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# Fundamentals of Logic Design (2nd Edition)

## Editor's recommendation

Examples Several simple examples that help make the concept clear and easy to understand are closely run through each chapter.

The Karnaugh map can be used flexibly to help students grasp the basic principles of switch algebra.

There are many exercises in each chapter of exercises, which are marked with colored bars. The answers to some exercises are in Appendix B.

Problem solving examples This is another feature of this book. A large number of problem solving examples at the end of each chapter enable students to see how concepts are applied to solve practical problems.

The "Chapter Quiz" section of the chapter end quiz is used to help students measure whether they have mastered the key content of this chapter. See Appendix C for the answers to the test questions.

Designing with standard small-scale and medium-scale integrated circuit chips and programmable logic devices is one of the main features of this book.

The author of the timing system also gives a unique design method for the timing system.

## Introduction

Logic design is the theoretical foundation of computer science, computer engineering and electrical engineering. Learning logic design requires three links: theoretical knowledge, exercises and experiments. Therefore, while emphasizing the basic knowledge, this book combines a large number of examples to teach, and gives a large number of example questions, and also includes a large number of exercises and test questions for each chapter. In addition, 4 experimental platforms and 26 experiments are arranged to closely link theory and practice.

This book is a textbook for students majoring in computer, electrical engineering, communications, and electronics to learn logic design, and it is also a reference book for related professional engineering and technical personnel.

## Book Catalog

Chapter 1 Introduction 1

A brief review of 1.1 number system 2

1.1.1 octal numbers and sixteen Base number 5

1.1.3 Signed number 9

1.1.4 Binary subtraction 12

1.1.5 Two-decimal code (BCD) 13

1.1.6 Other codes 15

1.2 The design process of the combined system 17

1.3 Irrelevant conditions 19

1.4 column truth table 20

1.5 laboratory 23

1.6 problem solving example 24

1.7 exercise 33

1.8 Quiz 36 in this chapter

Chapter 2 Switch Algebra and Logic Circuit 38

2.1 Definition of Switch Algebra 38

2.2 Basic Properties of Switch Algebra 41

2.3 Processing of algebraic functions 43

2.4 Realize logic functions with AND gates, OR gates and NOT gates 47

2.5 From truth tables to algebraic expressions Formula 51

2.6 Preliminary Karnaugh map 54

2.7 Inverse function and OR 60

2.8 NAND gate, NOR gate and XOR gate 63

2.9 Simplification of algebraic expression 68

2.10 Processing of algebraic function and realization of NAND gate 74

2.11 More general Boolean algebra 80

2.12 Problem-solving examples 82

2.13 Exercise 99

2.14 Quiz 105 in this chapter

Chapter 3 Karnaugh map 108

< p>3.1 Use Karnaugh map to solve the simplest AND OR expression 111

3.1.1 Karnaugh map method 1111

3.1.2 Karnaugh map method 2117

< p>3.2 irrelevant items 122

Karnaugh map 3124

3.3 or and formula 125

3.4 The most economical circuit implementation 128

< p>3.5 Five-variable and six-variable Karnaugh map 130

3.6 Multiple output problems 136

3.7 Problem solving examples 145

3.8 Exercises 166

3.9 Quiz 170 in this chapter

Chapter 4 The Simplified Algorithm of Function 174

4.1 Quinn McCluskey Method for Single Output Problem 174

4.2 Iterative consensus method for single-output problems 177

4.3 Table of qualitative implications for single-output problems 180

4.4 Quinn McCluskey method for multiple-output problems 187

4.5 Iterative consensus method for multiple output problems 190

4.6 The essence of multiple output problems Table with items 192

4.7 Examples of problem-solving 196

4.8 Exercises 214

4.9 Test questions in this chapter 215

Chapter 5 is larger Large-scale combinational logic system 216

5.1 Delay in combinational logic circuit 216

5.2 Adder and other arithmetic operation circuits 218

5.2.3 Comparator 221

5.3 Decoder 222

5.4 encoder and priority encoder 227

5.5 data selector 228

5.6 three-state gate 230

5.7 gate array-ROM, PLA and PAL231

5.7.1 Design with read-only memory 234

5.7.2 Design with programmable logic array 235

5.7.3 Use programmable array Logic design 237

5.8 Examples of larger-scale circuits239

5.8.1 Seven-segment display (first main example) 240

5.8. 2 Error coding system 246

5.9 Problem solving examples 248

5.10 Exercises 275

5.11 Test questions in this chapter 284

Chapter 6 Timing System analysis 288

6.1 State table and state diagram 289

6.2 Latches and flip-flops 291

6.3 Analysis of timing system 298

6.4 Problem solving examples 305

6.5 Exercises 314

6.6 Quiz 320 in this chapter

Chapter 7 Design of Timing System 322

< p>7.1 Design method of flip-flop 326

7.2 Design of synchronous counter338

7.3 Design of asynchronous counter347

7.4 Generate state table and state diagram 350

7.5 Problem Solving Examples 361

7.6 Exercises 375

7.7 Quiz 381 in this chapter

Chapter 8 Solving larger-scale time series Question 383

8.1 Shift Register 383

8.2 Counter 387

8.3 Programmable Logic Device (PLD)392

ASM for 8.4 Figure for design 396

8.5 single coding 399

8.6 hardware design language 399

8.7 more complex examples 402

8.8 solution Example Question 407

8.9 Exercise 413

8.10 Test Questions 416 in this chapter

Chapter 9 Sequence circuit simplification 418

9.1 List method for state simplification 419

9.2 Segmentation method 426

9.2.1 The nature of segmentation 429

< p>9.2.2 Find SP segmentation 429

9.3 Use segmentation method to simplify state 432

9.4 State allocation 437

9.5 Problem solving examples 443

p>

9.6 Exercise 456

9.7 Quiz 460 in this chapter

Appendix A Lab Experiment 462

A.1 Hardware Logic Lab 462

p>

A.3LogicWorks4 Introduction 466

A.4 AlteraMax+plusⅡ Introduction 470

A.5 A set of logic designs Experiment 472

A.5.1 Experiment 473 based on the content of Chapter 2

A.5.2 Experiment 474 based on the content of Chapter 5

A.5.3 Based on the content of Chapter 5 Experiment 476 based on the content of Chapter 6

A.5.4 Experiment 478 based on the content of Chapter 7

A.5.5 Experiment 478 based on the content of Chapter 8

A .6 The layout of the chip mentioned in the text of this book and the experiment 479

Appendix B Part 484 Answers to Exercises

Appendix C Answers to Each Chapter 506

< p>Chinese and English terminology comparison table 517

## Book Foreword

Logical Design Fundamentals (2nd Edition) Examples of the characteristics of this book Examples of characteristics of this book In the process of writing this book , Consider the needs of students everywhere. It emphasizes the basics and teaching through examples. The author believes that the best way to learn logical design is to study and solve a large number of design problems and give students the opportunity to practice. The following features are just to achieve the purpose of focusing on students.

? Examples Several simple examples that help make the concept clear and easy to understand are closely run through each chapter.

? Karnaugh map flexibly uses Karnaugh map to help students grasp the basic principles of switch algebra.

? There are many exercises in each chapter of the exercises, which are marked with colored bars. The answers to some exercises are in Appendix B.

? Problem solving examples This is another feature of this book. A large number of problem solving examples at the end of each chapter enable students to see how concepts are applied to solve practical problems.

? The “Chapter Quiz” section of the chapter-end quiz is used to help students measure whether they have mastered the key content of this chapter. See Appendix C for the answers to the test questions.

? Designing with standard small-scale and medium-scale integrated circuit chips and programmable logic devices is one of the main features of this book.

? The author of the timing system also gives a unique design method for the timing system.

? The four types of laboratory experiments in the laboratory organically combine the actual circuit and the theory. Students can make full use of traditional hands-on hardware experiments; use the analog board of the Windows system or the analog board of the Apple computer; Use one of two popular circuit design programs, LogicWorks or 4Altera Max+plusⅡ to conduct simulation laboratory work.

? Multiple output problems This book introduces a variety of methods to solve multiple output problems using Karnaugh map, Quinn McCluskey method and iterative consensus method. Logic Design Fundamentals (2nd Edition) Translator's Preface Translator's Preface "Logic Design Fundamentals" is an important technical foundation course for students majoring in computer, electrical engineering, communications, and electronics. Many professional courses in these majors need to be applied to the knowledge taught in this course. Therefore, to learn this course well is a basic requirement for students in each of the above majors. To learn this course well, you need to master three links, namely: theory, exercises and experiments. In order to help Chinese students learn this course well, Tsinghua University Press has introduced the "Basics of Logic Design" (2nd edition) edited by Professor Alan B. Marcovitz of Florida Atlantic University. The book firmly grasps these teaching links, and pays equal attention to theory and practice. It is a very distinctive textbook. This book comprehensively and systematically expounds the core content of logic design, especially the systematic analysis and design methods. The translator believes that the characteristics of this textbook are reflected in the following aspects.

1. Explain the content in a simple way

The teaching of questions always starts from giving the reader a rough overall concept. For example, Chapter 1 gives the process of combinatorial logic design, so that readers have a preliminary understanding of logic design, and will not make students feel at a loss in the learning of the following content. Then, introduce the theories, tools and methods required for each step in the logic design process, and then to the design of the entire system. From the shallower to the deeper, from the individual to the general, gradually expand the content later, until the problem is introduced very thoroughly. These characteristics are not only highlighted in the content of the entire book, but also in the introduction of certain methods. For example, in the simplification of logic functions, if a logic function formula has multiple optimal solutions, not only one optimal solution is given, but all possible optimal solutions are given. For many exercises, if there are multiple optimal solutions, the number of optimal solutions is given in parentheses, and students are required to find all the optimal solutions instead of just being satisfied with one solution.

2. Pay attention to method

The introduction of pure theory and method will make readers feel boring. This book uses two ways to bring readers to the track of correct methodology: One is to first give more than one actual problem of logic design, and then tell the reader how to get the actual logic circuit of the problem step by step. ; The other is to first solve a very simple problem, extract the specific method of analyzing and solving the problem, and deepen it. Many concrete and vivid examples make students feel that the course of logic design is practical and interesting. In order to help students learn this course well and master its theories and methods in depth and systematically, it provides fascinating learning links. In addition, for solving the same problem, a variety of methods and approaches are provided to solve the problem. For example, for the simplification of combinatorial logic, algebraic simplification method, Karnaugh map simplification method, Quinn McCluskey simplification method, iterative consensus simplification method, etc. are introduced, which embodies "all roads lead The idea of ​​"Rome" enables readers to gradually improve their skills, master the methods, and compare the advantages and limitations of the various methods used.

3. Strong practicality

This is mainly reflected in three aspects: First, there are a large number of examples, problem-solving examples and exercises in the book, so that students can learn and master the introduction in the book The various methods and techniques are easy for self-study; the second is that most of the circuits used in analysis and design are commercial integrated circuit chips, so that students can complete the transition from the principle circuit to the real circuit during the learning process, and improve the practical application ability; the third is In the appendix, 4 kinds of experimental platforms are introduced, and many laboratory homework are provided, so that students can integrate theory with practice, further consolidate the knowledge they have learned, and enhance the ability of practical engineering.

4. Optimized design

Optimized design can not only reduce the implementation cost, but also reduce the volume of the circuit and improve the reliability of the circuit. This is the basic idea carried out throughout this book. From the simplification of logic functions to find the optimal solution, to the least number of gates, the least number of chips, the least types of chips, and the least connections between chips in the design of combinatorial logic circuits, to the simplification of states in sequential circuit design And state distribution, the least memory circuit used, the least combinatorial logic, etc., all reflect this idea. To complete each design, the author must calculate the cost, be "careful", and strive to save the most, so that when students are learning such a professional basic course, they will unknowingly develop an "economic mind" and engage in actual design. When working, strive for the best.

5. Suitable as a textbook for college students

This book is a summary of the author’s years of teaching work. The manuscript has solicited opinions from colleagues in many universities in the United States and used the previous manuscripts. Many rounds of teaching have been conducted by the author himself and his colleagues. Finally, after peer review by many universities, it was officially published after several revisions. This shows that American university professors take their own textbooks very seriously. In the preface of the book, the author gives the reference hours of each part of the content, as well as the choice of content according to different specific situations, for teachers to refer to in teaching. Therefore, this book is very suitable as a textbook or teaching reference book for college students.

6. It is convenient for self-study and can be used as a review material for postgraduate entrance examinations

In each chapter, in addition to a large number of examples, problem-solving examples and exercises, there is also a test in this chapter. It also gives the reference time of the test and the answers to the test questions, which can help students test the mastery and proficiency of the theory, technology and methods of this chapter. For the typical exercises in each chapter, the answers are given at the end of the book, so that students can check whether they are right or wrong. In this way, it can prevent students from getting into a dead end when doing exercises, and save a lot of time for students.

It is these characteristics that make this book easy for self-study. In addition to being a textbook for full-time college students, it is also suitable for college students participating in adult education and online education as a textbook or teaching reference book. It is also a rare good book for reviewing students who are aspiring to take the postgraduate entrance examination for postgraduate studies. It can help you get twice the result with half the effort.

Some illustrations in the original edition of this book are printed in color, and some parts are in red, green or gray to highlight certain parts. Unfortunately, due to technical constraints, the translation cannot be printed in color, which will cause some inconvenience when reading illustrations. The original book has individual typographical errors, and the translator has corrected them one by one during translation.

The preface and chapter 1 of this book are translated by Professor Yang Kuanghan; chapters 2, 3, 4, 5, and 6 are translated by Dr. Yin Hongxi; chapters 7, 8 and the book’s Chinese and English terminology comparison The table was translated by Dr. Liu Xinyuan; Chapter 9 and Appendices A, B, and C were translated by Yu Ying. Dr. Yin Hongxi made a unified review of the translation of the book.

Due to the limited level of translators, coupled with the rush of time, and the improprieties in the translation, I hope readers can criticize and correct me. Finally, the translator would like to express his sincere gratitude to Tsinghua University Press, especially editor Long Qiming, for their support and help in the translation of this book.

Translator in Yanyuan in November 2005