project 1.1.9 Soldering: The Random Number Generator (RNG)

Day-by-Day Plans

Time: 20 days

Note: In preparation for teaching, it is strongly recommended to review the Lesson 1.1 Teacher Notes - Introduction to Electronics.

Day 1

Digital Electronics (DE) Course Overview

Guide students through the Introduction to Digital Electronics presentation.

Students will participate in a teacher-led discussion on electronic products that they use daily and what their lives would be like without such products. As part of this discussion, have each student mentally walk through their day and list all of the electronics products that they use regularly.

Present an overview of the PLTW Digital Electronics course, the make-up of its four units, and what skills the students will possess after they have completed the course. To help facilitate this overview, it is imperative that completed examples of each of the units’ major projects and/or problems are available for the students to examine.

Distribute an engineering notebook to each student.

Note: The instructor will determine whether students will record their notes in a daily journal, portfolio, or their engineering notebook. For purposes of written directions in the day-by-day plans for each lesson, it will be assumed that students will record their notes in an engineering notebook.

Lesson 1.1 Introduction to Electronics Overview

Present Understandings, Knowledge and Skills, and Essential Questions to provide a lesson

NOTE: You may wish to assign the review of Classroom and Laboratory Safety as homework in preparation for Day 2.

Day 2

General Safety and Preparation for Investigating Basic Circuits

Guide students through the Classroom and Laboratory Safety presentation while students take notes.

Assign Quiz 1.1.1 General Safety Quiz.

Using Quiz 1.1.1 General Safety Quiz Answer Key as a guide, review the answers to the General Safety Quiz with the class.

In preparation for Activity 1.1.2 Investigating Basic Circuits on Day 3, introduce the students to the layout of breadboards, show examples of LEDs and resistors, and introduce the Digital Multimeter (DMM). Students will discover the function and use of these items in Activity 1.1.2 Investigating Basic Circuits, so you do not need to go into these topics in any depth. Investigating Basic Circuits presentation is designed to be presented after Activity 1.1.2 Investigating Basic Circuits.

(Optional). You may wish to present The Breadboard presentation in preparation for Activity 1.1.2 Investigating Basic Circuits.

Day 3

Investigating Basic Circuits

Assign and facilitate Activity 1.1.2 Investigating Basic Circuits.

Activity 1.1.2 Investigating Basic Circuits is a guided investigation where students are introduced to the equipment, concepts, and skills that are foundations in the study of electronics.

Students should attempt to answer all questions without instructor input on what the “correct” answer is. This activity should be treated as a completion grade with no weight placed on the answers provided. The answers the students provide should be used to guide a classroom discussion capturing the major concepts, ideas, and skills of the activity.

Day 4

Investigating Basic Circuits - Discussion

Guide students through a discussion on what they have learned and introduce/reinforce the Glossary terms used in electronics for these concepts and equipment.

Day 5

Scientific and Engineering Notation

Guide students through the Scientific and Engineering Notation presentation while students take notes.

Introduce Activity 1.1.3 Scientific and Engineering Notation.

Students will work on Activity 1.1.3 Scientific and Engineering Notation.

Assess student work using Activity 1.1.3 Scientific and Engineering Notation Answer Key.

Day 6

Component Identification: Analog

Guide students through the Introduction to Resistors and Capacitors presentation while students take notes.

Introduce Activity 1.1.4 Component Identification: Analog.

Students will work on Activity 1.1.4 Component Identification: Analog.

Assess student work using Activity 1.1.4 Component Identification: Analog Quiz Answer Key.

Days 7–8

Circuit Theory Laws: Hand Calculations

Guide students through the Circuit Theory Laws presentation while students take notes.

Introduce Activity 1.1.5a Circuit Theory: Hand Calculations.

Students will work through Activity 1.1.5a Circuit Theory: Hand Calculations.

Assist the students as needed.

Assess student work using Activity 1.1.5a Circuit Theory: Hand Calculations Answer Key.

Circuit Theory Laws: Simulation

Introduce the Circuit Design Software (CDS) and will demonstrate how to use the feature tools needed to complete this activity.

Students will take notes in their engineering notebooks.

Introduce Activity 1.1.5b Circuit Theory: Simulation.

Students will work through Activity 1.1.5b Circuit Theory: Simulation.

Assess student work using Activity 1.1.5b Circuit Theory: Simulation Answer Key.

Days 10–11

Circuit Theory Laws: Breadboarding

Guide The Breadboard presentation or ask students to review the presentation if it has already been introduced.

Review the digital multimeter (DMM) and demonstrate how to use the meter to make voltage and current measurements.

Students will take notes in their engineering notebooks.

Introduce Activity 1.1.5c Circuit Theory: Breadboarding.

Students will work through Activity 1.1.5c Circuit Theory: Breadboarding.

Assist the students as needed. It is important to monitor DMM use, as improper placement of the DMM when reading current can blow the DMM fuse.

Days 12–15

Component Identification: Digital

Present the Transfers and Essential Questions to provide an overview of the investigation.

Introduce Activity 1.1.6 Component Identification: Digital.

Students will work through Activity 1.1.6 Component Identification: Digital.

Activity 1.1.6 Component Identification: Digital is a guided investigation where students are introduced to the equipment, concepts, and skills that are essential to understanding the components (AND, OR, INVERTER gates), skills, and concepts that are foundations of combinational logic design. Copyright © 2017 Project Lead The Way, Inc. All rights reserved. Students should attempt to answer all questions without input on what the “correct” answer is. This activity should be treated as a completion grade with no weight placed on the answers provided. The answers the students provide should be used to guide a classroom discussion capturing the major concepts, ideas, and skills of the activity.

Introduction to Logic Gates and Integrated Circuits is designed to be presented after Activity 1.1.6 Component Identification: Digital.

Assist the students as needed.

Days 16–17

Component Identification: Digital - Discussion

Guide students through the Introduction to Logic Gates and Integrated Circuits while students take notes.

Guide students through a discussion on what they have learned and introduce/reinforce the Key Teams used in electronics for these concepts and equipment.

Introduce students to the Glossary terms related to Activity 1.1.6 Component Identification: Digital.

Assess student work using Activity 1.1.6 Component Identification: Digital Answer Key.

Day 18

Data Sheets

Assign Activity 1.1.7 Introduction to Data Sheets.

Days 18–20 (Optional)

Soldering and Desoldering Components

Guide students through the Soldering and Desoldering presentation while students take notes.

(Optional). Introduce Activity 1.1.8 Solder Practice: Fun Light Project as well as the Solder Practice Board Kits.

Students will work through Activity 1.1.8 Solder Practice: Fun Light Project while you assist as needed.

Guide students through the Introduction to the Board Game Counter while students take notes.

Students will work on Project 1.1.9 Soldering: Random Number Generator.

Assist students as needed.

Procedure

1. Your partner has been working on your group’s circuit and has left the work area. Before you begin working on the circuit, what should you do to ensure that the circuit is not active and prevent yourself from getting a shock?

Disconnect the power source.

Measure the circuit with an ohmmeter for resistance.

Check the circuit with a continuity tester.

Use a voltmeter to measure voltage at the power source.

1. Disconnect the power source.

2. You used a tool and it accidentally became damaged. What should be the next action for you to take?

Continue to use the tool as long as it still somewhat works.

Label the tool that is broken and inform the instructor.

Throw the tool away.

Put the tool away and find another tool to use.

2. Label the tool that is broken and inform the instructor.

3. If you have not been given instruction on a tool or piece of equipment in the laboratory, you should:

Not use the tool until you have had proper instruction.

Use it anyway if you think you can figure it out.

Ask a classmate how to use it.

1. Not use the tool until you have had proper instruction.

4. Which of the following is appropriate for working in an electronics workspace?

Wearing multiple rings on your fingers.

Wearing an oversized, baggy hooded sweatshirt.

Wearing clothing that is not loose and no jewelry.

Dragging your feet on the carpet and shocking your friends.

3. Wearing clothing that is not loose and no jewelry.

5. Chemicals can be used to etch circuit board. Which of the following should be done before using the chemicals in an electronics classroom?

Read all instructions that come with the chemical.

Read the Safety Data Sheet to prepare for emergencies.

Wear goggles and a lab coat to protect from potential spills.

All of the above.

4. All of the above.

6. What is the maximum current level that a human body can withstand before sustaining injury?

100 uA

1.0 mA

15 mA

50 mA

7. A large voltage is applied to a circuit, and a fire is started on a circuit board in the lab. When you inform your instructor, which of the following should the instructor use to extinguish an electrical fire?

Water.

Class A fire extinguisher.

Class B fire extinguisher.

Class C fire extinguisher.

4. Class C fire extinguisher.

8. Before working with a chemical or solder, a student obtained a Safety Data Sheet. Which of the following will the student find on this document?

What the chemical is made of.

The first aid procedure that you should follow.

How to handle the material.

All of the above.

4. All of the above.

9. Which of the following is the appropriate scenario for wearing safety glasses in an electronics classroom?

Safety glasses or goggles should be worn to prevent eye injuries from chemicals that splash.

Safety glasses or goggles should be worn when using tools that may cause objects to be thrown.

Safety glasses or goggles should be used when soldering components.

All of the above.

10. Why should students not rush? Why should students take their time when working in an electronics classroom?

Taking your time allows you to double check your connections and to reduce the need for troubleshooting later.

Taking your time allows you to create your circuits more neatly. This allows you to pick up where you left off last time more easily.

Taking your time allows you to double check all part numbers and values. A common error.

All of the above.

4. All of the above.

11. What are the types of injury that are most common in an electronics classroom?

Electrical shock.

Sprained finger.

Answers (a) and (d).

Minor burns from active electrical components.

3. Answers (a) and (d).

12. The electrical cord for a soldering iron has a grounding prong. However, the extension cord you are trying to plug the iron into only has only a place for two prongs (no grounding prong). What should you do to plug in the tool?

Wire the grounding prong to the neutral prong on the soldering iron.

Use an appropriate adapter/extension cord.

Cut off the grounding pin.

2. Use an appropriate adapter/extension cord.

13. When you enter the electronics classroom, you notice there is water on the floor near an electrical outlet. The roof appears to be leaking. Which of the following should be done first?

Immediately mop the floor.

Make sure no one enters and turn the power off to the classroom at the circuit breaker.

Disregard the problem as long as it is not near project workspace.

Mop the floor with an insulated mop.

2. Make sure no one enters and turn the power off to the classroom at the circuit breaker.

14. You notice that the cord of your soldering iron is frayed and possibly broken. What should be done next?

If the cord works, continue to use the soldering iron.

Label the broken section and notify the instructor.

Put the soldering iron back and pick one without a frayed cord.

Throw the soldering iron away.

2. Label the broken section and notify the instructor.

15. A student obtained an injury in the electrical classroom. The accident should be brought to the attention of the instructor so that:

The teacher can document the injury.

The teacher can administer first aid.

The teacher can make sure other students are not injured.

4. All of the above.

16. It is important to keep your workspace clean and organized in an electronics classroom. Which of the following is not a reason for doing so?

This allows other classmates to easily locate materials when sharing the same workspace.

It minimizes the potential for injuries.

These practices help maintain the equipment in the electronics classroom.

It gives students something to do.

4. It gives students something to do.

17. Chemicals, materials, and processes in an electrical lab can be dangerous. Which of the following is not a potential hazard in typical electronics classrooms?

Burns from hot/active components or from a soldering iron.

Electrocution.

Fumes from soldering.

Falling objects.

4. Falling objects.

18. Certain devices in an electronics classroom such as capacitors can store a lethal amount of charge. When handling a capacitor, you need to ensure that the device is uncharged. How do you make certain a capacitor is discharged before handling?

Use an ammeter to read current.

Touch the leads with your finger.

Ask your instructor.

3. Ask your instructor.

19. You are getting ready to power another student’s electrical circuit in this class, but you are not sure of the voltage necessary to use. Students in this class should always use:

5V because all the components we use are always TTL.

3.3V because all the component we use are always CMOS.

9V because that is the battery lying next to the circuit.

Check with the other student who created it or the instructor. The design may require different voltages based on what it does and how it’s designed.

4. Check with the other student who created it or the instructor. The design may require different voltages based on what it does and how it’s designed.

20. It is a good practice in an electronics classroom to:

Always follow procedure.

Investigate before you act. Read and review all data sheets and service manuals.

When in doubt, ask your instructor

All of the above.

4. All of the above.

Procedure

Part A: Creating a Circuit and Measuring a Circuit’s Properties

1. A Simple Circuit. Arrange the components according to the photo. You will need to plug the USB cable from the myDAQ into your computer to provide power to the Protoboard. Notice that the LED has a flat notch on one side. Make sure the notch is initially oriented on the bottom as shown in the picture. In this arrangement, the flow of conventional current is from the top (5V) to the bottom (0V) through the resistor and the LED. What do you think the role is of the resistor in this circuit?

The role is to limit the amount of current moving through the LED or reduce the voltage across the LED to protect it from failure. (Note: This definition will be expanded later as the relationship between voltage and current R = V/I.)

In a circuit, the flow of conventional current can be described as a positive charge moving through a complete circuit path (VCC to GND). Can you trace the flow of conventional current in both of the above images?

Help students understand how a breadboard is laid out.

2. With the LED illuminated, flip the direction of the LED on the breadboard (notch on top now), and then flip it back to its original position (notch on bottom). What does your observation tell you about diodes (and LEDs)?

Good Answer: LEDs only light up with current flowing in one direction.

Best Answer: LEDs and diodes are polar components. Current is limited in one direction.

3. Using the DMM to Measure Values. Making sure that the RED lead is plugged into V and the black lead is plugged into COM on the myDAQ, open the DMM on your computer. With the Voltage Range set at 60V, select the Direct Current Voltage Measurement setting and Run (Continuously). Place the RED DMM lead on the top of the resistor and the black lead on the bottom of the LED. Note the reading on the DMM. Now switch the DMM leads.

Value should switch from approximately +4.8V to -4.8V in this example.

4. Select the next smallest voltage range (20V) and place the DMM leads across the circuit as you did initially in picture (3b). Note the value on the DMM. What is happening on the display each time you make the range smaller?

Value should switch from approximately:

4.7V to 4.77V 2 significant figures to 3 significant figures

These values will vary depending upon the voltage supply used.

The DMM reading becomes more precise by a factor of 10 each time the voltage range is decreased.

5. Select the next smallest range (2V). What happened and why? What was the most accurate measurement you were able to make of the voltage across the resistor and LED?

The value displayed on the DMM is +Over.

This means the value you are trying to measure is not in the range of 0 to 2.

6. Set the DMM to the range that will give you the most precise voltage measurement and touch the lead across the two ends of the red wire. Note the reading on the DMM. Now touch the leads across the two ends of the black wire. Note the reading.

(a) (b)

Copyright © 2017 Project Lead The Way, Inc. All rights reserved. Voltage (ΔV=Vf-Vi) is a description of a component’s potential to do work (1 volt means the component could do 1 joule of work for every coulomb of charge that passes though it (1V= 1J/1C). For a component to do work, there must be a difference in the potential across the component to do work (often called a potential difference). Why do you think the reading was the same for both of these sections of the circuit? What you have just observed is exactly why birds can land on high power lines unharmed.

Answers will vary based on student’s prior knowledge. Any answer is acceptable as this idea will be expanded upon in discussion and further APBs.

For each of these arrangements, the potential difference across the test points is zero.

(6a) ΔV = 5V−5V=0

(6b) ΔV = 0V−0V=0

Voltage (potential difference) must be measured across a component that is doing work. One side must have a higher potential to do work than the other. This is why birds can land on high voltage lines without doing work (being electrocuted).

(6a) ΔV = 20,000V-20,000V still equals zero.

7. In Step 3, you measured the voltage across the resistor and the LED combined. Now touch the leads across both ends of the resistor. Note the reading on the DMM.

(a) Voltage across LED and Resistor (b) Voltage across Resistor Only

Should be approximately 4.70V (5V) Should be approximately 3.00V (3V)

Can you guess the reading you will see when you touch the DMM leads across the LED only? Were you correct? Why did you guess that value?

Students should make the connection that:

the resistor voltage (3V) plus LED voltage (2V) should add up to terminal voltage (5V).

The actual values may vary slightly based on the components used and voltage source.

8. You might be asking why we need a resistor in this circuit. Is it doing any work? Some components have limitations on how much electrical current can pass through them or how much voltage they should have across them. We can calculate the relationships between voltage, current, and resistance for a component using Ohm’s Law (V=IR).

Let’s assume the voltage you saw across the 330Ω resistor was roughly 3V when the circuit was active. What is the conventional current (measured in Amps) traveling through the resistor according to Ohm’s Law?

Answers will vary based on the student’s prior knowledge. Any answer is acceptable, as this idea will be expanded upon in discussion and further APBs.

V=IR

I = V/R = 3V / 330 Ω = 0.00909 A = 9.1 mA

Most students should be able to find the value 0.0090909 A on their calculator, but may have forgotten their SI prefixes. A great question to ask is, “Wouldn’t it be nice to have a shortcut for expressing such a small number? Is 9 mA really small?”

Part B: Series and Parallel Circuits

9. These two identical 330Ω resistors are in series with each other. There is only one path through the circuit from the power source to the ground. In this diagram, the power source is a 9V battery. One end of the battery has 9V of potential to do work (positive terminal-top). The other end of the battery has zero potential to do work (negative terminal/ground-bottom).

Due to the fact that R1 and R2 are identical, what would you guess the voltage across each resistor is individually? Why?

The voltage across both individually would be 4.5V.

Added together, they would add up to the terminal voltage (total voltage of the circuit) 9V.

We can replace these two resistors with one resistor that would have the same impact on the circuit. (This theoretical resistor is called an equivalent resistor.) What would the value of this equivalent resistor have to be in Ohms (Ω)?

One 660 Ω resistor would be the same as two 330 Ω resistors in series.

10. Create this series circuit on your breadboard with a 5V power source. With both LEDs illuminated, remove one of the LEDs from the circuit path. What happened and why?

The other LED goes out. The circuit path is broken.

The combined resistance is too large, or the voltage is too small, or the current is too small.

12. Components in a circuit can also be arranged in parallel. Create this parallel circuit on your breadboard. With both LEDs illuminated, what happens if you remove one of the LEDS from the circuit path?

The other LED stays lit. They are both illuminated with the same brightness as if it were one LED in the circuit alone. All LEDs have their own path to the battery (same voltage source).

13. Using the diagram for a series circuit at the beginning of Part B as a reference, can you draw a circuit diagram showing 2 resistors in parallel?

Copyright © 2017 Project Lead The Way, Inc. All rights reserved. 14. In a series circuit, all components have the same current (Amps) flowing through them (even if the resistors have different values). That is not the case for components in parallel with each other. What do components in parallel have in common?

Voltage. All resistors have their own path from and to the battery (voltage source to ground).

15. Based on your observations and what you have learned about parallel circuits, use Ohm’s Law (V=IR) to calculate the current in each of the three resistors.

Imagine that you add more resistors (R4 and and R5) in parallel. For each new path to the battery you create, what do you think that does to the total amount of current going into and out of the battery?

Conclusion

1. Describe the proper way to place the digital multimeter (DMM) leads and the steps you use to get the most precise measurement value for voltage across components using a DMM.

To measure voltage, the circuit must be on (active).

Voltage measurements must be made across a component. (DMM must be in parallel with the component.)

Make sure the DMM leads are plugged in correctly for voltage (Red = V, Black = COM).

To get the most precise measurement, start with the largest range and keep reducing it until you no longer get a reading (out of range). Go back to the last one that gave you a value. That is the most precise voltage measurement.

2. If the value on the DMM is negative, what does that tell you about the orientation of the DMM leads in relation to the flow of conventional current?

If the voltage is reading negative on the DMM, the flow of conventional current is in the opposite direction than the orientation you have the leads placed. The conventional current is flowing from the black lead to the red lead in your circuit between these two test points (opposite of how you guessed).

3. LEDs and resistors transfer electrical energy into light and thermal energy. What is an important characteristic about LEDs (and diodes) that make them unique compared to a resistor?

LEDs and diodes are polar components. Current is limited in one direction.

4. In your own words, describe what it means for components to be in series with each other.

In series circuits:

Components are wired from end to end, completing one circuit path.

All components share the same current. Remove a component and current stops for the entire circuit.

For resistors in series, the total resistance in the circuit increases with each resistor you add to the circuit.

5. In your own words, describe what it means for components to be in parallel with each other. What characteristic do components in parallel always have in common? (Voltage, Current, or Resistance)

In parallel circuits:

Components are wired so that each has its own path to the voltage source and ground.

All components share the same voltage. Remove a component and current stops only for that section of the circuit.

For resistors in parallel, as more paths are created to the voltage source, more current flows from the voltage source.

(The total resistance of the circuit decreases as you add resistors in parallel.)

Going Further

6. In this investigation, you were introduced to the idea of equivalent resistance (replacing multiple resistors in a series with one that does the same job. Equivalent resistance for series circuits can be shown as a simple mathematical expression. How would you express this relationship to the total resistance in the circuit mathematically?

Copyright © 2017 Project Lead The Way, Inc. All rights reserved. 7. A theoretical equivalent resistor can be placed in parallel circuits and shown mathematically as well. This relationship is a little less straightforward than equivalent resistance in series circuits. With a little research, can you determine how the equivalent resistance for this parallel circuit would be expressed mathematically? We will expand our understanding on these concepts in later activities.

(Students will most likely need to look this up.)

Procedure

1. Express each of the following numbers in scientific notation.

0.00000000356 =

934,000,000 =

847 =

0.00092 =

3,510,000 =

1. 3.56 x 10-9

2. 9.34 x 108

3. 8.47 x 102

4. 9.2 x 10-4

5. 3.51 x 106

2. Express each of the following numbers in engineering notation.

0.00000000356 =

934,000,000 =

847 =

0.00092 =

3,510,000 =

2. 934 x 106

3. 847

4. 920 x 10-6

5. 3.51 x 106

3. Express each of the following numbers using the appropriate SI prefix. Don’t forget to retain the units.

0.000047 F =

17500000 Hz =

0.0000000157 A =

6800000 Ω =

0.00425 V =

1. 47 μF

2. 17.5 MHz

3. 15.7 nA

4. 6.8 MΩ

5. 4.25 mV

4. Convert the following numbers into the SI prefix shown.

6800 pF =

2.7 M Ω =

4.24 GHz =

25.67 μF =

0.0127 nSec =

2. 2700 kΩ

3. 4240 MHz

4. .02567 mF

5. 12.7 pSec

Conclusion

1. Why is it important to use a power-of-ten notation (scientific or engineering) when expressing very large or very small numbers?

Answers may vary.

It makes writing/reading the numbers easier/faster.

It makes calculations in decimal form easier/faster if a calculator is not available.

2. In engineering in general and in electronics specifically, why do we use engineering notation rather than scientific notation?

Answers may vary.

Many components in electronics have large/small values that need to be printed on them. It is easier to read the value on a component written with an SI prefix.

3. The SI prefix for 10-15 is femto and is abbreviated f. We do not use this prefix in electronics. Why?

Answers may vary.

This prefix represents an extremely small value. You would rarely (if ever) deal with a

Procedure

1. Using the attached resistor color code, determine the nominal resistance value for the following components.

(Yellow / Violet / Red / Gold)

Ra =

4.7 kΩ ± 5%

(Green / Blue / Yellow / Gold)

Rb =

560 kΩ ± 5%

Rc =

270 Ω ± 5%

(Brown / Red / Green / Gold)

Rd =

1.2 MΩ ± 5%

(Blue / Gray / Orange / Gold)

Re =

68 kΩ ± 5%

3. Use the Disc Capacitor Label Diagram to determine the nominal capacitance value for the following components.

.047 μF –20% +80%

Cb =

470 μF ±20%

0.220 μF ±10%

Cd =

0.1 μF ±20%

Ce =

0.001 μF ±20%

Conclusion

1. Why are the measured values of the resistors different from the nominal values?

Resistors may vary within limits (tolerances) without significantly affecting their function. There are a number of factors that can affect the tolerance of a resistor (material used, quality control of maker, temperature).

2. Identify each of the circled components for the printed circuit board.

1. Electrolytic Capacitor

2. Voltage Regulator

3. Dual In-Line Package (DIP) Integrated Chip (IC)

4. Resistor

5. Light-Emitting Diode (LED)

6. Disc Capacitor

Procedure

1. For each of the resistors shown below, use Ohm’s Law to calculate the unknown quantity. Be sure to put your answer in proper engineering notation and use the correct units.

I = 7.45 mA R = 226 kΩ V = 30.8 V

R = 240 Ω I = 2.94 mA V = 300 V

2. For each of the circuits shown below, calculate the value for RT.

Be sure to put your answer in proper engineering notation and use the correct units.

Calculations

3. Using the laws of circuit theory, solve for RT, IT, VR1, VR2, and VR3.

Be sure to put your answer in proper engineering notation and use the correct units.

4. Using the laws of circuit theory, solve for RT, IT, VR1, VR2, VR3, and VR4. Be sure to put your answer in proper engineering notation and use the correct units.

Using your calculations, verify your results using Kirchhoff’s Voltage Law.

5. Using the laws of circuit theory, solve for RT, IT, IR1, IR2, and IR3. Put your answer in proper engineering notation and use the correct units.

6. Using the laws of circuit theory, solve for RT, IT, IR1, IR2, IR3, and IR4. Put your answer in proper engineering notation and use the correct units.

Using your calculations, verify your results using Kirchhoff’s Current Law.

Conclusion

1. State two rules for the voltage and current in a series circuit.

Kirchhoff’s Voltage Law (KVL) Series. The sum of all of the voltage drops (VR1 + VR2 + VR2) is equal to the total applied voltage (VT) in a series circuit.

2. State two rules for the voltage and current in a parallel circuit.

Kirchhoff’s Current Law (KCL) Parallel. The sum of all of the currents in each branch (IR1 + IR2 + IR3) is equal to the total current (IT) in a parallel circuit.

Kirchhoff’s Voltage Law (KVL) Parallel. The voltage across every parallel component is equal.

3. If you remove a single bulb from an inexpensive string of Christmas tree lights, all of the lights in the entire string go off. Are the bulbs connected in series or parallel? Explain.

The bulbs are connected in series. The components are connected end-to-end. and there is only a single path for current to flow. Removing the bulb disrupts the path of current for the entire circuit.

Going Further (Optional)

The circuit shown below is a series/parallel circuit. That is, some of its resistors are connected in series and some are in parallel. Using the laws of circuit theory, solve for RT and IT.

IT=20.8 mA

Voltage Current

VR1 = 6.875 V IR1 = 20.8 mA VR2 = 8.33 V IR2 =13.9 mA VR3 = 4.17 V IR3 = 6.94 mA VR4 = 12.5 V IR4 = 13.9 mA VR5 = 5.625 V IR5 = 20.8 mA

Procedure

1. Below is the schematic for a simple series circuit. Analyze this circuit to determine its total current and the voltage across each of the two resistors. Document your calculations in your notebook. To make these measurements, add an ammeter and two voltmeters. The second schematic is the original circuit with the added meters.

Using the CDS, enter and simulate this circuit. Measure and record the circuit’s total current and the voltage across each of the resistors.

2. Using the CDS, analyze the circuit shown below to determine IT, VR1, VR2, and VR3.

Add the appropriate ammeters and voltmeters. Be sure to put your answer in proper engineering notation and use the correct units.

Copyright © 2017 Project Lead The Way, Inc. All rights reserved. You analyzed this circuit by hand in Activity 1.1.5.a. How do these measured values compare to the previously calculated values? If they do not match, review your circuit, your calculations, and make any necessary corrections.

3. Using the CDS, analyze the circuit shown below to determine IT, VR1, VR2, VR3, and VR4. Do the measured values compare to your previously calculated values in Activity 1.1.5.a?

4. Using the CDS, analyze the circuit shown below to determine IT, IR1, IR2, & IR3. Do the

5. Using the CDS, analyze the circuit shown below to determine IT, IR1, IR2, IR3, and IR4. Do the measured values compare to your previously calculated values in Activity 1.1.5a?

Conclusion

1. It should be obvious that using a CDS to analyze circuits is far easier than performing the calculations by hand. Yet, being able to perform these calculations by hand is still an important skill for a circuit designer. Why?

You might not have access to Circuit Design Software (CDS).

You might want to verify that the software is correct.

2. Using the results from step 2 of the procedure, verify Kirchhoff’s Voltage Law.

3. Using the results from step 5 of the procedure, verify Kirchhoff’s Current Law.

Conclusion

1. You have now analyzed the same circuits three times:

By hand in Activity 1.1.5.a

By simulation in Activity 1.1.5.b

By breadboarding in this activity 1.1.5.c

How did these values compare, and what might account for any differences?

They should all be the same within accepted values due to rounding rules and tolerances.

2. How does the technique for measuring current with a DMM differ from measuring voltage?

Voltmeters are placed in parallel with components.

Ammeters are placed in series with components.

3. What is the origin of the name “breadboard”?

In the early days of radio, amateurs nailed bare copper wires or terminal strips to a wooden board (often literally a cutting board for bread) and soldered electronic components to them.

Procedure

Combinational Logic

1. Use a switch for the input X and a probe for the output Z. Toggle the switch to complete the truth table shown.

X Z

0 1

1 0

From analysis of the truth table, why do you think this is called an “INVERTER” gate?

The gate switches or inverts the signal.

2. Use switches for the inputs X and Y and a probe for the output Z.

Toggle the switches to complete the truth table shown.

0 0 0

0 1 0

1 0 0

1 1 1

From analysis of the truth table, why do you think this is called an “AND” gate?

The output is only high when input X AND input Y are high.

3. Use switches for the inputs X and Y and a probe for the output Z. Toggle the switches to complete the truth table.

0 0 1

0 1 1

1 0 1

1 1 0

From analysis of the truth table, why do you think this is called a “NAND” gate? (NOT AND)

The NAND gate is an exact opposite of an AND gate.

4. Use switches for the inputs X and Y and a probe for the output Z. Toggle the switches to complete the truth table.

0 0 0

0 1 1

1 0 1

1 1 1

From analysis of the truth table, why do you think this is called an “OR” gate?

The output is only high when input X OR input Y are high.

5. Use switches for the inputs X and Y and a probe for the output Z. Toggle the switches to complete the truth table.

0 0 1

0 1 0

1 0 0

1 1 0

From analysis of the truth table, why do you think this is called a “NOR” gate? (NOT OR)

The NOR gate is an exact opposite of an OR gate.

6. Use switches for the inputs X and Y and a probe for the output Z. Toggle the switches to complete the truth table shown.

0 0 0

0 1 1

1 0 1

1 1 0

From analysis of the truth table, why do you think this is called an “XOR” gate? (EXCLUSIVE OR)

The output is only high when input X OR input Y is high, but not both.

Sequential Logic

In the previous combinational logic circuits, YOU made all the outputs change based on the inputs YOU entered with switches. What if you wanted the changes to happen without YOU needing to flip a switch? There are two ICs that allow us to do this.

7. Using the Circuit Design Software (CDS), enter the 74LS74N test circuit shown below.

Use a switch for the input T and probes for the outputs Que and NOT_Que.

The 74LS74N has two inputs (Data in and a clock signal CLK). In this circuit, the clock signal input will be a switch T that you flip. The Data in is tied to the NOT_Q.

Copyright © 2017 Project Lead The Way, Inc. All rights reserved. The 74LS74 also has preset and clear inputs. In this circuit the PR (preset) and CLR (clear) are connected to 5v (high), which makes them both inactive. These PR and CLR inputs on the 74LS74 are said to be “active low” inputs. (It takes a low signal to activate them.)

74LS74N Test Circuit

To help with the class discussion (and make sure everyone is seeing the same thing), toggle the input T several times until T is low and NOT_Que is low. (Toggle means to change the state of the switch. One “toggle” of the switch would change the state of the switch from low to high. Another toggle of the switch would change the state of the switch from high to low.)

Starting with the switch on GROUND, what happens to output Que when the switch is moved from GROUND to 5V? One toggle of the switch.

Que comes on. NOT_Que turns off.

What happens to output Que when the switch is moved from 5V to GROUND? One toggle of the switch.

Nothing

Toggle the switch one more time. What happened to output Que? What does this tell you about when Que changes (toggles) in relation to when the input at the CLK

Not_Que comes on. Que turns off.

What is the relationship of Que to NOT_Que always?

They are always opposite of each other.

What is the relationship of D Data in to Que always?

They are always opposite of each other because D Data in is wired to NOT_Que

The 74LS74N is called a “flip-flop”. Based on your observations. can you explain the relationship between the D Data in, Que, NOT_Q, and the CLK signal? What does a flip- flop do?

Toggling the input switch toggles the output state of the flip-flop.

The output toggles every cycle of the switch.

Every two clicks of the switch trigger a change in the output.

The flip-flop only changes when the input signal goes from GND to 5V.

8. Using the Circuit Design Software (CDS), create the three LM555CN test circuits shown below on the same sheet. The 555 Timer Oscillator is one of the most common circuits used in introductory electronics. We will use this design to generate a clock signal in the Random Number Generator (our first full circuit design). We will look more closely at this circuit in the next lesson. In each of the three circuits, the only value that is changed is capacitor C2.

Circuit A Circuit B Circuit C

a) When C2 is changed from 12 μF to 6 μF. What happens?

The frequency of the clock signal increases.

b) When C2 is changed from 12 μF to 24 μF. What happens?

The frequency of the clock signal decreases.

Conclusion

1. Can you combine the 555 Timer circuit with the flip-flop circuit so the changes on the flip-flop happen without your input at a rate you desire? Share this simulation with your instructor.

Procedure

2. As a digital designer, you will occasionally need to redesign an existing circuit. In doing so, you will come across part numbers that you are not familiar with. Use the internet to identify the functionality and manufacturer of each of the part numbers listed below. Note that many parts will have several manufacturers. For the purpose of completing this table, only list one. Also, do not print these datasheets. Simply view them online and extract the necessary information.

Part IC Name / Function Manufacturer Number

DM74LS00 Quad 2-Input NAND Gate Fairchild Semiconductor

Texas Instruments or ON SN74LS02 Quad 2-Input NOR Gate Semiconductor

DM74LS75 Quad Latch Fairchild Semiconductor

Quad 2-Input Exclusive-OR Texas Instruments or ON SN74LS86 Gate Semiconductor 0.560-In Seven-Segment MAN6760 Fairchild Semiconductor Display

3. When you design a digital logic circuit, you will often need a gate that performs a specific function. You may be unsure of its part number. Use the internet to identify the 74LS series part number for each of the following five gates. Again, do not print these datasheets. Simply view them online and extract the necessary information.

Gate Symbol Gate Name / Function 74LS Series Part Number

3 input AND gate 74LS11

3 input NAND gate 74LS10

4 input AND gate 74LS21

3 input NOR gate 74LS27

4. The world of electronics is filled with TLAs (Three Letter Acronyms). Use the internet to identify the following IC package styles and download a sample picture of each type.

IC Package Full Name Picture (copyandpaste) Style

Dual In-line DIP Package

Small Outline SOIC Integrated Circuit

QFP Quad Flat Pack

BGA Ball grid array

Conclusion

1. Using the datasheet obtained for the 74LS04 Hex Inverter Gates as a reference, answer the following questions:

What is the nominal Supply Voltage (Vcc)?

5 V

What is the maximum Free Air Operating Temperature (TA)?

70 °C

What is the typical LOW-to-HIGH Propagation Delay (TPLH)?

What is the typical distance between two adjacent pins on a 14-Pin, Dual In-Line IC Package?

0.1 in

2. Who is Jack Kilby? What was his contribution to the field of digital electronics?

Jack Kilby is recognized as the co-inventor of the first integrated circuit while working for Texas Instruments.

3. In the purpose section, you were asked: (i) Who fought in the Battle of Hastings in 1066, (ii) Who invented Silly Putty, and (iii) Which of the Wright brothers flew first. We can’t leave these questions unanswered, can we?

(i) England and France, (ii) James Wright, and (iii) Orville.

4. Likewise, in the purpose section, you were asked:

(i) What is the function of a MAN6760?

(ii) How many pins does an LM555 time have?

(iii) What is the maximum supply voltage for a 74LS08?

MAN6760

Single Digit, Common Anode Seven-Segment Display, Red, Right Hand DP

LM555

7 V or 5.25 V

Conclusion

1. Solder is an alloy of what two metals?

Tin (Sn) and Lead (Pb)

2. What is tinning and why is it important to keep the tip of your soldering iron tinned?

Tinning is the action of applying a small amount of solder to the tip of a soldering iron. This helps facilitate the heat transfer process creating a good solder connection.

3. List the six most common types of bad solder connections.

Too much solder

Too little solder

Cold solder joint

Not soldered

Solder bridge

Lifted trace/pad

Disturbed joint

4. What are the two techniques that can be used to desolder a component from a PCB?

Solder Sucker

Solder Wick

5. The solder used in electronic application is frequently called “60/40” solder. Why?

6. What is a cold solder joint?

A cold solder joint is a solder connection that exhibits poor wetting and is characterized by a grayish, porous appearance due to excessive impurities in the solder, inadequate cleaning prior to soldering, and/or the insufficient application of heat during the soldering process.

7. What is the melting point of 60/40 solder?

372 °F (190 °C)

8. What is the typical wattage of a soldering iron used in electronic application?

25–30 Watts

Conclusion

1. How evenly distributed were the numbers for your Random Number Generator? If your game was perfect, then each number should have come up approximately 16.67% of the time. Do you think your Random Number Generator is fair? Why or why not?

Some students may be surprised that the Random Number Generator may in fact favor certain numbers.

If the button is pressed exactly the same way each time, the same numbers can be generated.

Dueck, R., & Reid, K. (2008). Introduction to digital electronics. Clifton Park, NY: Thompson Delmar Learning.

Floyd, T. (2006). Digital fundamentals. Upper Saddle River, NY: Pearson Education.

International Technology Education Association. (2000). Standards for technological literacy. Reston, VA: ITEA.

National Council of Teachers of English (NCTE) and International Reading Association (IRA). (1996). Standards for the English language arts. Newark, DE: IRA; Urbana, IL: NCTE.

National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: Author.

National Research Council (NRC). (1996). National science education standards. Washington, D.C.: National Academies Press.

Pecht, M. (1993). Soldering processes and equipment. New York, NY: John Wiley & Sons.

Schultz, M. E. (2007). Grob’s basic electronics: Fundamentals of DC and AC circuits. New York, NY: McGraw Hill.

Tocci, R., Widmer, N., & Moss, G. (2007). Digital systems: Principles and applications. Upper Saddle River, NJ: Pearson Education.

Tokeim, R. L. (2003). Digital electronics principles and applications. Columbus, OH: Glencoe/McGraw-Hill.

Lesson 1.2 Introduction to Circuit Design

Teacher Notes

PLTW recommends that you present the activities, projects, problems, and presentations in the following sequence. Circuit Design

This presentation provides an overview of the circuit design process specifically related to combinational logic design. Illustrate that each activity, project, or problem will advance student knowledge of digital circuit design. One goal of this course is for students to be able to create their own unique designs, not just interpret existing designs. Activity 1.2.1 Introduction to Combinational Logic Design: Seat Belt Circuit

In this activity, students will use the Circuit Design Software to build and test their first combinational logic circuit. This circuit uses only AND, OR, and INVERTER gates. The students will not be designing this circuit. They will only be expected to analyze a given circuit to verify that it meets the design specifications.

Analog and Digital Signals

After reviewing the definition of analog and digital signals, this presentation details the components of analog and digital signals (period, frequency, amplitude, duty cycle). Additionally, the function of the CDS’s oscilloscope will be reviewed. This presentation should be covered prior to assigning Activity 1.2.2 Analog and Digital Signals. Activity 1.2.2 Analog and Digital Signals

Note: You may download a printable student version of the activity from Lesson 1.2 Teacher Resources page.

In this activity students will examine several analog and digital signals to determine their amplitude, period, and frequency. Additionally, they will use the oscilloscope within the Circuit Design Software (CDS). The Binary Number System

Copyright © 2017 Project Lead The Way, Inc. All rights reserved. This presentation provides a brief explanation of the binary number system and details the process for converting numbers between the binary and decimal number systems. The examples given in the presentation are directly related to the exercises in Activity 2.1.2 Binary Numbers and Conversion. The presentation should be used to help students begin the activity. You will need to demonstrate the number-base conversion feature on the students’ calculators and explain that, despite having these tools readily available, they must understand the conversion process. You will also explain that they will be expected to perform the conversion without the use of their calculator. Activity 1.2.3 Binary Number System

Note: You may download a printable student version of the activity from Lesson 1.2 Teacher Resources page.

This activity is designed to give students practice converting numbers between the binary and decimal numbers systems. The activity includes several problems of each type. You may determine how many problems to assign. The ultimate goal is for students to master the conversion process. Activity 1.2.4 Introduction to Sequential Logic Design: Counters

Note: You may download a printable student version of the activity from Lesson 1.2 Teacher Resources page.

In this activity, students will use the Circuit Design Software to build and test their first sequential logic circuits. This circuit uses only D flip-flops. The students will not be designing this circuit. They will only be expected to analyze a given circuit to verify that it meets the design specifications. After simulating a 2-bit counter, students will be asked to add to/modify to create a 4-bit counter on their breadboards. Using a Clock Signal

Digital MiniSystem (DMS) – Students will be introduced to the NI™ myDAQ ELVIS Instrumentation. The will learn to use the Digital Writer to create a clock signal.

Digital Logic Board (DLB) – Students will be introduced to the rotCLK of the DLB to create a usable clock signal.

Clock Signals: 555 Timer

After reviewing the characteristic equations for the charging and discharging of the capacitor, the operations of a 555 Timer Oscillator will be detailed. The design equations (period/frequency/duty cycle) of the 555 Timer based oscillator are given. This presentation should be covered prior to assigning Activity 1.2.5 Clock Signals: 555 Timer. At the end of this presentation there is a Going Further section. This section goes into greater detail on how the 555 timer works and how the

In this activity, students will simulate and build a 555 Timer Oscillator and observe the effect that varying the value of its resistor and capacitor values has on the oscillation frequency and duty cycle. Students will be asked to apply this knowledge to their own 555 Timer Oscillator design. They can then use this clock signal with the 4-bit counter created in Activity 1.2.3 Introduction to Sequential Logic Design: Counters. Understanding Analog Design: Random Number Generator

This presentation in meant to introduce students to a fully implemented design. Building on the knowledge gained from the previous activities on analog electronics, this presentation reviews the analog section of the Random Number Generator design. It is absolutely essential that this presentation be given prior to assigning Project 1.2.5 Understanding Analog Design: Random Number Generator. Project 1.2.6 Understanding Analog Design: The Random Number Generator

In this activity, students will use the Circuit Design Software to build and test the analog section of the Random Number Generator. Remember, the intent of this activity is for the students to understand how this design works, not for them to learn how to design such a circuit. Understanding Digital Design: Random Number Generator

This presentation in meant to introduce students to a fully implemented design. Building on the knowledge gained from the previous activities on combinational and sequential logic, this presentation reviews the digital logic sections of the Random Number Generator design. It is essential that this presentation be given prior to assigning Project 1.2.5 Understanding Digital Design: Random Number Generator. Project 1.2.7 Understanding Digital Design: Random Number Generator

In this activity, students will use the Circuit Design Software to build and test the digital logic sections of the Random Number Generator. To help simplify the process, they will first build and test the combinational and sequential logic sections separately and then combine them as one design. Remember, the intent of this activity is for the students to understand how this design works. They are not yet expected to learn how to design such a circuit.

Lesson 1.2 Introduction to Circuit Design

Teacher Resources

View Student Course Preface

In Lesson 1.1 Introduction to Electronics, students learned to distinguish between analog and digital components. They explored basic components, basic circuits, and used measurement tools to characterize and validate calculations that predict a circuit’s behavior.

In Lesson 1.2 Introduction to Circuit Design, students will explore fundamental circuit designs, manipulate circuits to understand their function, and explore the Random Number Generator circuit design example.

This lesson is meant to be a broad overview of circuit design and to expose students to basic designs they will be exploring and incorporating into their own future designs.

Established Goals

It is expected that students will…

1. Recognize and contrast the characteristics of analog and digital circuits.

2. Understand how analog and digital circuit designs work by altering the characteristics of existing circuits.

3. Use a design process to design and create a circuit.

4. Use calculations and measurement tools to troubleshoot circuits.

Transfers

Students will be able to independently use their learning to …

1. Recognize common analog and digital circuits. Identify and compare the characteristics of analog and digital circuits.

2. Calculate, identify, and accurately measure characteristics of electrical circuits, such as wavelength, period, and duty cycle.

4. Contrast analog circuits, combinational logic circuits, and sequential logic circuits. Explain how the fundamental building blocks of each give a circuit its desired function.

5. Create circuits using a design process.

6. Manipulate circuit designs to alter the characteristics of a circuit to fit desired outcomes.

Essential Questions

Students will keep considering …

1. How are the characteristics of digital circuits different than analog circuits?

2. Why is the understanding of binary and decimal number systems essential to your ability to design combinational logic circuits?

3. What might a design process look like for creating an analog or digital circuit?

4. How are calculations, computer software design (CDS) tools, and measurement tools used in electronics to guide development and troubleshoot a circuit?

5. Why is the 555 timer design such an important and commonly used design in electronics?

Understandings

Students will understand that …

1. Waveforms can be used to trigger events in a circuit.

2. The concepts of frequency, wavelength, and duty cycle are all related to one another and can be calculated in a waveform.

3. Analog and digital signals have different waveforms with distinctive characteristics.

4. Analog signals have an infinite number of voltage levels that vary continuously over the voltage range for that particular system.

5. Digital signals have two well-defined voltage levels, one for a logic high and one for a logic low.

6. Circuit design processes have evolved over time to create circuits. These processes have changed as new strategies and new technologies have become available.

7. Engineers and technicians use Circuit Design Software (CDS) and instrumentation to verify functionality of their analog and digital design.

Students will:

1. Know formulas for Ohm’s Law, Kirchhoff’s Voltage Law, and Kirchhoff’s Current Law.

2. Know the characteristics of series, parallel, and combination circuits.

3. Identify digital and analog components.

4. Know the characteristics and differences between analog and digital signals and circuits.

5. Measure characteristics of a circuit using a digital multimeter (DMM).

6. Know the formulas for period, frequency, and duty cycle.

7. Relate schematic symbols to logic gates and logic gates to schematic symbols.

8. Relate truth tables to logic gates and logic gates to truth tables.

9. Relate logic expressions to logic gates and logic gates to logic expressions.

10. There is a formal design process for translating a set of design specifications into a functional circuit.

Skills

Students will …

1. Solve for unknown values within circuits (series, parallel, and combination circuits) using Ohm’s Law, Kirchhoff’s Voltage Law, and Kirchhoff’s Current Laws.

2. Use Circuit Design Software (CDS) to validate hand calculations to analog circuit solutions.

3. Demonstrate series and parallel circuits on a breadboard.

4. Analyze simple analog circuits using a digital multimeter.

5. Analyze and interpret the amplitude, period, frequency, and duty cycle of analog and digital signals based on instrumentation and calculations.

6. Interpret the design of a simple 555 Timer oscillator and how the analog components affect the wave generated.

7. Use the Circuit Design Software (CDS) to simulate and test a complete analog design.

8. Use Circuit Design Software (CDS) to simulate and test a simple combinational logic circuit designed with AND, OR, and INVERTER gates.

9. Identify and describe the function of a D flip-flop.

11. Use Circuit Design Software (CDS) to simulate and test a complete design containing both combinational and sequential logic.

Resources

Activity 1.2.1 Post-Combinational Logic Design: Seat Belt Presentation

Activity 1.2.2 Analog and Digital Signals

Activity 1.2.3 Binary Numbers System

Activity 1.2.4 Introduction to Sequential Logic Design: Counters (DMS)

Sequential Logic Post-Activity Discussion: An Overview

Day-by-Day Plans

Time: 20 days

Note: In preparation for teaching, it is strongly recommended to review the Lesson 1.2 Teacher Notes - Introduction to Circuit Design.

Days 1–3

Circuit Design Process and Troubleshooting Overview

Present Understandings, Knowledge and Skills, and Essential Questions to provide a lesson overview.

Present the Circuit Design presentation.

Introduction to Combinational Logic Circuit Design

Assign Activity 1.2.1 Introduction to Combinational Logic Design: Seat Belt Circuit.

Activity 1.2.1 Introduction to Combinational Logic Design: Seat Belt Circuit is a guided investigation where students are introduced to a design statement and explore how that design statement is translated into a truth table and functioning circuit.

Assess student work using Answer Key 1.2.1 Introduction to Combinational Logic Design.

Present the Analog Digital Signals presentation.

Model use of the virtual oscilloscope in the circuit design software (CDS).

Assign Activity 1.2.2 Analog and Digital Signals.

Assess student work using Answer Key 1.2.2 Analog and Digital Signals.

Day 5

The Binary Number System and Conversions

Present The Binary Number System presentation.

Assign Activity 1.2.3 The Binary Number System.

Assess student work using Answer Key 1.2.3 The Binary Number System.

Days 6–8

Introduction to Sequential Logic Design

Model generating a clock signal from the Digital Logic Board (DLB) or Digital MiniSytem (DMS).

Assign Activity 1.2.4 Introduction to Sequential Logic Design: Counters.

Assess student work using Answer Key 1.2.4 Introduction to Sequential Logic Design: Counters.

Days 9–12

Clock Signals: 555 Timer

Present Clock Signals: 555 Timer.

Guide students through a discussion on what they have learned and introduce/reinforce the Key Terms used in electronics for these concepts and equipment.

Assign Activity 1.2.5 Clock Signals: 555 Timer.

Assess student work using Answer Key 1.2.5 Clock Signals: 555 Timer.

Understanding Analog Design: Random Number Generator

Present Understanding Analog Design: Random Number Generator presentation.

Guide students through a discussion on what they have learned and introduce/reinforce the Key Terms used in electronics for these concepts and equipment.

Assign Project 1.2.6 Understanding Analog Design: Random Number Generator.

Assess student work using Answer Key 1.2.6 Understanding Analog Design: Random Number Generator.

Days 16–20

Understanding Digital Design: Random Number Generator

Present Understanding Digital Design: Random Number Generator.

Guide students through a discussion on what they have learned and introduce/reinforce the Key Terms used in electronics for these concepts and equipment.

Assign Project 1.2.7 Understanding Digital Design: Random Number Generator.

Assess student work using Answer Key 1.2.7 Understanding Digital Design: Random Number Generator.

Procedure

It’s time for you to implement your first AOI combinational logic circuit. The circuit we will use for this purpose is a Car Safety Buzzer design. The design specifications are as follows:

The buzzer is on whenever the door is open or when the key is in the ignition and the seat belt is not buckled.

1. Create a table that describes these design specification in terms of “highs” (1) and “lows” (0). This is when the sensor or indicator is active or not active.

0 = SEAT BELT NOT BUCKLED Seat Belt 1 = SEAT BELT BUCKLED

0 = KEY NOT IN THE IGNITION Key 1 = KEY IN THE IGNITION

0 = DOOR IS NOT OPEN Door 1 = DOOR IS OPEN

0 = BUZZER is OFF Buzzer 1 = BUZZER is ON

2. Using the Circuit Design Software (CDS), enter the Car Buzzer circuit shown below. Use switches for the inputs Seat Belt, Key, and Door and a probe for the output Buzzer.

Copyright © 2017 Project Lead The Way, Inc. All rights reserved. 3. Based on the design specification you defined, enter a “1” in the Buzzer Output Expected column when the BUZZER should be ON. Toggle the input switches to complete the Buzzer Output Actual column in the truth table below.

Inputs Buzzer Output

Seat Belt Key Door Actual Expected

0 0 0 0 0

0 0 1 1 1

0 1 0 1 1

0 1 1 1 1

1 0 0 0 0

1 0 1 1 1

1 1 0 0 0

1 1 1 1 1

If the Actual Buzzer Output column matches the Expected Output column, then your first combinational logic circuit works. Congratulations! Print a copy of your circuit and put it in your PLTW Engineering Notebook. If the Actual Output does not match the Expected Output, review your circuit diagram and the design specifications that you defined. Make any

Conclusion

1. Combinational logic circuits surround us everywhere in our daily lives. Identify 3–5 examples of circuits that contain combinational logic that you interact with almost daily.

Answers may vary.

Calculators

Watches

Warnings and sensors in vehicles (seat belts, windows, engine sensors)

Thermostats

Household appliances (coffee maker, dishwasher)

Toys

Computers

Cameras

2. In this activity we used switches for the circuit inputs and a probe for the circuit output. Though this works fine for testing purposes, it does not reflect the actual sensors and indicators used in real-world applications of combinational logic circuits. List three input and three output devices that could be used with real world applications of combinational logic.

Answers may vary.

Outputs Inputs LEDs Mechanical Switches (SPDT, SPST) Buzzers Phototransistors Motors Servos

Going Further (Optional)

As mentioned in the purpose section of this activity, combinational logic circuits can be implemented with a variety of different logic gates. One such gate is introduced in the previous lesson and is

Using what you know about the AND gate and INVERTER gates, complete the truth table for the NAND gate.

NAND Gate

A B C

0 0 1

0 1 1

1 0 1

1 1 0

What does a NOR gate look like? What do you think its truth table would look like? (NAND and NOR gates are sometimes referred to as “Universal Gates”. We will find out why later.

NOR Gate

XYZ NOR Gate 0 0 1

0 1 0

1 0 0

1 1 0

Procedure

1. For each of the two analog signals shown below, determine their amplitude (peak), amplitude (peak-peak), period (T), and frequency (f). Be sure to put your answer in proper engineering notation and use the correct units.

Amp(peak): 7.5 V

Amp (peak-peak): 15 V

Period: 500 ns

Frequency: 2 MHz

Amp(peak): 2 V

Amp (peak-peak): 4 V

Period: 1 ms

Frequency: 1 kHz

Note: Why isn’t the above signal considered a digital signal?

In a digital signal, low is 0 V and high is generally 5 V. In other words, the total amplitude would be 5 V. The signal also changes direction.

2. For each of the two digital signals shown below, determine the amplitude, period (T), frequency (f), time high (tH), time low (tL), and duty cycle (DC). Be sure to put your answer in proper engineering notation and use the correct units.

Period: 400 µs

Frequency: 2.5 kHz

Time High: 300 µs

Time Low: 100 µs

Duty Cycle: 75%

Amplitude: 5 V

Period: 1.65 ms

Frequency: 606.06 Hz

Time High: 150 µs

Time Low: 1.5 ms

Duty Cycle: 10%

3. Using the CDS, enter the test circuit shown below. This circuit consists of a CLOCK_VOLTAGE, a DC_POWER (battery), and two 5v LAMPS. This circuit doesn’t do much of anything useful other than make the two lamps flash, but we will use it to gain experience in using the oscilloscope to measure signals.

Open the DC_POWER and set the voltage to 5 volts.

Connect the OSCILLOSCOPE to the positive side of the CLOCK_VOLTAGE component.

Start the simulation. Are the lamps flashing? Does the flashing rate make sense for the frequency and duty cycle of the CLOCK_VOLTAGE? If not, review your setup and make any necessary corrections.

Now that the circuit is working, use the oscilloscope to measure the signal being generated by the CLOCK_VOLTAGE. Use the markers to measure the period, time high, and time low. Use this data to calculate the frequency and duty cycle of the signal.

The markers are flags marked “1” and “2” at the top of the oscilloscope. These can be dragged from side-to-side and lined up on the vertical transitions of the wave. The readings for these markers are found in the area to the right of the labels T1 and T2. In the figure below, Marker 1 is showing the Time High to be about 5 ms. Marker 2 is showing the period to be about 50 ms.

Duty Cycle = (5 ms ÷ 50 ms) x 100 = 10% Frequency = 1 ÷ .050 s = 20 Hz

The Duty Cycle is verified to be 10% and the Frequency is verified to be 20 Hz.

Copyright © 2017 Project Lead The Way, Inc. All rights reserved. Do the measured (and calculated) values match those set up in the CLOCK_VOLTAGE device? If not, review your measurements and make any necessary corrections.

Conclusion

1. List the characteristic that makes a digital signal different from an analog signal.

An analog signal can have any value within a defined range.

A digital signal can only have specific discrete values.

2. In the diagram below, label the parts of the analog signal.

A – Amplitude (Peak to Peak)

B – Amplitude (Peak)

C – Period

3. In the diagram below, label the parts of the digital signal.

B – Time High (tH)

C – Period (T)

D – Time Low (tL)

E – Rising Edge

F – Falling Edge

4. What are the two standard voltage levels that are acceptable for a digital signal?

0 V and 5 V

Procedure

1. Complete the following decimal-to-binary number conversions. An example problem is shown below. If available, use the base conversion feature of your calculator to check your answers.

Solution:

Answer: 19 (10) = 10011 (2)

17 (10) = 10001 (2)

34 (10) = 100010 (2)

58 (10) = 111010 (2)

92 (10) = 1011100 (2)

119 (10) = 1110111 (2)

178 (10) = 10110010 (2)

413 (10) = 110011101 (2)

2. Complete the following binary-to-decimal number conversions. An example problem is shown below. If available, use the base conversion feature of your calculator to check your answers.

Solution:

Answer: 101001 (2)= 41 (10)

1100 (2) = 12 (10)

11010 (2) = 26 (10)

111001 (2) = 57 (10)

1010011 (2) = 83 (10)

10000101 (2) = 133 (10)

10011001 (2) = 153 (10)

100100001 (2) = 289 (10))

111101010 (2) = 490 (10)

3. Perform the remaining decimal-to-binary conversions to complete the table.

Binary Number Decimal Number MSB LSB

1 = 0 0 1

2 = 0 1 0

3 = 0 1 1

4 = 1 0 0

5 = 1 0 1

6 = 1 1 0

7 = 1 1 1

Conclusion

1. The decimal number system has served humans well since the beginning of mankind. Ug the caveman didn’t call it the decimal number system, but he undoubtedly used his fingers to count objects in his world. If the decimal system is so good, why do computer and other digital electronic devices use the binary number system?

Transistors only have two states requiring base 2 mathematics.

2. Because we are using a number system other than decimal, it is important to properly subscript our numbers (for example, 3510, 23410, 100102). Why is this so important? Provide at least three examples where neglecting to subscript numbers could lead to confusion.

Example 1616 = 2210 = 101102

Answers may vary. Students should recognize the same number can be represented by different values depending on the subscript.

3. Without performing the binary-to-decimal conversions, which of the following two binary numbers is the larger number?

011010 (2) = 2610

4. How were you able to determine which was the larger number?

It has a 1 in the MSB placeholder

6. Examine the table that you completed in the procedure portion of the activity. What do you notice about the LSB (least-significant-bit)? What do you notice about the middle bit? What do you notice about the MSB (most-significant-bit)? Do you see a pattern?

Students should see the alternating patterns (0,1,0,1,0,1,0,1) (00,11,00,11) (0000,1111) (00000000)

7. Based on your observations above, complete the table below.

Binary Number Decimal Number MSB LSB

0 = 0 0 0 0

1 = 0 0 0 1

2 = 0 0 1 0

3 = 0 0 1 1

4 = 0 1 0 0

5 = 0 1 0 1

6 = 0 1 1 0

7 = 0 1 1 1

8 = 1 0 0 0

10 = 1 0 1 0

11 = 1 0 1 1

12 = 1 1 0 0

13 = 1 1 0 1

14 = 1 1 1 0

15 = 1 1 1 1

Going Further (Optional)

8. What number system do you think the space alien character would use? (Hint: count the fingers).

Alien = Base 6

9. For some reason, most cartoon characters have traditionally been drawn with four fingers on

Cartoon = Base 8

10. Use your conclusions above to complete the following conversion table.

Decimal Binary Space Alien Cartoon Character Number Number Number Number

35 1000112 556 438

2210 10110 346 268

Procedure

Let’s begin the study of sequential logic by reviewing the basic operations of the D flip-flop.

1. Using the Circuit Design Software (CDS), create the circuit below.

Start the simulation.

Set the input switches P and C to 5 V. Again, since PR and CLR are active low inputs, this will make them both inactive. Toggle the input T several times. The circuit should behave exactly like the circuit in Activity 1.1.6.

Set the input switch P to GROUND and C to 5 V.

What is the state of the two outputs?

Que is on. NOT Que is off.

Record what effect this has on the two outputs.

No change. The flip-flop is “preset” to “1”.

Set the input switch P to 5 V and C to GROUND.

What is the state of the two outputs?

Que is off. NOT Que is on.

Toggle the input T several times.

Record what effect this has on the two outputs.

No change. The flip-flop is “cleared” to “0”.

3. Using the Circuit Design Software (CDS), enter the two-bit binary counter shown above. Use a switch for the input Clock-In and probes for the outputs A and B.

In Activity 1.1.6 we learned that the output on the first flip-flop (A) changes only when the Clock-In goes from low to high. Toggle the input Clock-In (switch T) until both outputs A and B are both low and switch T is low. Now cycle switch T (cycle means to toggle from low to high back to low) and record what effect this has on the two outputs in the table below.

Clock-In AB

Initial Values 0 0

1st Cycle of switch T 0 1

2nd Cycle of switch T 1 0

3rd Cycle of switch T 1 1

4th Cycle of switch T 0 0

5th Cycle of switch T 0 1

6th Cycle of switch T 1 0

7th Cycle of switch T 1 1

8th Cycle of switch T 0 0

9th Cycle of switch T 0 1

Based on these results, explain the pattern that you observe in the two outputs.

The clock changes A, and output from A changes B.

The outputs create a binary count from 0 to 3 (002 to 112).

4. Using the CDS, modify the circuit used in step 1 so that it matches that shown below.

The first modification is to replace the switch input with a CLOCK_VOLTAGE. This change will result in the input being continuously toggled. Be sure the

The second modification is to add a four-channel oscilloscope that is set up to view the four signals A, B, and Clock-In.

Be sure to set the oscilloscope’s time-base to 20 ms/div and the vertical bases of the four channels to 10 volts/div. Also, adjust the Y position of the three channels such that the four signals are all clearly visible.

Start the simulation and let it run until you have captured several periods of each signal.

Using the oscilloscope’s markers, measure the period of the three signals. Use this data to calculate the frequency for each signal. Record your data in the table below. Be sure to use the correct units.

Signal Period Frequency

Clock-In 16.7 ms 60 HZ

B 33.4 ms 30 HZ

A 66.7 ms 15 HZ

Based on these results, explain the relationship of the period and frequency between the three signals. Was this expected?

Frequency and period are inversely related. The frequency gets cut in half each time a flip-flop is added to the design.

Copyright © 2017 Project Lead The Way, Inc. All rights reserved. 5. Analyze the 4-bit binary counter shown below to determine the frequency and period for the signals A, B, C, and D. Use the table below to record your answers.

Signal Period Frequency

Clock-In 1 ms 1000 Hz

D 2 ms 500 HZ

C 4 ms 250 HZ

B 8 ms 125 HZ

A 16 ms 62.5 HZ

7. Using the pin diagram on the datasheet for the 74LS74 D flip-flop, create the 4-Bit counter you explored in this activity on your protoboard. Wire the four outputs to Y3, Y2, Y1, Y0 of your protoboard. Wire the DIO3 to the CLK input of the first flip-flop.

1. The 2-Bit and 4-Bit counters you explored in this activity are referred to as “divide-by-two” counters. Explain the relationship between each consecutive flip-flop and the order in which they are laid out in the design from right to left that creates a binary count.

The frequency gets cut in half each time a flip-flop is added to the design.

If the outputs are arranged from lowest frequency to highest frequency from left to right, the outputs create a binary count.

With four flip-flops, the count is 0 to 15 (00002 to 11112).

2. If you added a fifth bit, what would you guess is the highest number you could count to?

With five flip-flops, the count is 0 to 31 (000002 to 111112).

16 + 8 + 4 + 2 + 1 = 3

3. Can you think of three to five everyday items/products that might have a counter incorporated

Answers may vary.

Virtually all circuits in practical digital devices have a mixture of combinational and sequential logic.

Vending Machines

Security Alarms

Thermostats

Electronic Games

Anything requiring memory

Procedure

1. For the 555 Timer oscillator circuit shown, calculate the frequency and duty cycle of the output signal based on the component values given.

2. Use the CDS to enter and simulate the 555 Timer oscillator circuit. Use the oscilloscope’s markers to make the necessary measurements. Determine the frequency and duty cycle of the output signal. How do these values compare to the calculated values?

How do these values compare to the calculated values?

Should be the same.

3. Repeat steps 1 and 2 for each set of component values in the table below. Note that the shaded areas are the values that were measured from the original circuit.

RA RB C2 Period(T) Frequency(ƒ) tH tL Duty Cycle

100 Ω 330 Ω 22 μF 11.6ms 86.2Hz 6.6ms 5ms 57%

330 Ω 330 Ω 22 μF 15.1ms 66.2Hz 10.1ms 5ms 67%

560 Ω 330 Ω 22 μF 18.6ms 53.8Hz 13.6ms 5ms 73%

330 Ω 100 Ω 22 μF 8.1ms 123.5Hz 6.5ms 1.6ms 80%

330 Ω 330 Ω 22 μF 15.1ms 66.2Hz 10.1ms 5ms 67%

330 Ω 560 Ω 22 2F 22.2ms 45.1Hz 13.6ms 8.6ms 61%

330 Ω 330 Ω 10 μF 6.9ms 144.9Hz 4.6ms 2.3ms 67%

330 Ω 330 Ω 22 μF 15.1ms 66.2Hz 10.1ms 5ms 67%

330 Ω 330 Ω 47 μF 32.3ms 31Hz 21.5ms 10.8ms 67%

4. Review the results of the data collected in step 3 of the procedure.

What effect did varying the RA have on the frequency and duty cycle?

As the resistor value for RA increases, frequency (ƒ) decreases and Duty Cycle (DC) increases.

As the resistor value for RB increases, frequency (ƒ) decreases and Duty Cycle (DC) decreases.

What effect did varying the C2 have on the frequency and duty cycle?

As the capacitor value for C increases, frequency (ƒ) decreases and Duty Cycle (DC) remains constant.

Simulation

5. Once you have your 555 Timer circuit functioning, use the clock signal to trigger the 4-bit binary counter you created previously.

Procedure

Shown below is the analog section of the Random Number Generator.

Analog Section - Random Number Generator

Unfortunately, there are two issues with simulating this circuit as shown. First, it is difficult to obtain accurate simulation results using the push-button switch (S1). Additionally, the 100 μf capacitor (C1) causes the simulation to run too long.

To fix these issues, we must make two simple changes to the circuit. First, replace the push-button switch with an SPST switch. Second, change the 100 μf capacitor to 50 μf. These changes are shown below. Also shown are the oscilloscope connections (highlighted).

1. Using the CDS, enter the modified analog section of the Random Number Generator shown.

2. With the switch closed, start the simulation.

3. Open the oscilloscope tool and adjust the scale of the time base and channels so that the three signals are easy to see and measure.

4. Restart the simulation.

Copyright © 2017 Project Lead The Way, Inc. All rights reserved. 5. After the first few square waves are observed on the output signal, open the switch. Let the simulation run until the output signal stops oscillating. When the oscillation stops, stop the simulation. This may take a few minutes.

6. Adjust the oscilloscope to display the third or fourth square wave of the output signal. Using the oscilloscope’s markers, measure the period of this signal. Use this data to calculate the frequency. Record your result in the table.

Signal Period Frequency

First Square Wave 15.5 ms 64.5 Hz

Middle Square Wave 27.5 ms 36.4 Hz

Last Square Wave 51.6 ms 19.4 Hz

Note: Period results will vary depending on the wave that an individual considers to be the middle wave. First and Last Wave results may vary slightly.

7. Repeat step 6 for a signal in the middle of the simulation, approximately half way between the first and last square wave observed.

Conclusion

1. When you press the push-button of the Random Number Generator, the 555 Timer oscillates at approximately 65 Hz. If you want the oscillation to start at 100 Hz, what value would you apply to C2? Copyright © 2017 Project Lead The Way, Inc. All rights reserved. 2. The values of R9 and C1 determine the time from when the push-button is released to when the oscillation stops. If you wanted to lengthen this time period, what changes would you make to one or both of these components? Explain.

Increase the resistance (lower current = longer time to charge) or

Increase the capacitance (larger capacitance = longer time to charge)

Procedure

Since we learned how the digital electronics of the Random Number Generator worked by analyzing its sequential and combinational logic sections separately, we will construct and simulate the device the same way. We will begin with the combinational logic section.

1. Using the Circuit Design Software (CDS), enter the combinational logic section of the Random Number Generator shown below. For testing purposes connect three switches for the inputs A, B, and C.

Combinational Logic Section – Random Number Generator

Start the simulation.

Toggle the switches and complete the truth table below.

A B C L1 L2 L3 L4 L5 L6 L7

0 0 0 ------

0 0 1 0 0 0 1 0 0 0

0 1 0 0 0 1 0 0 0 1

0 1 1 1 0 0 1 1 0 0

1 0 0 1 0 1 0 1 0 1

1 1 0 1 1 1 0 1 1 1

1 1 1 ------

Did the outputs for the inputs 001–110 display what was expected? If they didn’t, check your circuit to make sure that it was built correctly. Make any necessary corrections and repeat steps a and b.

Did the outputs for the inputs 000 and 111 make sense?

Does it matter?

Zero and 7 will not display on the RNG.

2. Now that the combinational logic section is working, let’s construct and simulate the sequential logic section. Using the CDS, enter the sequential logic section of the Random Number Generator shown below. For the initial analysis, we will use a switch to generate the signal CLOCK.

Sequential Logic Section – Random Number Generator

Start the simulation.

Cycle the input CLOCK several times until the initial value is 001. Cycle the input CLOCK and record the value of the outputs A, B, and C in the table below. (Remember, 1 Cycle = 2 Toggles of the switch.)

CLOCK ABC

1st Cycle 0 1 0

2nd Cycle 0 1 1

3rd Cycle 1 0 0

4th Cycle 1 0 1

5th Cycle 1 1 0

6st Cycle 0 0 1

7th Cycle 0 1 0

Is the counter counting as expected (see below)? If not, check your circuit to make sure that it was built correctly. Make any necessary corrections and repeat steps 2a and 2b.

Modify the circuit by replacing the input switch with a CLOCK_VOLTAGE set to 5 volts, 50% duty cycle at 50 Hz (see below). The CLOCK_VOLTAGE will continuously toggle the input, causing the output to repeatedly cycle through the count 001 to 110.

Sequential Logic Section – Random Number Generator

Start the simulation.

Is the counter counting as expected? If not, check your circuit to make sure that it was built correctly. Make any necessary corrections and repeat steps (e) and (f).

3. Finally, let’s connect the combinational and sequential logic sections together to complete the Random Number Generator.

Using the combinational logic and sequential logic sections created in steps (1) and (2) enter the circuit shown below into the CDS.

Combinational and Sequential Logic Section – Random Number Generator

Start the simulation.

Observe the outputs L1, L2, L3, L4, L5, L6, and L7. They should be cycling through the

Are the outputs working as expected? If they are not, check your circuit to make sure that it was built correctly. Make any necessary corrections and repeat steps b and c.

Conclusion

1. The combinational logic used in the Random Number Generator was AOI logic. What are three gates that are used to implement AOI logic?

AND, OR, INVERTER

2. On the 74LS74 D flip-flop, the CLK input has a small triangle. What does this symbol mean?

The clock signal triggers a change when it changes from low to high.

3. The PR (preset) and CLR (clear) inputs have a circle. What does this symbol mean?

The inputs are ACTIVE LOW. A digital “0” or low activates them.

4. What is the primary characteristic that differentiates combinational and sequential logic?

Combinational Logic – What do you want to happen?

Sequential Logic – When do you want it to happen?

Dueck, R., & Reid, K. (2008). Introduction to digital electronics. Clifton Park, NY: Thompson Delmar Learning.

Floyd, T. (2006). Digital fundamentals. Upper Saddle River, NY: Pearson Education.

International Technology Education Association, (2000). Standards for technological literacy. Reston, VA: ITEA.

National Council of Teachers of English (NCTE) and International Reading Association (IRA). (1996). Standards for the English language arts. Newark, DE: IRA; Urbana, IL: NCTE.

National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: Author.

National Research Council (NRC). (1996). National science education standards. Washington, D.C.: National Academies Press.

Pecht, M. (1993). Soldering processes and equipment. New York, NY: John Wiley & Sons.

Schultz, M. E. (2007). Grob’s basic electronics: Fundamentals of DC and AC circuits. New York, NY: McGraw Hill.

Tocci, R., Widmer, N., & Moss, G. (2007). Digital systems: Principles and applications. Upper Saddle River, NJ: Pearson Education.

Tokeim, R. L. (2003). Digital electronics principles and applications. Columbus, OH: Glencoe/McGraw-Hill.

Lesson 2.1 Combinational Logic Design

Teacher Notes

It is recommended that you present the activities, projects, problems, and presentations in the following sequence. Combinational Logic Design Process

This presentation addresses the three versions of the Combinational Logic Design Process. Version 1, which is the version used throughout this lesson, describes the steps taken to write a logic expression, simplify the logic expression, and implement the design with AOI logic gates. This process will be referenced frequently as the students complete their Majority Vote – Voting Machine and its associated activities. Versions 2 and 3 of the Combinational Logic Design Process are used in later lessons in this unit. AOI Design: Truth Tables to Logic Expressions

This presentation explains how to properly construct 2-, 3-, and 4-variable truth tables. The presentation illustrates the process for writing unsimplified Sum-of-Products (SOP) logic expressions directly from a truth table. The presentation explains how a truth table can be constructed from a given logic expression. Additionally, the steps for constructing a truth table from a set of written design specifications (a word problem) are detailed. The examples given in the presentation are directly related to the exercises in Activity 2.1.1 AOI Truth Tables to Logic Expressions and should be used to help students begin the activity.

Activity 2.1.1 AOI Design: Truth Tables to Logic Expressions

Note: You may download a printable student version of the activity from Lesson 2.1 Teacher Resources page.

This activity is designed to give students practice writing unsimplified SOP logic expressions from truth tables, constructing truth tables from logic expressions, and constructing truth tables from written design specifications. AOI Design: Logic Analysis

This presentation provides a brief explanation for the need to analyze circuits implemented with AND-OR-Inverter Logic (AOI Logic) and details the two methods of analysis. With the first method, the truth table is extracted from the circuit from which the unsimplified logic expression is derived. Copyright © 2017 Project Lead The Way, Inc. All rights reserved. Using the second method, the unsimplified logic expression is extracted from the circuit from which the truth table can be constructed. The examples given in the presentation are directly related to the exercises in Activity 2.1.2 AOI Logic Analysis and should be used to help students begin the activity. Activity 2.1.2 AOI Logic Analysis: Circuit to Truth Table to Logic Expressions

Note: You may download a printable student version of the activity from Lesson 2.1 Teacher Resources page.

This activity is designed to give students practice in analyzing AOI logic circuits. This skill will become important when students begin testing their circuit designs. AOI Logic Implementation

This presentation explains how to properly construct AOI logic circuits from Sum-of-Products (SOP) and Product-of-Sums (POS) logic expressions. Initially, the circuit implementations are constructed assuming that gates of any number of inputs are available. After students understand the process, these designs are re-implemented using only gates that are commercially available. The examples given in the presentation are directly related to the exercises in Activity 2.1.3 AOI Logic Implementation and should be used to help students begin the activity. Activity 2.1.3 AOI Logic Implementation

This activity is designed to give students practice in implementing AOI logic circuits. This is the first activity in this lesson where students will be using the CDS (circuit design software) and DLB (Digital Logic Board). The ICs required are listed in the activity. If the students construct a circuit and it does not work, they may be tempted to pull out all of the wires and start over. DO NOT LET THEM DO THIS. A faulty circuit provides students the opportunity to analyze (or debug) their circuit. During this process, students will determine what the circuit is doing and will make the changes necessary to correct the circuit. Circuit Simplification: Boolean Algebra

This presentation offers the 10 theorems and three laws of Boolean algebra and explains how they are used to simplify logic expressions. Initially the students may struggle with these problems, but with enough practice, they will become proficient. The examples given in the presentation are directly related to the exercises in Activity 2.1.4 Circuit Simplification: Boolean Algebra and should be used to help students begin the activity. Activity 2.1.4 Circuit Simplification: Boolean Algebra

This activity gives students practice in simplifying logic expressions using the theorems and laws of Boolean algebra. The activity includes numerous practice problems. You may determine how many problems to assign. The ultimate goal is for students to master the conversion process. In addition

Copyright © 2017 Project Lead The Way, Inc. All rights reserved. to the math problems, this activity also contains a problem that relates Boolean algebra to a circuit implementation. The intent of this problem is to put the use and importance of logic simplification into a practical context. Circuit Simplification: DeMorgan’s Theorems

This presentation presents DeMorgan’s two theorems and how they are used with Boolean algebra to simplify logic expressions. After completing the activity on Boolean algebra, most students will pick up these concepts quickly. Remember the saying Break the Line / Change the Sign. The examples given in the presentation are directly related to the exercises in Activity 2.1.5 DeMorgan’s Theorems and should be used to help students begin the activity. Activity 2.1.5 Circuit Simplification: DeMorgan’s Theorems

This activity is designed to give students practice in simplifying logic expressions using DeMorgan’s theorems (along with Boolean algebra). The activity includes numerous practice problems. You may determine how many problems to assign. The ultimate goal is for students to master the conversion process. In addition to the math problems, this activity also contains a problem that relates DeMorgan’s theorems to a circuit implementation. The intent of this problem is to put the use and importance of logic simplification into a practical context. Digital Electronics Equations and Theorems

This handout lists the 10 Boolean Theorems, three Boolean Laws, and two DeMorgan’s Theorems. Students will use this handout while completing activities 2.1.4 and 2.1.5. The handout should be kept as a reference. Project 2.1.6 AOI Logic Design: Majority Vote

In this project students will design, simulate, and build a Majority Vote - Voting Machine using AOI logic gates.

Lesson 2.1 Combinational Logic Design

Teacher Resources

View Student Course Preface

In Unit 1 Foundations in Electronics, students were introduced to the components and basic designs used in digital electronics. In this unit, students will explore in greater detail the designs related to combinational logic. How do you design a circuit to “do what you want it to do?”

Lesson 2.1 focuses on AND, OR, Inverter (AOI) combinational logic circuit design. Students will reinforce concepts that they were introduced to in the previous units, such as Binary Number Systems, Truth Tables, and Boolean Expressions. They will then expand on these concepts by exploring how mathematics can be used to reduce circuit size, cost, and complexity. Using the systematic approaches of AOI Simplification, AOI Logic Analysis, and AOI Implementation, students will learn to take design specifications and translate them into the most efficient circuit possible.

Established Goals

It is expected that students will…

1. Translate a set of design specifications into a functional AOI combinational logic circuit following a formal design process.

2. Understand the relationships between truth tables, logic gates, and logic expressions.

3. Recognize and apply simplification strategies to create the most efficient AOI combinational logic circuit design.

Transfer

Students will be able to independently use their learning to …

1. Translate a set of design specifications into a functional AOI combinational logic circuit following a formal design process.

2. Recognize and apply simplification strategies to create the most efficient AOI combinational logic circuit design.

Essential Questions

Students will keep considering …

1. How would you use a design process to convert a set of design specifications into a functional combinational logic circuit?

2. What is the relationship between a combinational logic circuit’s truth table, logic expression, and circuit implementation? Can I describe the process of obtaining either of the first two design items given the third?

3. When you simplify logic expressions using Boolean algebra, how do you know that you have the simplest solution and that the solution is correct?

4. In terms of circuit implementation, what is the advantage of representing all logic expressions in either the SOP or POS form?

5. Defend the following statement: “All logic expressions, regardless of complexity, can be implemented with AND, OR, and INVERTER gates.”

Understandings

Students will understand that …

1. There is a formal design process for translating a set of design specifications into a functional combinational logic circuit.

2. The first step in designing a combinational logic circuit is to translate a set of design specifications into a truth table.

3. A truth table describes the behavior of a combinational logic design by listing all possible input combinations and the desired output for each.

4. Logic expressions can be derived from a given truth table; likewise, a truth table can be constructed from a given logic expression.

5. All logic expressions can be expressed in one of two forms: sum-of-products (SOP) or products of sum (POS).

6. Simplified logic expressions are used to create circuits with fewer gates.

7. All logic expressions, whether simplified or not, can be implemented using AND, OR, and INVERTER gates.

Knowledge

Students will …

2. Know the truth tables and logic expressions associated with AND gates, OR gates, and INVERTER gates.

3. Know rules and laws of Boolean algebra including DeMorgan’s Theorems.

4. Know that a truth table can be interpreted into an algebraic expression representing the output of the circuit.

5. Know that a simplified logic expression can produce the same outputs with fewer gates.

6. Recognize sum-of-product expressions and product-of-sum expressions.

Skills

Students will…

1. Know the formal design process for designing combinational logic circuits.

2. Know the truth tables and logic expressions associated with AND gates, OR gates, and INVERTER gates.

3. Know rules and laws of Boolean Algebra including DeMorgan’s Theorems.

4. Know that a truth table can be interpreted into an algebraic expression representing the output of the circuit.

5. Know that a simplified logic expression can produce the same outputs with fewer gates.

6. Recognize sum-of-product expressions and product-of-sum expressions.

Resources

Activity 2.1.1 AOI Design: Truth Tables to Logic Expressions

Activity 2.1.2 AOI Logic Analysis: Circuit to Truth Table to Logic Expression

Day-by-Day Plans

Time: 11 days

Note: In preparation for teaching, it is strongly recommended to review the Lesson 2.1 Teacher Notes – Combinational Logic Design.

Days 1–2

Present Combinational Logic Design Process.

Present Concepts and Essential Questions to provide a lesson overview.

AOI Truth Tables to Logic Expressions

Guide students through AOI Design: Truth Tables to Logic Expressions while students take notes.

Introduce Activity 2.1.1 AOI Design: Truth Tables to Logic Expressions.

Assess student work using Activity 2.1.1 AOI Design: Truth Tables to Logic Expressions Answer Key.

Day 3

AOI Logic Analysis

Guide students through the AOI Design: Logic Analysis while students take notes.

Introduce Activity 2.1.2 AOI Design: Logic Analysis.

Assess student work using Activity 2.1.2 AOI Logic Analysis Answer Key.

Days 4–5

AOI Logic Implementation

Guide students through AOI Logic Implementation while students take notes.

Introduce Activity 2.1.3 AOI Logic Implementation.

Assess student work using Activity 2.1.3 AOI Logic Implementation Answer Key.

Days 6–7

Circuit Simplification: Boolean Algebra

Present Circuit Simplification: Boolean Algebra.

Introduce Activity 2.1.4 Circuit Simplification: Boolean Algebra and Digital Electronics Equations and Theorems.

Days 8–9

Circuit Simplification: DeMorgan’s Theorems

Present Circuit Simplification: DeMorgan’s Theorems.

Introduce Activity 2.1.5 Circuit Simplification: DeMorgan’s Theorems.

Assess student work using Activity 2.1.5 Circuit Simplification: DeMorgan’s Theorems Answer Key.

Days 10–11

AOI Design: Majority Vote

Introduce Project 2.1.6 AOI Logic Design: Majority Vote.

Students will design, simulate, and build a Majority Vote - Voting Machine using AOI logic gates.

Assess student work using Project 2.1.6 AOI Logic Design: Majority Vote Answer Key.

Procedure

Truth Tables to Logic Expressions

Using the example as a guide, write the unsimplified logic expression for each of the following truth tables. Though it is not required, you may find it helpful to first write the Minterm expression for every place containing a 1 in the output function.

Logic Expressions to Truth Tables

Now that you have mastered the process of writing an unsimplified logic expression from a completed truth table, let’s reverse the process. For the following logic expressions, create a corresponding truth table. Note that some terms in the logic expression may map to more than one place in the truth table.

C D F1

0 0 1

0 1 1

1 0 0

1 1 0

R S T F2

0 0 0 1

0 0 1 0

0 1 0 1

0 1 1 1

1 0 0 1

1 0 1 1

1 1 0 0

1 1 1 1

A B C F3

0 0 0 1

0 0 1 0

1 0 0 1

1 0 1 1

1 1 0 0

1 1 1 1

Seat Belt Alarm Circuit

Now that you understand the mechanics of converting from a truth table to a logic expression (and vice-versa), let’s revisit a circuit design we were introduced to in Unit 1. Your new car has an audio alarm that buzzes whenever the door is open and the key is in the ignition or when the key is in the ignition and the seat belt is not buckled.

Note: This seat belt alarm design is slightly different than the one you created earlier.

9. Using the following variable names and assignment conditions:

Complete the truth table below that captures the functionality of this audio alarm.

D: Door → 0 = Door Open / 1 = Door Close

K: Key → 0 = Key Not in Ignition / 1 = Key in Ignition

S: Seat Belt → 0 = Not Buckled / 1 = Buckled

B: Buzzer → 0 = Buzzer Off / 1 = Buzzer On

D K S B (Door) (Key) (Seat Belt) (Buzzer)

0 0 0 0

0 0 1 0

0 1 0 1

0 1 1 1

1 0 0 0

1 0 1 0

1 1 1 0

10. Using the truth table you just created, write the un-simplified logic expression for the buzzer (i.e., variable B). Be sure that your answer is in the Sum-of-Products form.

Humidity Sensor Circuit

Your Aunt Mary would like you to design a digital logic circuit that monitors the conditions in a room of her house where her seven cats live. The room’s temperature is monitored by a temperature sensor. The room’s humidity is monitored by a humidity sensor. The air quality of the room is monitored by a special sensor that measures air particle density. The three sensors output a one (1) to indicate an out-of-range condition. Located outside of the room is an ALERT light that is on (1) whenever two or more sensors are out of range.

11. Create a truth table that captures the functionality of this room monitoring system.

T H F A (Temperature) (Humidity) (FB density) (ALERT)

0 0 0 0

0 0 1 0

0 1 0 0

0 1 1 1

1 0 0 0

1 0 1 1

1 1 0 1

1 1 1 1

12. Using the truth table that you just created, write the unsimplified logic expression for the

Conclusion

A digital logic circuit with two inputs has four input combinations. One with three inputs has eight combinations. One with four inputs has 16 combinations.

1. How many input combinations would a digital logic circuit have if it has five inputs?

How about six inputs?

2. Mathematically express the relationship between the number of input (N) and the number of input combinations (C).

Number of Input Combinations = 2N

3. Write the unsimplified logic expression for the truth table below.

X Y Z

0 0 1

0 1 1

1 0 1

1 1 1

Going Further (Optional)

The unsimplified logic expression for the truth table is:

ABC

0 0 1 Another way to write this is:

0 1 1

. 1 0 0

1 1 1

Explain why this is true.

This is the expression for the only term that is zero. It is the opposite truth table if the output were inverted.

Procedure

Let’s start by analyzing the relatively simple AOI logic circuit shown below. You will use the technique where you first extract the truth table and then use the truth table to derive the output’s logic expression.

1. Using the assigned test points (TP1–TP4), complete the following truth table.

X Y F1 TP1 TP2 TP3 TP4

0 0 0 1 0 1 0

0 1 1 0 0 1 1

1 0 1 1 1 0 0

1 1 0 0 0 0 0

2. Using the truth table, write out the Minterms for every location that contains a (1) in the F1 column.

Re-analyze the simple AOI logic circuit using the technique where you first extract the logic expression for the output and then use the logic expression to derive the truth table.

4. Using the circuit diagram below, write the logic expression at the output of each gate until you reach the output of the circuit.

5. Using the logic expression, complete the truth table shown below.

X Y F1

0 0 0

0 1 1

1 0 1

1 1 0

How do the logic expressions and truth tables obtained from the two techniques compare? Are they the same? They should be. If they are not, review your work and correct any mistakes.

Let’s analyze a more complex circuit. Complete the following steps for the three input AOI

6. Using the analysis technique where you first extract the truth table and then use it to derive the output’s logic expression, analyze the circuit. Record your results below.

Create test points along the circuit as in 1a. Record corresponding test point columns in the truth table. Alternatively, the student can trace each minterm along the circuit. For example, in minterm 0, all three inputs have a zero value. Given these inputs, the final output at F2 is 0.

R S T F2

0 0 0 0

0 0 1 0

0 1 0 1

0 1 1 0

1 0 0 1

1 0 1 1

1 1 0 0

1 1 1 1

7. Using the analysis technique where you first extract the logic expression for the output and then use it to derive the truth table, analyze the circuit. Record your results below.

0 0 0 0

0 0 1 0

0 1 0 1

0 1 1 0

1 0 0 1

1 0 1 1

1 1 0 0

1 1 1 1

8. How do the truth tables obtained from the two techniques compare? Are they the same? They should be. If they are not, review your work and correct any mistakes.

The truth tables are the same.

9. How do the logic expressions obtained from the two techniques compare? Are they the same?

The logic expressions are not the same. The second technique produced a logic expression with fewer terms.

Conclusion

1. In your own words, describe the process used to analyze a logic circuit where you first extract a truth table and then derive the logic expression.

By testing the circuit, the truth table is filled out and the minterms are identified by output values of 1. The minterms are added together to give the logic expression for the circuit.

Copyright © 2017 Project Lead The Way, Inc. All rights reserved. 2. Again, in your own words, describe the process used to analyze a logic circuit where you first extract the logic expression and then derive the truth table.

By analysis of the circuit diagram, the minterms are identified and the logic expression is written. The truth table is then created from the logic expression.

3. Did you find one of the processes easier than the other? Which one and why?

Analysis of the logic expression and creating the truth table from it should be easier and faster. You do not have to simulate or test the circuit to create the truth table.

4. How can two logic equations that are not identical be equal or equivalent?

The equations outputs produce identical truth tables.

Procedure

Let’s examine the process of implementing an AOI logic circuit by designing a circuit for the relatively simple Sum-of-Products (SOP) logic expression F1.

3. Using the CDS, enter and test the logic circuit that you designed. Use switches for the inputs A, B, and C and a probe or LED circuit for the output F1. Verify that the circuit is working as expected. Print a copy of the circuit and attach it in your notebook.

F1 – CDS

Copyright © 2017 Project Lead The Way, Inc. All rights reserved. 7. Using the CDS, enter and test the logic circuit that you designed. Use switches for the inputs A, B, and C and a probe or LED circuit for the output F2. Verify that the circuit is working as expected. Print a copy of the circuit and attach in your notebook.

F2 – CDS

Conclusion

1. The two circuits shown below are equivalent, meaning that they both produce the same output, Minterm = WXYZ.

Since the two versions produce the same output and require the same number of gates to implement, is one version any better than the other?

Note: Think delays. Though we don’t normally worry about it in our designs, remember that all logic gates have propagation delay.

The second might be a better choice, because it would experience the least amount of propagation delays.

2. Below are two equivalent circuits. One was implemented from an SOP logic expression and the other from the equivalent POS form.

Copyright © 2017 Project Lead The Way, Inc. All rights reserved. First analyze the SOP version to determine the logic expression for F3 in SOP form. Use this expression to generate a truth table for the circuit.

A B C F3

0 0 0 0

0 0 1 1

0 1 0 1

0 1 1 1

1 0 0 0

1 0 1 1

1 1 0 0

1 1 1 0

Now analyze the POS version to determine the logic expression for F3 in POS form. Use this expression to generate a truth table for the circuit.

0 0 0 0

0 0 1 1

0 1 0 1

0 1 1 1

1 0 0 0

1 0 1 1

1 1 0 0

1 1 1 0

How do the two truth tables compare? Is the column for F3 the same for both? They should be. If they are not the same, review your work and make any necessary corrections.

How do the two truth tables compare? They are the same. Is the column for F3 the same for both? They should be. If they are not the same, review your work and make any necessary corrections.

Since the truth tables are the same for F3, what could be said about the two logic expressions?

They are equivalent.

Procedure

Using the theorems and laws of Boolean algebra, simplify the following logic expressions. Note the Boolean theorem/law used at each simplification step. Be sure to put your answer in Sum-of- Products (SOP) form.

Consensus Theorem

Boolean Theorem 14

Boolean Theorem 4

Boolean Theorem 5

Distributive Law 14

Boolean Theorem 8

Boolean Theorem 2

Consensus Theorem 19

Distributive Law 14

Boolean Theorem 8

Boolean Theorem 2

Boolean Theorem 8

Boolean Theorem 2, Distributive Law 14

Boolean Theorem 6

Boolean Theorem 2

Boolean Theorem 3 and 4

Distributive Law 14

Boolean Theorem 8

Boolean Theorem 2

Boolean Theorem 7

Distributive Law 14

Boolean Theorem 7

Distributive Law 14

Multiply by 1 - Boolean Theorem 8

Distributive Law 14 twice

Boolean Theorem 6

Boolean Theorem 2

Consensus Theorem 16

Distributive Law 14

Boolean Theorem 8

Boolean Theorem 2

An alternative solution for 6 using DeMorgan’s theorem is shown below.

Commutative Law 11, DeMorgan’s 20

Boolean Theorem 7

Consensus Theorem 16

Distributive Law 14 and Theorem 7

Boolean Theorem 5

Consensus Theorems 16 and 18

Distributive Law 15

Boolean Theorem 3

Boolean Theorem 4

Distributive Laws 14, Boolean Theorem 8

Boolean Theorem 2

Boolean Theorem 7

Distributive Laws 14, Boolean Theorem 3

Almost as important as being able to use the laws of Boolean algebra (associative, commutative, or distributive) to simplify logic expressions, it is also critical that you are able to identify them. Identify the law of Boolean algebra upon which the following equalities are based.

Commutative

10.

Associative

11.

Associative

12.

Distributive

13.

Distributive

Now that you’ve practiced simplifying logic expressions, apply your knowledge to simplifying an actual circuit.

14. Shown below is a very poorly designed AOI circuit that is part of a coffee vending machine. Write the un-simplified logic expression for the output Brew Cut Off.

Copyright © 2017 Project Lead The Way, Inc. All rights reserved. 15. Using the theorems and laws of Boolean algebra, simplify the logic expression Brew Cut Off. Be sure to put your answer in Sum-of-Products (SOP) form.

Distributive Law 14

Boolean Theorem 4, 1

Boolean 5, Distributive Law 14, Boolean Theorem 2

16. In your notebook, draw an AOI circuit that implements the simplified logic expression Brew Cut Off. For your implementation, assume that only 2-input AND gates (74LS08), 2-input OR gates (74LS32), and inverters (74LS04) are available.

Brew Cut Off

Conclusion

1. Describe the process that you would use to simplify a logic expression using Boolean algebra.

Use the laws of Boolean algebra (associative, commutative, or distributive) to organize/group similar terms.

Then use the theorems and laws of Boolean algebra to simplify.

There are no Boolean theorems left to apply that will make the expression any shorter.

3. Other than using Boolean algebra, how could you prove that two circuits are equivalent?

Compare the truth tables.

4. If you worked for a company that manufactured the coffee vending machine that used the poorly designed circuit, how much money would your new design save the company annually if each GATE cost 15¢ and the company made 500,000 vending machines per year?

7 gates x $.15 x 500,000 = $525,000

3 gates x $.15 x 500,000 = $225,000

You would save the company $300,000 annually.

Procedure

Using DeMorgan’s theorems and the other theorems and laws of Boolean algebra, simplify the following logic expressions. Note the theorem/law used at each simplification step. Be sure to put your answer in Sum-of-Products (SOP) form.

DeMorgan's Theorem 21, Boolean Theorem 9

DeMorgan's Theorem 20

DeMorgan's Theorem 21 (twice)

Boolean Theorem 9

DeMorgan's Theorem 20

DeMorgan's Theorems 20 and 21

Boolean Theorem 9 (Used twice)

DeMorgan's Theorem 21

Boolean Theorem 9

Boolean Theorem 12

Boolean Theorem 4 (Use 3 times)

Boolean Theorem 1

Boolean Theorem 9 (use twice)

DeMorgan's Theorem 20

Boolean Theorem 9

Boolean Theorem 14

7. Write the unsimplified logic expression for the output Do-Nothing in the logic circuit shown below.

The output is call Do-Nothing because that is exactly what the circuit does, nothing; yet it’s a good example for learning about DeMorgan’s theorems.

8. Using DeMorgan’s theorems and the other theorems and laws of Boolean algebra, simplify the logic expression Do-Nothing. Be sure to put your answer in Sum-of-Products (SOP) form.

Boolean Theorem 9 (use four times)

Distributive Law 14

Boolean Theorem 4

Boolean Theorem 5

9. In the space provided, draw an AOI circuit that implements the simplified logic expression Do Nothing. For this implementation you may assume that AND and OR gates are available with any number of inputs.

Do Nothing - I

10. Re-implement the circuit assuming that only 2-input AND gates (74LS08), 2-input OR gates (74LS32), and inverters (74LS04) are available. Draw this circuit in the space provided.

Do Nothing - II

1. Draw the gate equivalent for DeMorgan’s two theorems.

2. How would you prove that the original Do-Nothing circuit and the simplified version are equivalent?

Compare the truth tables.

3. If each GATE cost 5¢ and you made 100,000 of the unsimplified units, how much of the company’s money did you waste on the unsimplified Do-Nothing project?

Do Nothing Unsimplified Do Nothing Simplified A = 2 Gates (2-input) A = 3 Gates (2-input) O = 3 Gates (2-input) O = 1 Gates (2-input) I = 6 Gates (2-input) I = 2 Gates (2-input)

11 GATES x (.05) x 100,000 = $55,000 6 GATES x (.05) x 100,000 = $30,000 You would have wasted $25,000.

Procedure

Complete the following steps to design, simulate, build, and test your Majority Vote - Voting Machine. For each step, be sure to document all your work in your engineering notebook.

1. Using the following variable names and assignment conditions, create a truth table shown for your Majority Vote – Voting Machine.

P: President → 0 = No / 1 = Yes

V: Vice President → 0 = No / 1 = Yes

S: Secretary → 0 = No / 1 = Yes

T: Treasurer → 0 = No / 1 = Yes

Decision → 0 = Fail / 1 = Pass

P V S T Decision

0 0 0 0 0

0 0 0 1 0

0 0 1 0 0

0 0 1 1 0

0 1 0 0 0

0 1 0 1 0

0 1 1 0 0

0 1 1 1 1

1 0 0 0 0

1 0 1 0 1

1 0 1 1 1

1 1 0 0 1

1 1 0 1 1

1 1 1 0 1

1 1 1 1 1

2. Using the truth table, write the unsimplified logic expression for the output function Decision. Be sure that your answer is in the Sum-of-Products form.

Passing Vote =

4. Using the CDS, enter and test your unsimplified Majority Vote – Voting Machine. Use switches for the inputs P, V, S, and T and a probe or LED circuit for the output Decision. Verify that the circuit is working as expected. Print a copy of the final circuit and paste it in your engineering notebook/portfolio.

The following is only one of several possible layouts.

Copyright © 2017 Project Lead The Way, Inc. All rights reserved. 7. Using the CDS, enter and test your simplified Majority Vote – Voting Machine. Use switches for the inputs P, V, S, and T and a probe or LED circuit for the output Decision. Verify that the circuit is working as expected. Print a copy of the final circuit and paste it in your engineering notebook/portfolio.

The following are two layout examples. The location of switches is dependent upon personal preference.