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CHAPTER 1 Introduction 1

1.1 Digital Systems in the World Around Us 1

1.2 The World of Digital Systems 4

Digital versus Analog 4

Digital Encodings and Binary Numbers——0s and 1s 9

1.3 Implementing Digital Systems：Microprocessors versus Digital Circuits 22

Software on Microprocessors：The Digital Workhorse 22

Digital Design——When Microprocessors Aren’t Good Enough 26

1.4 About this Book 28

1.5 Exercises 29

CHAPTER 2 Combinational Logic Design 35

2.1 Introduction 35

2.2 Switches 36

Electronics 101 36

The Amazing Shrinking Switch 37

2.3 The CMOS Transistor 40

2.4 Boolean Logic Gates——Building Blocks for Digital Circuits 43

Boolean Algebra and its Relation to Digital Circuits 43

AND，OR，＆ NOT Gates 46

Building Simple Circuits Using Gates 49

2.5 Boolean Algebra 52

Notation and Terminology 53

Some Properties of Boolean Algebra 55

Complementing a Function 60

2.6 Representations of Boolean Functions 61

Equations 62

Circuits 62

Truth Tables 62

Converting among Boolean Function Representations 64

Standard Representation and Canonical Form 68

Multiple-Output Combinational Circuits 71

2.7 Combinational Logic Design Process 73

2.8 More Gates 80

NAND＆NOR 80

XOR＆XNOR 81

Interesting Uses of these Additional Gates 82

Completeness of NAND and of NOR 82

Number of Possible Logic Gates 83

2.9 Decoders and Muxes 84

Decoders 84

Multiplexers（Muxes） 86

2.10 Additional Considerations 91

Nonideal Gate Behavior——Delay 91

Active Low Inputs 92

Demultiplexers and Encoders 93

Schematic Capture and Simulation 93

2.11 Combinational Logic Optimizations and Tradeoffs（See Section 6.2） 95

2.12 Combinational Logic Description UsingHardware Description Languages（See Section 9.2） 95

2.13 Chapter Summary 96

2.14 Exercises 96

CHAPTER 3 Sequential Logic Design：Controllers 105

3.1 Introduction 105

3.2 Storing One Bit——Flip-Flops 106

Feedback——The Basic Storage Method 106

Basic SR Latch 107

Level -Sensitive SR Latch 111

Level-Sensitive D Latch——A Basic Bit Store 112

Edge-Triggered D Flip-Flop——A Robust Bit Store 113

Clocks and Synchronous Circuits 117

Basic Register——Storing Multiple Bits 120

3.3 Finite-State Machines（FSMs） 122

Mathematical Formalism for Sequential Behavior——FSMs 124

How to Capture Desired System Behavior as an FSM 129

3.4 Controller Design 132

Standard Controller Architecture for Implementing an FSM as a Sequential Circuit 132

Controller（Sequential Logic）Design Process 133

Converting a Circuit to an FSM（Reverse Engineering） 140

Common Mistakes when Capturing FSMs 142

FSM and Controller Conventions 145

3.5 More on Flip-Flops and Controllers 146

Non-Ideal Flip-Flop Behavior 146

Flip-Flop Reset and Set Inputs 149

Initial State of a Controller 150

Non-Ideal Controller Behavior：Output Glitches 151

3.6 Sequential Logic Optimizations and Tradeoffs（See Section 6.3） 153

3.7 Sequential Logic Description Using Hardware Description Languages（See Section 9.3） 153

3.8 Product Profile——Pacemaker 153

3.9 Chapter Summary 156

3.10 Exercises 157

CHAPTER 4 Datapath Components 167

4.1 Introduction 167

4.2 Registers 168

Parallel-Load Register 168

Shift Register 173

Multifunction Registers 175

Register Design Process 179

4.3 Adders 181

Adder——Carry-Ripple Style 183

4.4 Comparators 191

Equality（Identity）Comparator 191

Magnitude Comparator——Carry-Ripple Style 192

4.5 Multiplier——Array-Style 195

4.6 Subtractors and Signed Numbers 196

Subtractor for Positive Numbers Only 196

Representing Negative Numbers：Two’s Complement Representation 200

Building a Subtractor Using an Adder and Two’s Complement 203

Detecting Overflow 205

4.7 Arithmetic-Logic Units——ALUs 207

4.8 Shifters 210

Simple Shifters 211

Barrel Shifter 214

4.9 Counters and Timers 215

Up-Counter 216

Up/Down-Counter 217

Counter with Load 218

Timers 222

4.10 Register Files 225

4.11 Datapath Component Tradeoffs（See Section 6.4） 230

4.12 Datapath Component Description Using Hardware Description Languages（See Section 9.4） 230

4.13 Product Profile：An Ultrasound Machine 230

Functional Overview 231

Digital Circuits in an Ultrasound Machine’s Beamformer 234

Future Challenges in Ultrasound 237

4.14 Chapter Summary 237

4.15 Exercises 238

CHAPTER 5 Register-Transfer Level（RTL）Design 247

5.1 Introduction 247

5.2 High-Level State Machines 248

5.3 RTL Design Process 255

Step 2A——Greating a Datapath using Components from a Library 259

Step 2BConnecting the Datapath to a Controller 262

Step 2C——Deriving the Controller’s FSM 263

5.4 More RTL Design 264

Additional Datapath Components for the Library 264

RTL Design Involving Register Files or Memories 265

RTL Design Pitfall Involving Storage Updates 271

RTL Design Involving a Timer 272

A Data-Dominated RTL Design Example 275

5.5 Determining Clock Frequency 278

5.6 Behavioral-Level Design：C to Gates（Optional） 281

5.7 Memory Components 285

Random Access Memory（RAM） 286

Bit Storage in a RAM 288

Using a RAM 290

Read-Only Memory（ROM） 292

ROM Types 294

Using a ROM 297

The Blurring of the Distinction between RAM and ROM 299

5.8 Queues（FIFOs） 299

5.9 Multiple Processors 303

5.10 Hierarchy——A Key Design Concept 305

Managing Complexity 305

Abstraction 306

Composing a Larger Component from Smaller Versions of the Same Component 307

5.11 RTL Design Optimizations and Tradeoffs（See Section 6.5） 309

5.12 RTL Design Using Hardware Description Languages（See Section 9.5） 310

5.13 Product Profile：Cell Phone 310

Cells and Basestations 310

How Cellular Phone Calls Work 311

Inside a Cell Phone 312

5.14 Chapter Summary 316

5.15 Exercises 317

CHAPTER 6 Optimizations and Tradeoffs 325

6.1 Introduction 325

6.2 Combinational Logic Optimizations and Tradeoffs 327

Two-Level Size Optimization Using Algebraic Methods 327

A Visual Method for Two-Level Size Optimization——K-Maps 329

Don’t Care Input Combinations 336

Automating Two-Level Logic Size Optimization 339

Multilevel Logic Optimization——Performance and Size Tradeoffs 348

6.3 Sequential Logic Optimizations and Tradeoffs 351

State Reduction 351

State Encoding 354

Moore versus Mealy FSMs 360

6.4 Datapath Component Tradeoffs 365

Faster Adders 365

Smaller Multiplier——Sequential（Shift-and-Add）Style 375

6.5 RTL Design Optimizations and Tradeoffs 377

Pipelining 377

Concurrency 380

Component Allocation 381

Operator Binding 382

Operator Scheduling 383

Moore versus Mealy High-Level State Machines 386

6.6 More on Optimizations and Tradeoffs 386

Serial versus Concurrent Computation 386

Optimizations and Tradeoffs at Higher versus Lower Levels of Design 387

Algorithm Selection 388

Power Optimization 389

6.7 Product Profile：Digital Video Player/Recorder 393

Digital Video Overview 393

DVD——One Form of Digital Video Storage 393

MPEG-2 Video Encoding——Sending Frame Differences Using I-，P-，and B-Frames 395

Transforming to the Frequency Domain for Further Compression 396

6.8 Chapter Summary 402

6.9 Exercises 403

CHAPTER 7 Physical Implementation on ICs 413

7.1 Introduction 413

7.2 Manufactured IC Types 414

Full-Custom Integrated Circuits 414

Semicustom（Application-Specific）Integrated Circuits——ASICs 415

7.3 Off-the-Shelf Programmable IC Type——FPGA 423

Lookup Tables 424

Mapping a Circuit among Multiple Lookup Tables 426

Programmable Interconnects（Switch Matrices） 432

Configurable Logic Block 434

Overall FPGA Architecture 436

7.4 Other Off-the-Shelf IC Types 438

Off-the-Shelf Logic（SSI）IC 438

Simple Programmable Logic Device（SPLD） 441

Complex Programmable Logic Device（CPLD） 445

FPGA-to-Structured-ASIC Flows 445

7.5 IC Tradeoffs，Trends，and Comparisons 446

Tradeoffs Among IC Types 447

IC Technology Trend——Moore’s Law 448

Relative Popularity of IC Types 450

ASSPs 450

IC Types versus Processor Varieties 451

FPGAs alongside Microprocessors 452

7.6 Product Profile：Giant LED-Based Video Display with FPGAs 453

7.7 Chapter Summary 457

7.8 Exercises 457

CHAPTER 8 Programmable Processors 461

8.1 Introduction 461

8.2 Basic Architecture 462

Basic Datapath 462

Basic Control Unit 465

8.3 A Three-Instruction Programmable Processor 469

A First Instruction Set with Three Instructions 469

Control Unit and Datapath for the Three-Instruction Processor 471

8.4 A Six-Instruction Programmable Processor 475

Extending the Instruction Set 475

Extending the Control Unit and Datapath 476

8.5 Example Assembly and Machine Programs 478

8.6 Further Extensions to the Programmable Processor 480

Instruction Set Extensions 480

Input/Output Extensions 481

Performance Extensions 481

8.7 Chapter Summary 482

8.8 Exercises 483

CHAPTER 9 Hardware Description Languages 487

9.1 Introduction 487

9.2 Combinational Logic Description Using Hardware Description Languages 489

Structure 489

Combinational Behavior 494

Testbenches 498

9.3 Sequential Logic Description Using Hardware Description Languages 501

Register 501

Oscillator 503

Controllers 505

9.4 Datapath Component Description Using Hardware Description Languages 509

Full-Adders 509

Carry-Ripple Adders 511

Up-Counter 514

9.5 RTL Design Using Hardware Description Languages 517

High-Level State Machine of the Laser-Based Distance Measurer 517

Controller and Datapath of the Laser-Based Distance Measurer 523

9.6 Chapter Summary 532

9.7 Exercises 532

APPENDIX A Boolean Algebras 537

A.1 Boolean Algebra 537

A.2 Switching Algebra 538

A.3 Important Theorems in Boolean Algebra 540

A.4 Other Examples of Boolean Algebras 545

A.5 Further Readings 545

APPENDIX B Additional Topics in Binary Number Sys-tems 547

B.1 Introduction 547

B.2 Real Number Representation 547

B.3 Fixed Point Arithmetic 550

B.4 Floating Point Representation 551

The IEEE 754-1985 Standard 552

B.5 Exercises 556

APPENDIX C Extended RTL Design Example 557

C.1 Introduction 557

C.2 Designing the Soda Dispenser Controller 558

C.3 Understanding the Behavior of the Soda Dispenser Controller and Datapath 562