Reverse converters for RNSs with diminished-one encoded channels

The diminished-one encoding is often considered when representing the operands in the modulo 2k+1 channels of a Residue Number System (RNS) since it can offer increased arithmetic processing speed. However, limited research is available on the design of residue-to-binary (reverse) converters for RNSs that use the diminished-one encoding in one or more channels. In this paper we introduce a simple methodology for designing such converters which can be applied to reverse converters based on the Chinese Remainder Theorem (CRT) or the New CRT-I method. Efficient converters for three moduli sets, covering different dynamic ranges, are also analytically presented. The proposed converters are shown to be area, delay and power efficient for several moduli sets.