A comprehensive study of three moduli sets for residue arithmetic

One important problem in residue arithmetic is the choice of modulo sets to represent the binary numbers in a certain range. In recent years, several general three-modulo sets have been introduced, and each of them is claimed to have some advantages. In this paper, we carry out a comprehensive study for all these modulo sets from the point of view of the hardware complexity and the speed of their residue-to-binary converters. Based on a performance evaluation of the VLSI implementation in terms of area and delay, we conclude that to represent 8-bit, 16-bit, 32-bit and 64-bit binary numbers, the set of moduli {2/sup n/-1, 2/sup n/, 2/sup n/+1} has the fastest residue-to-binary converter requiring the smallest area. The converter for this moduli set is designed based on the new Chinese remainder theorem of Y. Wang (1998).