Using Carry-Save Adders

• Can Be Used to Generate 3a – No Booth’s• Slight Delay Penalty from CSA – 3 Gates

Upper Half P in Stored Carry

• Better Use in Keeping Cummulative Product in Redundant Form

for First k-1 Cycles• Then Use a CPA in the Last Cycle

CSA With Booth Recoding

• Better Usage when Combined with Booth’s

Recoding

– Reduces Cycles by 50%

• Each Cycle Faster Due to CSA

• Sign of a, 2a Incorporated Directly in

Recoder/Selector Instead of Add/Subtract

Signal Generation

CSA Combined with Booth Recoding

Booth Recoder/Selector• Circuitry Shown on Following Slide

• Negative Multiples –a, -2a in 2’s Complement

• a, 2a Aligned at Right with Position i

• Must be Padded with i Zeros to Right

• Bitwise Complement (when –a, -2a Needed) Converts zeros to ones Followed by LSb add of 1 Converts Back to zeros

• Causes a Carry-in of 1 into Position i

• Can Ignore Positions 0 through i-1 (in neg. multiples) Insert carry-in directly (dot)

Booth Recoder – Selector Circuit

Radix-4 with CSA – No Booth

Radices > 4• Radix-8 (3 bits at a time-k/3 multiples) Requires 3-Level

CSA Tree

– Might as Well Use Radix-16 (4 bits at a time)

– Still 3-level tree with one more CSA

• MUXes Can Be Replaced with Booth Recoder/Selector

Circuits in Higher Radix Multipliers

• Can Continue to Increase Radix (256-8bits) Leading to

Wider Trees

• Tradeoff is Speed Versus Area

Radix-16 Multiplication

Classification of Multipliers

Twin-beat Mult. with Radix-8 Booth Recoding