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

Alberto A. Del Barrioa and Román Hermidab
Architecture and Technology of Computing Systems, Universidad Complutense de Madrid (UCM), Spain.


In 1951 A. Booth published his algorithm to efficiently multiply signed numbers. Since the appearance of such algorithm, it has been widely accepted that radix 4-based Booth multipliers are the most efficient. They allow the height of the multiplier to be halved, at the expense of a simple recoding that consists of just shifts and negations. Theoretically, higher radix should produce even larger reductions, especially in terms of area and power, but the recoding process is much more complex. Notably, in the case of radix 8 it is 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 extra operation within the application's Dataflow Graph (DFG). Experiments show that typically there is enough slack in the DFGs to do this without degrading the performance of the circuit, which permits the efficient deployment of radix 8 multipliers that do not calculate the 3X multiple. Results show that our approach is 10% and 17% faster than radix 4 and radix 8 Booth based implementations, respectively, and 12% and 10% more energy efficient in terms of Energy Delay Product.

Keywords: Multiplier, Booth, Radix 8, Slack, Modulo scheduling.

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