Preface xi
CHAPTER l Digital Concepts and Number Systems
Introduction l
l.l Digital and Analog: Basic Concepts 1
l.2 Some History of Digital Systems 4
l.3 Impact of Digital Technology on Society 6
1.4 Defining the Problem, an Introduction to Algorithms 7
1.5 Digital Systems Overview 9
l.6 Introduction to Number Systems 9
l.7 Positional Number Systems 10
1.7.l Decima1Numbers l0
l.7.2 Binary Numbers 11
l.7.3 Octal Numbers l2
1.7.4 Hexadecimal Numbers 12
1.7.5 Counting in Baser 13
l.8 Number System Conversion l4
1.8.l Binary to Hexadecimal Conversion 15
l.8.2 Hexadecimal and Octal to Binary Conversion 16
l.8.3 Binary to Decimal Conversion l6
1.8.4 Successive Division Radix Conversion l7
1.8.5 Fractional Radix Conversion, Successive Multiplication 18
l.8.6 Radix Conversion Algorithm 20
l.8.7 Decimal to Any Radix 2l
l.8.8 Any Radix to Decimal 23
l.9 Binary Codes 23
l.9.l Natural Binary Coded Decimal 23
l.9.2 Binary Codes (Weighted) 24
1.9.3 BCD Self Complementing Codes 25
l.9.4 Unit Distance Code 26
1.9.5 Alphanumeric Codes 28
l.9.6 Signed Number Binary Codes 28
l.9.7 Signed Magnitude Codes 28
l.9.8 Complement Codes 29
l.l0 Arithmetic 32
l.l0.l Binary Arithmetic 32
l.l0.2 Binary Arithmetic Using Complement Codes 35
1.l0.3 Hexadecimal Arithmetic 38
Summary 42
References 43
Glossary 44
Questions and Problems 45
CHAPTER 2 Boolean Switching Algebra
Introduction 48
2.1 Binary Logic Functions 48
2.1.l IEEE Logic Symbols 54
2.l.2 Functions, Symbols, and Truth Tables 55
2.2 Switching Algebra 57
2.2.l Equivalence 58
2.2.2 Closure 58
2.2.3 Identity 59
2.2.4 Associative Properties 59
2.2.5 Distributive Properties 6l
2.2.6 Commutative Properties 62
2.2.7 Complement Property 62
2.2.8 Duality Property 62
2.2.9 Absorption Property 62
2.2.l0 Idempotency Property 63
2.2.ll Binary Variables and Constants 63
2.2.12 DeMorgan's Theorems
2.3 Functionally Complete Operation Sets 68
2.4 Reduction of Switching Equations Using Boolean Algebra 70
2.5 Realization of Switching Functions 73
2.5.1 Conversion of Switching Functions to Logic Diagrams 73
2.5.2 Converting Logic Diagrams to Switching Equations 77
Summary 80
References 80
Glossary 81
Questions and Problems 82
CHAPTER 3 Principles of Combinational Logic
Introduction 84
3.l Definition of Combinational Logic 84
3.l.l Problem Statements to Truth Tables 85
3.1.2 Deriving Switching Equations 89
3.2 Canonical Forms 91
3.3 Generation of Switching Equations from Truth Tables 93
3.4 Karnaugh Maps 96
3.4.l Three-and Four-Variable Karnaugh Maps 97
3.4.2 Five-and Sis-Variable Karnaugh Maps l07
3.4.3 Simplification Using Five-Variable Karnaugh Maps 109
3.4.4 Simplification Using Six-Variable Karnaugh Maps 112
3.4.5 Incompletely Specified Functions (Don't Care Terms) 1l3
3.4.6 Simplifying Maxterm Equations ll7
3.5 Quine - McClusky Minimization Technique l20
3.5.1 Quine-McClusky Using Don't Care Terms 123
3.5.2 Reduced Prime Imp1icant Tables l25
3.6 Map-Entered Variables l29
3.7 Mixed Logic Combinational Circuits l35
3.7.1 Logic Symbols l36
3.7.2 Conversion to Bubble Logic 140
3.7.3 Synthesizing Switching Functions Using Bubble Notation l42
3.8 Multiple Output Functions l46
Summary l49
References 150
Glossary l50
Questions and Problems l5l
CHAPTER 4 Analysis and Design of Combinational Logic
Introduction l56
4.1 General Approach to Combinational Logic Design l56
4.2 Introduction to Digital Integrated Circuits l64
4.3 Decoders l71
4.3.l BCD Decoders l8l
4.4 Encoders l85
4.5 Digital Multiplexers l90
4.5.l Using Multiplexers as Boolean Function Generators l94
4.6 Adders and Subtractors 20l
4.6.l Cascading Full-Adders 205
4.6.2 Look-Ahead Carry 206
4.6.3 MSI Adders 207
4.6.4 Using MSI Adders as Subtractors 208
4.6.5 Using an MSI Adder as a BCD to Excess-3 Code Converter 211
4.6.6 BCD Adder 212
4.7 Binary Comparators 215
4.8 Arithmetic Logic Units 222
4.9 Array Multipliers 225
4.10 Tristate Buffers 228
4.l1 Combinational Logic Hazards 23l
4.ll.l Static Hazards 232
4.ll.2 Dynamic Hazards 236
Summary 237
References 237
Glossary 238
Questions and Problems 239
CHAPTER 5 Flip-Flops, Simple Counters, and Registers
Introduction 243
5.1 Sequential Circuit Models 243
5.2 Flip-Flops 248
5.2.l Flip-Flop Logic Symbols, Function, and Triggering 248
5.3 Flip-F1op Timing Specifications 265
5.3.l Clock Parameters, Pulse Width, and Skew 265
5.3.2 Flip-Flop Timing, Setup, Hold, and Delay 267
5.3.3 Flip-Flop Metastability 268
5.4 Simple Counters 27l
5.4.l Divide by 2, 4, and 8 Counters (Asynchronous) 272
5.4.2 Johnson Counter (Synchronous) 274
5.4.3 Ring Counter (synchronous) 275
5.5 MSI Integrated Circuit Counters 276
5.5.1 MSI Asynchronous Counters 277
5.5.2 MSI Synchronous Counters 279
5.5.3 Contro1 Signal Generation by Decoding Counter Outputs 283
5.5.4 A Counter Application: Digital Clock 287
5.5.5 IEEE Standard Symbols for MSI Counters 29l
5.6 Registers 295
5.6.l Registers Data Input and Output 295
5.6.2 Tristate Registers 300
5.6.3 Registers Connected to a Common Data Bus 305
5.6.4 R6gister Transfer Timing Considerations 3l0
Summary 312
References 313
Glossary 3l4
Questions and Problems 3l6
CHAPTER 6 Introduction to Sequential Circuits
Introduction 322
6.l Mea1y and Moore Models 322
6.2 State Machine Notation 323
6.2.l Present State, Next State 324
6.2.2 State Diagram 324
6.2.3 State Table 328
6.2.4 Transition Table 329
6.2.5 Excitation Table and Equations 330
6.2.6 Excitation Realization Cost 336
6.3 Synchronous Sequential Circuit Analysis 339
6.3.l Analysis Principles 340
6.3.2 Analysis Examples 340
6.4 Construction of State Diagrams 348
6.4.l Up-Down Decade Counter 349
6.4.2 Sequence Detectors 349
6.4.3 Serial EX-3 to BCD Code Converter 354
6.5 Counter Design 356
6.5.l Modulo-8 Synchronous Counter 357
6.5.2 Up-Down Decade Counter Design 360
Summary 369
References 370
Glossary 370
Questions and Problems 37l
CHAPTER 7 Sequential Circuit Design
Introduction 375
7.l State Equivalence 375
7.2 State Reduction 376
7.2.l Equivalence Classes 376
7.2.2 Implication Charts 378
7.3 State Reduction of Incompletely Specified State Tables 384
7.3.1 Merger Graphs 386
7.4 State Assignment Techniques 389
7.4.1 State Assignment Permutations 390
7.4.2 State Assignment Algorithm 392
7.4.3 Implication Graph 396
7.5 A1gorithm State Machines 399
7.5.l ASM Symbols 399
7.5.2 Elapsed Time Measurement, an ASM Design Example 404
7.6 Linked Sequential Machines 4l3
7.6.l Computer Simulator and Graphic Plotter Interface,
a Linked Sequential Machine Design Example 4l5
Summary 432
References 433
Glossary 433
Questions and Problems 434
CHAPTER 8 Asynchronous Sequential Circuits
Introduction to Asynchronous Sequential Machines
8.l Fundamental and Pulse Mode Asynchronous Sequential Machines 442
8.2 Analysis of Asynchronous Sequential Machines 444
8.3 Deriving Flow Tables 452
8.4 State Assignment 456
8.4.l Races and Cycles 456
8.4.2 Shared Row State Assignment 458
8.4.3 Multiple Row State Assignment 460
8.4.4 One Hot State Assignment 46l
8.5 Asynchronous Design Problems 462
8.5.l Asynchronous Design Problem l 463
8.5.2 Asynchronous Design Problem 2 465
8.6 Data Synchronizers 470
8.6.l Interface Protocol Asynchronous Cell 472
8.7 Mixed Operating Mode Asynchronous Circuits 474
Summary 477
References 478
Glossary 479
Questions and Problems 480
CHAPTER 9 Programmable Logic and Memory
Introduction 485
9.1 Memory 486
9.1.1 ROM, PROM, and EPROM 486,
9.2 Using an EPROM to Realize a Sequential Circuit 49l
9.3 Programmable Logic Devices 495
9.3.l Programmable Logic Array (PLA) 496
9.3.2 Programmable Array Logic 498
9.3.3 Designing an Up-Down Decade Counter Using a PAL 502
9.3.4 Generic Array Logic 507
9.3.5 Designing a Synchronous Sequential Circuit Using a GAL 509
9.4 Erasable Programmable Logic Devices 5l4
9.4.l Altera EP600 EPLD 5l7
9.4.2 Sequential Circuit Realization Using an EP600 5l9
9.5 PLD Computer-Aided Design 523
9.5.l PLD Realization of Combinational Logic 525
9:5.2 Realizing Truth Tables Using a PLD Language 529
9.5.3 Realizing Flip-Flops Using a PLD Language 530
9.5.4 Realizing State Machines Using a PLD Language 530
9.6 Field Programmable Gate Arrays 534
9.6.l Xilinx FPGA 535
9.6.2 System Development Tools for the Xilinx FPGA 542
9.6.3 Xilinx Macro Library 543
9.6.4 Actel FPGA 543
Summary 549
References 550
Glossary 55l
Questions and Problems 552
CHAPTER l0 Digital Integrated Circuits
Introduction 556
l0.1 Diodes as Switches 556
l0.l.l Diode Gates 558
l0.2 Bipolar Transistor Switch 56l
l0.3 Diode Transistor Logic 562
l0.4 Evolution from DTL to TTL 563
10.5 Transistor--Transistor Logic 565
l0.5.l TTL Circuit Operation 567
l0.5.2 TTL Specifications 569
l0.5.3 TTL Subfamilies 573
l0.5.4 Schottky Junctions 578
l0.5.5 Comparison of TTL Subfamily Specifications 579
l0.5.6 Open Collector TTL Circuits 580
l0.5.7 Tristate TTL Devices 584
l0.5.8 Mixed TTL Subfamily Fan-Out 585
l0.5.9 Other TTL Circuits 587
l0.6 Emitter-Coupled Logic 590
l0.6.1 Emitter-Coupled Logic Circuit 590
l0.6.2 ECL Specifications 594
l0.6.3 ECL to TTL and TTL to ECL Interfacing 595
l0.7 Complementary Metal Oxide Semiconductor 597
l0.7.l Field Effect Transistors 597
l0.7.2 MOSFETs 603
l0.7.3 MOSFET Logic Gates 606
l0.7.4 CMOS Logic Gates 609
l0.7.5 Power Dissipation for High-Speed CMOS 6l2
l0.7.6 Propagation Delay for High-Speed CMOS 6l3
l0.7.7 CMOS Noise Margins 613
l0.7.8 CMOS Subfamilies 613
Summary 6l5
References 615
Glossary 616
Questions and Problems 617
Appendix l TTL Analysis Spice Exercise
Appendix 2 Answers to Odd-Numbered Questions and Problems
Index
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