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Chapter 6 - Combinational Logic Systems GCSE Electronics – Component 1: Discovering Electronics

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Chapter 6 - Combinational logic systems GCSE Electronics – Component 1: Discovering Electronics Combinational logic systems Learners should be able to: (a) recognise 1/0 as two-state logic levels (b) identify and use NOT gates and 2-input AND, OR, NAND and NOR gates, singly and in combination (c) produce a suitable truth table from a given system specification and for a given logic circuit (d) use truth tables to analyse a system of gates (e) use Boolean algebra to represent the output of truth tables or logic gates and use the basic Boolean identities A.B = A+B and A+B = A.B (f) design processing systems consisting of logic gates to solve problems (g) simplify logic circuits using NAND gate redundancy (h) analyse and design systems from a given truth table to solve a given problem (i) use data sheets to select a logic IC for given applications and to identify pin connections (j) design and use switches and pull-up or pull-down resistors to provide correct logic level/edge-triggered signals for logic gates and timing circuits 180 © WJEC 2017 Chapter 6 - Combinational logic systems GCSE Electronics – Component 1: Discovering Electronics Introduction In this chapter we will be concentrating on the basics of digital logic circuits which will then be extended in Component 2. We should start by ensuring that you understand the difference between a digital signal and an analogue signal. An analogue signal Voltage (V) Max This is a signal that can have any value between the zero and maximum of the power supply. Changes between values can occur slowly or rapidly depending on the system involved. Min time (s) 0 V A digital signal Voltage (V) This is a signal that can only have two finite values, usually at zero Max and maximum of the power supply. Changes between these two values occur instantaneously. Min time (s) 0 V For this part of the course we will concentrate on digital systems. Recap of work covered in Chapter 1 . When an input or output signal is at the minimum power supply voltage (usually 0 V) this is referred to as a LOW signal or LOGIC 0 signal. When an input or output signal is at the maximum power supply voltage this is referred to as a HIGH signal or LOGIC 1 signal. Remember then that a digital signal is a two-state system with input and output signals being either referred to as high/low, 0/1, on/off depending on the application. The behaviour of a logic gate is summarised in a table, called a ‘truth table’ We will now look at the basic building blocks of all digital systems, logic gates and their associated truth tables. 181 © WJEC 2017 Chapter 6 - Combinational logic systems GCSE Electronics – Component 1: Discovering Electronics Truth Tables The behaviour of a logic gate is summarised in a table, called a truth table. In this course we will only consider the truth tables for logic gates with up to two inputs. Here is a summary of the three logic gates you have already studied: GATE SYMBOL TRUTH TABLE FUNCTION Signal out of gate Input Output is the opposite of A Q the signal in, i.e. it inverts the input NOT 0 1 signal (INVERTER) 1 0 Inputs Output The output Q is only B A Q at a logic 1 when input input 0 0 0 A AND B are at a logic 1 0 1 0 AND 1 0 0 1 1 1 Inputs Output B A Q The output Q is at a logic 1 when input A 0 0 0 OR input B OR both OR are at a logic 1 0 1 1 1 0 1 1 1 1 182 © WJEC 2017 Chapter 6 - Combinational logic systems GCSE Electronics – Component 1: Discovering Electronics We will now look at two additional logic gates: • The NAND gate The symbol for a 2-input NAND gate is: The truth table for the 2-input NAND gate is shown below. Inputs Output B A Q 0 0 1 0 1 1 1 0 1 1 1 0 If you compare this truth table with that for the AND gate, you will find that the output Q is the exact opposite of the AND gate output. • The NOR gate The symbol for a 2-input NOR gate is: The truth table for the 2-input NOR gate is shown below. Inputs Output B A Q 0 0 1 0 1 0 1 0 0 1 1 0 If you compare this truth table with that for the OR gate, you will find that the output Q is the exact opposite of the OR gate output. 183 © WJEC 2017 Chapter 6 - Combinational logic systems GCSE Electronics – Component 1: Discovering Electronics Practical Logic Gates Logic gates are available within an integrated circuit (IC) – a set of electronic circuits built on the same wafer of semiconductor material. These logic ICs are usually supplied in plastic DIL (dual in line) packages containing several logic gates of the same type. The diagram shows one of these logic IC packages. Pin 1 identification There are two common types of package available, known as TTL or 7400 series and CMOS or 4000 series. Examination questions will only test CMOS devices. However, you may choose to use TTL devices for your project work. The data sheet for a logic gate package includes the pinout diagram showing how the pins connect to the logic gates inside it. The pinout diagrams below relate to ICs known as quad 2-input AND gates. The TTL AND gate is referred to as a ‘7408’ whilst the CMOS version is referred to as a ‘4081B’. TTL AND gate CMOS AND gate Using the right pinout is important, as incorrect connections can damage the whole package. We will look at some more pinout diagrams later on. 184 © WJEC 2017 Chapter 6 - Combinational logic systems GCSE Electronics – Component 1: Discovering Electronics Analysis of Simple Logic Circuits You will need to recognise truth tables for the five basic gates individually and in simple combinations. You will also need to be able to complete a truth table for a larger system. We will now consider a couple of examples of these systems. Example 1: Study the following logic system carefully and then complete the truth table that follows: Inputs Outputs B A C Q 0 0 0 1 1 0 1 1 In this problem, the output of the NOT gate has been labelled C. The first stage is to complete the output column for C which is the NOT of A as shown below. Inputs Outputs B A C Q 0 0 1 0 1 0 1 0 1 1 1 0 Now we need to complete the final column Q which is the output of the AND gate with B and C as the inputs. Inputs Outputs B A C Q 0 0 1 0 0 1 0 0 1 0 1 1 1 1 0 0 Do not fall into the trap of writing the answer to the Q column in the order you would normally do for the truth table for an AND gate. Because in this case the inputs to the AND gate are not in the same order as that given in the ‘standard’ AND gate truth table provided earlier. 185 © WJEC 2017 Chapter 6 - Combinational logic systems GCSE Electronics – Component 1: Discovering Electronics Example 2: Study the following logic system carefully and then complete the truth table that follows: Inputs Outputs C B A F G Q 0 0 0 1 0 1 0 0 1 1 0 0 0 1 0 0 0 1 0 1 1 0 0 0 1 0 0 1 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 1 1 0 0 0 You can see that the truth table for a 3-input logic system contains eight possible input combinations. Notice the way the logic state of each input changes as you move down the table. First check the output column for the NOT gate (Column F) – {The input is B.} Then check the output column for the AND gate (Column G) – {The inputs are F and C.} Finally check the final output from the NOR gate (Column Q) – {The inputs are A and G.} 186 © WJEC 2017 Chapter 6 - Combinational logic systems GCSE Electronics – Component 1: Discovering Electronics Investigation 6.1 You will need to use a simulation program such as ‘Circuit Wizard’ or ‘Yenka Technology’ to complete this investigation. Note: You can use the ’built-in‘ inputs and outputs that are available in these simulation programs. The input switches and logic indicator turn red to indicate logic 1.The circuit being tested would look something like this diagram: Set up each of the logic systems using your simulation program and use the program to complete the truth table for each system: 1. Inputs Output B A Q 0 0 0 1 2. 1 0 1 1 Inputs Output C B A Q 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 187 © WJEC 2017 Chapter 6 - Combinational logic systems GCSE Electronics – Component 1: Discovering Electronics Exercise 6.1 1. Look at the following logic symbols labelled A–E. A B C D E a) Which is the correct symbol for an AND gate. …………… b) Which is the correct symbol for a NOT gate. …………… c) Which is the correct symbol for a NOR gate.
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