High-radix residue number system forward and inverse converters

Novel radix-r modulo-rⁿ forward and inverse converters for residue number system (RNS)-based processors are introduced in this paper. The proposed circuits convert conventional radix-2 data to high-radix residues and vice-versa with low complexity requirements. The complexity reduction is achieved by extending the carry-ignore property of modulo-2ⁿ operations to radices higher than 2, which are not powers of 2. The carry-ignore property is efficiently exploited by introducing simplified digit adders, instead of general radix-r adders