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Fourth Edition, last update November 01, 2007 2 Lessons In Electric Circuits, Volume IV – Digital By Tony R. Kuphaldt Fourth Edition, last update November 01, 2007 i c 2000-2011, Tony R. Kuphaldt This book is published under the terms and conditions of the Design Science License. These terms and conditions allow for free copying, distribution, and/or modification of this document by the general public. The full Design Science License text is included in the last chapter. As an open and collaboratively developed text, this book is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the Design Science License for more details. Available in its entirety as part of the Open Book Project collection at: openbookproject.net/electricCircuits PRINTING HISTORY • First Edition: Printed in June of 2000. Plain-ASCII illustrations for universal computer readability. • Second Edition: Printed in September of 2000. Illustrations reworked in standard graphic (eps and jpeg) format. Source files translated to Texinfo format for easy online and printed publication. • Third Edition: Printed in February 2001. Source files translated to SubML format. SubML is a simple markup language designed to easily convert to other markups like LATEX, HTML, or DocBook using nothing but search-and-replace substitutions. • Fourth Edition: Printed in March 2002. Additions and improvements to 3rd edition. ii Contents 1 NUMERATION SYSTEMS 1 1.1 Numbers and symbols .................................. 1 1.2 Systems of numeration .................................. 6 1.3 Decimal versus binary numeration ........................... 8 1.4 Octal and hexadecimal numeration .......................... 10 1.5 Octal and hexadecimal to decimal conversion ..................... 12 1.6 Conversion from decimal numeration ......................... 13 2 BINARY ARITHMETIC 19 2.1 Numbers versus numeration .............................. 19 2.2 Binary addition ...................................... 20 2.3 Negative binary numbers ................................ 20 2.4 Subtraction ........................................ 23 2.5 Overflow .......................................... 25 2.6 Bit groupings ....................................... 27 3 LOGIC GATES 29 3.1 Digital signals and gates ................................ 30 3.2 The NOT gate ....................................... 33 3.3 The ”buffer” gate ..................................... 45 3.4 Multiple-input gates ................................... 48 3.5 TTL NAND and AND gates ............................... 60 3.6 TTL NOR and OR gates ................................. 65 3.7 CMOS gate circuitry ................................... 68 3.8 Special-output gates ................................... 81 3.9 Gate universality ..................................... 85 3.10 Logic signal voltage levels ................................ 90 3.11 DIP gate packaging .................................... 100 3.12 Contributors ........................................ 102 4 SWITCHES 103 4.1 Switch types ........................................ 103 4.2 Switch contact design .................................. 108 4.3 Contact ”normal” state and make/break sequence .................. 111 iii iv CONTENTS 4.4 Contact ”bounce” ..................................... 116 5 ELECTROMECHANICAL RELAYS 119 5.1 Relay construction .................................... 119 5.2 Contactors ......................................... 122 5.3 Time-delay relays ..................................... 126 5.4 Protective relays ..................................... 132 5.5 Solid-state relays ..................................... 133 6 LADDER LOGIC 135 6.1 ”Ladder” diagrams .................................... 135 6.2 Digital logic functions .................................. 139 6.3 Permissive and interlock circuits ............................ 144 6.4 Motor control circuits .................................. 147 6.5 Fail-safe design ...................................... 150 6.6 Programmable logic controllers ............................. 154 6.7 Contributors ........................................ 171 7 BOOLEAN ALGEBRA 173 7.1 Introduction ........................................ 173 7.2 Boolean arithmetic .................................... 175 7.3 Boolean algebraic identities ............................... 178 7.4 Boolean algebraic properties .............................. 181 7.5 Boolean rules for simplification ............................. 184 7.6 Circuit simplification examples ............................. 187 7.7 The Exclusive-OR function ............................... 192 7.8 DeMorgan’s Theorems .................................. 193 7.9 Converting truth tables into Boolean expressions .................. 200 8 KARNAUGH MAPPING 219 8.1 Introduction ........................................ 219 8.2 Venn diagrams and sets ................................. 220 8.3 Boolean Relationships on Venn Diagrams ....................... 223 8.4 Making a Venn diagram look like a Karnaugh map ................. 228 8.5 Karnaugh maps, truth tables, and Boolean expressions ............... 231 8.6 Logic simplification with Karnaugh maps ....................... 238 8.7 Larger 4-variable Karnaugh maps ........................... 245 8.8 Minterm vs maxterm solution ............................. 249 8.9 Σ (sum) and Π (product) notation ............................ 261 8.10 Don’t care cells in the Karnaugh map ......................... 262 8.11 Larger 5 & 6-variable Karnaugh maps ........................ 265 9 COMBINATIONAL LOGIC FUNCTIONS 273 9.1 Introduction ........................................ 273 9.2 A Half-Adder ....................................... 274 9.3 A Full-Adder ....................................... 275 CONTENTS v 9.4 Decoder .......................................... 282 9.5 Encoder .......................................... 286 9.6 Demultiplexers ...................................... 289 9.7 Multiplexers ........................................ 293 9.8 Using multiple combinational circuits ......................... 294 10 MULTIVIBRATORS 299 10.1 Digital logic with feedback ............................... 299 10.2 The S-R latch ....................................... 303 10.3 The gated S-R latch ................................... 307 10.4 The D latch ........................................ 308 10.5 Edge-triggered latches: Flip-Flops ........................... 310 10.6 The J-K flip-flop ...................................... 315 10.7 Asynchronous flip-flop inputs .............................. 317 10.8 Monostable multivibrators ............................... 319 11 SEQUENTIAL CIRCUITSCOUNTERS 323 11.1 Binary count sequence .................................. 323 11.2 Asynchronous counters ................................. 325 11.3 Synchronous counters .................................. 332 11.4 Counter modulus ..................................... 338 11.5 Finite State Machines .................................. 338 Bibliography ........................................... 347 12 SHIFT REGISTERS 349 12.1 Introduction ........................................ 349 12.2 Serial-in/serial-out shift register ............................ 352 12.3 Parallel-in, serial-out shift register ........................... 361 12.4 Serial-in, parallel-out shift register .......................... 372 12.5 Parallel-in, parallel-out, universal shift register ................... 381 12.6 Ring counters ....................................... 392 12.7 references ......................................... 405 13 DIGITAL-ANALOG CONVERSION 407 13.1 Introduction ........................................ 407 13.2 The R/2nR DAC ...................................... 409 13.3 The R/2R DAC ...................................... 412 13.4 Flash ADC ......................................... 414 13.5 Digital ramp ADC .................................... 417 13.6 Successive approximation ADC ............................. 419 13.7 Tracking ADC ....................................... 421 13.8 Slope (integrating) ADC ................................. 422 13.9 Delta-Sigma (∆Σ) ADC ................................. 425 13.10Practical considerations of ADC circuits ........................ 427 vi CONTENTS 14 DIGITAL COMMUNICATION 433 14.1 Introduction ........................................ 433 14.2 Networks and busses ................................... 437 14.3 Data flow .......................................... 441 14.4 Electrical signal types .................................. 442 14.5 Optical data communication .............................. 446 14.6 Network topology ..................................... 448 14.7 Network protocols .................................... 450 14.8 Practical considerations ................................. 453 15 DIGITAL STORAGE (MEMORY) 455 15.1 Why digital? ........................................ 455 15.2 Digital memory terms and concepts .......................... 456 15.3 Modern nonmechanical memory ............................ 458 15.4 Historical, nonmechanical memory technologies ................... 460 15.5 Read-only memory .................................... 466 15.6 Memory with moving parts: ”Drives” ......................... 467 16 PRINCIPLES OF DIGITAL COMPUTING 471 16.1 A binary adder ...................................... 471 16.2 Look-up tables ...................................... 472 16.3 Finite-state machines .................................. 477 16.4
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