Binary multiplication radix-32 and radix-256

Abstract

Multipliers are used at many different places in microprocessor design. As the non-memory sub-blocks of the microprocessor with the largest size and delay, multipliers have a big impact on the cycle time of the microprocessor. Targeting deeper pipelines and higher clock frequencies, there is a growing demand for multiplier designs that can be split into shorter stages. For this purpose, the use of Booth recoding has been a popular method to cut down the number of partial products in a multiplier to reduce the delay of the partial product accumulation and to simplify the partition of the multiplier into several shorter stages. The complexity to pre-compute an increasing number of digit multiples of the multiplicand within the multiplier unit limits the use of Booth recoding mainly to radices 4 and 8. We propose novel encoding schemes for the implementation of higher radix multiplication. In particular we consider multiplication radix-32 and radix-256. The features provide more flexible multiplier designs that can be implemented in shorter pipeline stages. We compare the proposed designs with multipliers that use traditional Booth recoding.