High-Speed Parallel Decimal Multiplication with Redundant Internal Encodings

Abstract

The decimal multiplication is one of the most important decimal arithmetic operations which have a growing demand in the area of commercial, financial, and scientific computing. In this paper, we propose a parallel decimal multiplication algorithm with three components, which are a partial product generation, a partial product reduction, and a final digit-set conversion. First, a redundant number system is applied to recode not only the multiplier, but also multiples of the multiplicand in signed-digit (SD) numbers. Furthermore, we present a multioperand SD addition algorithm to reduce the partial product array. Finally, a digit-set conversion algorithm with a hybrid prefix network to decrease the number of the logic gates on the critical path is discussed. An analysis of the timing delay and an HDL model synthesized under 90 nm technology show that by considering the tradeoff of designs among three components, the overall delay of the proposed 16 x 16-digit multiplier takes about 11 percent less timing delay with 2 percent less area compared to the current fastest design.