New Arithmetic Residue to Binary Converters

The residue number system (RNS) is a carry-free number system which can support high-speed and parallel arithmetic. Two major issues in efficient design of RNS systems are the moduli set selection and the residue to binary conversion. In this paper, we present two efficient residue to binary converters for the new three-moduli set {2, 2 + 1, 2 – 1}. This moduli set consists of pairwise relatively prime and balanced moduli, which can offer fast internal RNS processing and efficient implemenatation of the residue to binary converter. The proposed residue to binary converters are memoryless and consist of adders. In comparison with other residue to binary converters for a three-moduli set, the proposed converters have better area-time complexity.