Digital Design

Preface i x
1 Digital Systems and Binary Numbers 1
1.1 Digital Systems 1
1.2 Binary Numbers 3
1.3 Number-Base Conversions 6
1.4 Octal and Hexadecimal Numbers 8
1.5 Complements of Numbers 10
1.6 Signed Binary Numbers 14
1.7 Binary Codes 18
1.8 Binary Storage and Registers 27
1.9 Binary Logic 30
2 Boolean Algebra and Logic Gates 38
2.1 Introduction 38
2.2 Basic Definitions 38
2.3 Axiomatic Definition of Boolean Algebra 40
2.4 Basic Theorems and Properties of Boolean Algebra 43
2.5 Boolean Functions 46
2.6 Canonical and Standard Forms 51
2.7 Other Logic Operations 58
2.8 Digital Logic Gates 60
2.9 Integrated Circuits 66
3 Gate-Level Minimization 73
3.1 Introduction 73
3.2 The Map Method 73
3.3 Four-Variable K-Map 80
3.4 Product-of-Sums Simplification 84
3.5 Don't-Care Conditions 88
3.6 NAND and NOR Implementation 90
3.7 Other Two-Level Implementations 97
3.8 Exclusive-OR Function 103
3.9 Hardware Description Language 108
4 Combinational Logic 125
4.1 Introduction 125
4.2 Combinational Circuits 125
4.3 Analysis Procedure 126
4.4 Design Procedure 129
4.5 Binary Adder-Subtractor 133
4.6 Decimal Adder 144
4.7 Binary Multiplier 146
4.8 Magnitude Comparator 148
4.9 Decoders 150
4.10 Encoders 155
4.11 Multiplexers 158
4.12 HDL Models of Combinational Circuits 164
5 Synchronous Sequential Logic 190
5.1 Introduction 190
5.2 Sequential Circuits 190
5.3 Storage Elements: Latches 193
5.4 Storage Elements: Flip-Flops 196
5.5 Analysis of Clocked Sequential Circuits 204
5.6 Synthesizable HDL Models of Sequential Circuits 217
5.7 State Reduction and Assignment 231
5.8 Design Procedure 236
6 Registers and Counters 255
6.1 Registers 255
6.2 Shift Registers 258
6.3 Ripple Counters 266
6.4 Synchronous Counters 271
6.5 Other Counters 278
6.6 HDL for Registers and Counters 283
7 Memory and Programmable Logic 299
7.1 Introduction 299
7.2 Random-Access Memory 300
7.3 Memory Decoding 307
7.4 Error Detection and Correction 312
7.5 Read-Only Memory 315
7.6 Programmable Logic Array 321
7.7 Programmable Array Logic 325
7.8 Sequential Programmable Devices 329
8 Design at the Register Transfer Level 351
8.1 Introduction 351
8.2 Register Transfer Level Notation 351
8.3 Register Transfer Level in HDL 354
8.4 Algorithmic State Machines (ASMs) 363
8.5 Design Example (ASMD CHART) 371
8.6 HDL Description of Design Example 381
8.7 Sequential Binary Multiplier 391
8.8 Control Logic 396
8.9 HDL Description of Binary Multiplier 402
8.10 Design with Multiplexers 411
8.11 Race-Free Design (Software Race Conditions) 422
8.12 Latch-Free Design (Why Waste Silicon?) 425
8.13 Other Language Features 426
9 Laboratory Experiments with Standard ICs and FPGAs 438
9.1 Introduction to Experiments 438
9.2 Experiment 1: Binary and Decimal Numbers 443
9.3 Experiment 2: Digital Logic Gates 446
9.4 Experiment 3: Simplification of Boolean Functions 448
9.5 Experiment 4: Combinational Circuits 450
9.6 Experiment 5: Code Converters 452
9.7 Experiment 6: Design with Multiplexers 453
9.8 Experiment 7: Adders and Subtractors 455
9.9 Experiment 8: Flip-Flops 457
9.10 Experiment 9: Sequential Circuits 460
9.11 Experiment 10: Counters 461
9.12 Experiment 11: Shift Registers 463
9.13 Experiment 12: Serial Addition 466
9.14 Experiment 13: Memory Unit 467
9.15 Experiment 14: Lamp Handball 469
9.17 Experiment 16: Parallel Adder and Accumulator 475
9.18 Experiment 17: Binary Multiplier 478
9.19 Verilog HDL Simulation Experiments and Rapid Prototyping with FPGAs 480
10 Standard Graphic Symbols 488
10.1 Rectangular-Shape Symbols 488
10.2 Qualifying Symbols 491
10.3 Dependency Notation 493
10.4 Symbols for Combinational Elements 495
10.5 Symbols for Flip-Flops 497
10.6 Symbols for Registers 499
10.7 Symbols for Counters 502
10.8 Symbol for RAM 504
Appendix 507
Answers to Selected Problems 521
Index 539