A Slack-based Approach to Efficiently Deploy Radix 8 Booth Multipliers - 2017


In 1951 A. Booth published his algorithm to efficiently multiply signed numbers. Since the looks of such algorithm, it has been widely accepted that radix four-based mostly Booth multipliers are the foremost efficient. They allow the height of the multiplier to be halved, at the expense of a easy recoding that consists of simply shifts and negations. Theoretically, higher radix ought to manufacture even larger reductions, especially in terms of space and power, but the recoding process is abundant additional complicated. Notably, within the case of radix 8 it's necessary to compute 3X, X being the multiplicand. In order to avoid the penalty due to this calculation, we propose decoupling it from the product and considering 3X as an additional operation within the appliance's Dataflow Graph (DFG). Experiments show that usually there's enough slack in the DFGs to do this while not degrading the performance of the circuit, which permits the economical deployment of radix 8 multipliers that don't calculate the 3X multiple. Results show that our approach is tenp.c and 17p.c faster than radix 4 and radix eight Booth based mostly implementations, respectively, and twelvepercent and 10% a lot of energy economical in terms of Energy Delay Product.

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