Computer Logic Design M Morris Mano Part 1

BINARY SYSTEMS 1

1-1 Digital Computers and Digital Systems 1

1-2 Binary Numbers 4

1-3 Number Base Conversions 6

1-4 Octal and Hexadecimal Numbers 9

1-5 Complements 10

1-6 Binary Codes 15

1-7 Binary Storage and Registers 22

1-8 Binary Logic 26

BOOLEAN ALGEBRA 33

2-1 Basic Definitions 33

2-2 Axiomatic Definition of Boolean Algebra 35

2-3 Basic Theorems and Properties of Boolean Algebra 38

2-4 Boolean Functions 42

2-5 Canonical Forms 47

2-6 Other Binary Operators 52

SIMPLIFICATION OF
BOOLEAN FUNCTIONS 57

3-1 The Map Method 57

3-2 Two- and Three- Variable Maps 58

3-3 Four- Variable Map 63



Viii CONTENTS

3-4 Five- and Six- Variable Maps 65

3-5 Product of Sums Simplification 68

3-6 Don't-Care Conditions 72

3-7 The Tabulation Method 74

3-8 Determination of Prime-Implicants 74

3-9 Selection of Prime-Implicants 80

3-10 Concluding Remarks 82

4 COMBINATIONAL LOGIC 87

4-1 Introduction to Combinational Logic Circuits 87

4-2 Design Procedure 89

4-3 Adders 90

4-4 Subtractors 95

4-5 Code Conversion 97

4-6 Comparators 99

4-7 Analysis Procedure 103

4-8 Decoders and Encoders 108

4-9 Multiplexers or Demultiplexers 113



GATE IMPLEMENTATION 120

5-1 Integrated Circuits 120

5-2 Digital Logic Gates 122

5-3 Positive and Negative Logic 1 24

5-4 Simplification Criteria 126

5-5 NAND Logic 129

5-6 NOR Logic 143

5-7 Other Two-Level Implementations 148

5-8 Exclusive-or and Equivalence Functions 154



6 SEQUENTIAL LOGIC 165

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