Page 10 - Engineering Digital Design

Contents

Preface xix

1. Introductory Remarks and Glossary 1
1.1 What Is So Special about Digital Systems? 1
1.2 The Year 2000 and Beyond? 3
1.3 A Word of Warning 5
1.4 Glossary of Terms, Expressions, and Abbreviations 5

2. Number Systems, Binary Arithmetic, and Codes 31
2.1 Introduction 31
2.2 Positional and Polynomial Representations 32
2.3 Unsigned Binary Number System 33
2.4 Unsigned Binary Coded Decimal, Hexadecimal, and Octal 34
2.4.1 The BCD Representation 34
2.4.2 The Hexadecimal and Octal Systems 36
2.5 Conversion between Number Systems 37
2.5.1 Conversion of Integers 38
2.5.2 Conversion of Fractions 40
2.6 Signed Binary Numbers 43
2.6.1 Signed-Magnitude Representation 44
2.6.2 Radix Complement Representation 45
2.6.3 Diminished Radix Complement Representation 48
2.7 Excess (Offset) Representations 49
2.8 Floating-Point Number Systems 49
2.9 Binary Arithmetic 52
2.9.1 Direct Addition and Subtraction of Binary Numbers 52
2.9.2 Two's Complement Subtraction 53
2.9.3 One's Complement Subtraction 54
2.9.4 Binary Multiplication 55
2.9.5 Binary Division 58
2.9.6 BCD Addition and Subtraction 62
2.9.7 Floating-Point Arithmetic 64
2.9.8 Perspective on Arithmetic Codes 67
2.10 Other Codes 68
2.10.1 The Decimal Codes 68
2.10.2 Error Detection Codes 69
2.10.3 Unit Distance Codes 70
2.10.4 Character Codes 70
Further Reading 72
Problems 72

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