Residue-Weighted Number Conversion with Moduli Set {2^p-1, 2^p+1, 2^{2p}+1, 2^p} Using Signed-Digit Number Arithmetic

Abstract

By introducing a signed-digit (SD) number arithmetic into a residue number system (RNS), arithmetic operations can be performed efficiently. In this study, an algorithm for residue-to-binary with four moduli set {2^p− 1, 2^p +1, 2^{2p}+1, 2^p} using the SD number high-speed residue addition is proposed. Based on the proposed algorithm, the converters are designed with 2-level binary tree structure of SD number residue additions. The comparison of the new converter using SD number arithmetic and the converter using binary arithmetic yields reductions in delays of 22% and 40% for p=4 and p=8, respectively.