DIGITAL COMPUTER ARITHMETIC DATAPATH DESIGN

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DIGITAL COMPUTER ARITHMETIC DATAPATH DESIGN
JAMES E. STINE

Preface ix
1. MOTIVATION 1
1.1 Why Use Verilog HDL? 1
1.2 What this book is not : Main Objective 2
1.3 Datapath Design 3
2. VERILOG AT THE RTL LEVEL 7
2.1 Abstraction 7
2.2 Naming Methodology 10
2.2.1 Gate Instances 11
2.2.2 Nets 12
2.2.3 Registers 12
2.2.4 Connection Rules 13
2.2.5 Vectors 14
2.2.6 Memory 14
2.2.7 Nested Modules 15
2.3 Force Feeding Verilog : the Test Bench 16
2.3.1 Test Benches 18
2.4 Other Odds and Ends within Verilog 19
2.4.1 Concatenation 19
2.4.2 Replication 21
2.4.3 Writing to Standard Output 21
2.4.4 Stopping a Simulation 21
2.5 Timing: For Whom the Bell Tolls 22
2.5.1 Delay-based Timing 22
2.5.2 Event-Based Timing 23
2.6 Synopsys DesignWare Intellectual Property (IP) 24
2.7 Verilog 2001 24
2.8 Summary 26
3. ADDITION 27
3.1 Half Adders 28
3.2 Full Adders 28
3.3 Ripple Carry Adders 30
3.4 Ripple Carry Adder/Subtractor 31
3.4.1 Carry Lookahead Adders 34
3.4.1.1 Block Carry Lookahead Generators 36
3.5 Carry Skip Adders 40
3.5.1 Optimizing the Block Size to Reduce Delay 42
3.6 Carry Select Adders 43
3.6.1 Optimizing the Block Size to Reduce Delay 46
3.7 Prefix Addition 47
3.8 Summary 52
4. MULTIPLICATION 55
4.1 Unsigned Binary Multiplication 56
4.2 Carry-Save Concept 56
4.3 Carry-Save Array Multipliers (CSAM) 60
4.4 Tree Multipliers 61
4.4.1 Wallace Tree Multipliers 61
4.4.2 Dadda Tree Multipliers 65
4.4.3 Reduced Area (RA) Multipliers 68
4.5 Truncated Multiplication 71
4.6 Two’s Complement Multiplication 78
4.7 Signed-Digit Numbers 82
4.8 Booth’s algorithm 86
4.8.1 Bitwise Operators 87
4.9 Radix-4 Modified Booth Multipliers 89
4.9.1 Signed Radix-4 Modified Booth Multiplication 91
4.10 Fractional Multiplication 92
4.11 Summary 93
5. DIVISION USING RECURRENCE 103
5.1 Digit Recurrence 104
5.2 Quotient Digit Selection 105
5.2.1 Containment Condition 106
5.2.2 Continuity Condition 106
5.3 On-the-Fly-Conversion 108
5.4 Radix 2 Division 112
5.5 Radix 4 Division with α = 2 and Non-redundant Residual 115
5.5.1 Redundant Adder 118
5.6 Radix 4 Division with α = 2 and Carry-Save Adder 119
5.7 Radix 16 Division with Two Radix 4 Overlapped Stages 122
5.8 Summary 126
6. ELEMENTARY FUNCTIONS 129
6.1 Generic Table Lookup 131
6.2 Constant Approximations 133
6.3 Piecewise Constant Approximation 134
6.4 Linear Approximations 136
6.4.1 Round to Nearest Even 138
6.5 Bipartite Table Methods 141
6.5.1 SBTM and STAM 142
6.6 Shift and Add: CORDIC 147
6.7 Summary 152
7. DIVISION USING MULTIPLICATIVE-BASED
METHODS 161
7.1 Newton-Raphson Method for Reciprocal Approximation 161
7.2 Multiplicative-Divide Using Convergence 166
7.3 Summary 168
References 171
Index 179

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