viii Contents
2.1.3 Addressing and Byte Ordering 42
2.1.4 Representing Strings 49
2.1.5 Representing Code 49
2.1.6 Introduction to Boolean Algebra 50
2.1.7 Bit-Level Operations in C 54
2.1.8 Logical Operations in C 56
2.1.9 Shift Operations in C 57
2.2 Integer Representations 59
2.2.1 Integral Data Types 60
2.2.2 Unsigned Encodings 62
2.2.3 Two’s-Complement Encodings 64
2.2.4 Conversions between Signed and Unsigned 70
2.2.5 Signed versus Unsigned in C 74
2.2.6 Expanding the Bit Representation of a Number 76
2.2.7 Truncating Numbers 81
2.2.8 Advice on Signed versus Unsigned 83
2.3 Integer Arithmetic 84
2.3.1 Unsigned Addition 84
2.3.2 Two’s-Complement Addition 90
2.3.3 Two’s-Complement Negation 95
2.3.4 Unsigned Multiplication 96
2.3.5 Two’s-Complement Multiplication 97
2.3.6 Multiplying by Constants 101
2.3.7 Dividing by Powers of 2 103
2.3.8 Final Thoughts on Integer Arithmetic 107
2.4 Floating Point 108
2.4.1 Fractional Binary Numbers 109
2.4.2 IEEE Floating-Point Representation 112
2.4.3 Example Numbers 115
2.4.4 Rounding 120
2.4.5 Floating-Point Operations 122
2.4.6 Floating Point in C 124
2.5 Summary 126
Bibliographic Notes 127
Homework Problems 128
Solutions to Practice Problems 143
3
Machine-Level Representation of Programs 163
3.1 A Historical Perspective 166
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