Chapter 14 Arithmetic Circuits II Multiplier Rev 1

Chapter 14 Arithmetic Circuits (II): Multiplier Rev. 1. 0 05/12/2003 Rev. 2. 0 06/05/2003 Rev. 2. 1 06/12/2003 1 EE 141 Arithmetic Circuits

Binary Multiplication 2 EE 141 Arithmetic Circuits

Binary Multiplication 3 EE 141 Arithmetic Circuits

Array Multiplier 4 EE 141 Arithmetic Circuits

Mx. N Array Multiplier — Critical Path 5 EE 141 Arithmetic Circuits

Wallace-Tree Multiplier 6 EE 141 Arithmetic Circuits

Wallace-Tree Multiplier 7 EE 141 Arithmetic Circuits

Multipliers —Summary • Identify Critical Paths • Possible techniques for speed up: • Multiplier Encoding (Booth encoding) • Wallace Tree Multiplier • Pipelining (multi-phase multiplication) 8 EE 141 Arithmetic Circuits

Shifters 9 EE 141 Arithmetic Circuits

The Binary Shifter 10 EE 141 Arithmetic Circuits

The Barrel Shifter Area Dominated by Wiring 11 EE 141 Arithmetic Circuits

4 x 4 barrel shifter Widthbarrel ~ 2 pm M 12 EE 141 Arithmetic Circuits

Logarithmic Shifter 13 EE 141 Arithmetic Circuits

0 -7 bit Logarithmic Shifter A A 3 Out 3 2 Out 2 1 Out 1 0 Out 0 14 EE 141 Arithmetic Circuits

Summary q Datapath designs are fundamentals for highspeed DSP, Multimedia, Communication digital VLSI designs. q Most adders, multipliers, division circuits are now available in Synopsys Designware under different area/speed constraint. q For details, check “Advanced VLSI” notes, or “Computer Arithmetic” textbooks 15 EE 141 Arithmetic Circuits