Secondary Radix Recodings for Higher Radix Multipliers
IEEE Transactions on Computers
Design of a radix-2m hybrid array multiplier using carry save adder format
SBCCI '05 Proceedings of the 18th annual symposium on Integrated circuits and system design
A new array architecture for signed multiplication using Gray encoded radix-2m operands
Integration, the VLSI Journal
A new high radix-2r (r≥8) multibit recoding algorithm for large operand size (N≥32) multipliers
ACM SIGARCH Computer Architecture News
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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. In the high-radix representations each digit of the multiplier is represented in a secondary radix which is 7 in the case of radix-32 and which is 11 in the case of radix-256, so that the multiplier is represented by roughly 2p/5 resp. 3p/8 terms. All non zero digits of the secondary radix system are a power of two, simplifying partial product generation. The partial products depending on multiples of the radices 7 or 11 can be separately accumulated, with multiplication by the radix a pre- or post-computation option. These 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.