SUT-RNS Residue-to-Binary Converters Design

Abstract—The Stored Unibit Transfer (SUT) encoding has been recently proposed as a redundant high-radix encoding for each of the channels of a Residue Number System (RNS) that can improve the efficiency of Binary Signed Digit (BSD)-encoded RNS. However, a residue-to-binary (reverse) converter for it has not yet been reported in the open literature. In this paper we introduce SUT-RNS reverse converters for two different moduli sets, that is, for the 3-moduli {2n-1, 2n, 2n+1} and for the 4-moduli {2n-1, 2n, 2n+1, 22n+1} sets. The area and delay costs of the proposed converters are shown to be less than those required by the corresponding RNS converters for the BSD encoding. In the 4-moduli set case, the converters ’ costs are shown to be close to those of the corresponding converters for the binary encoding. Keywords-Redundant arithmetic; residue number system; reverse converter; stored unibit transfer; I