Performance Evaluation of Signed-Digit Architecture for Weighted-to-Residue and Residue-to-Weighted Number Converters with Moduli Set (2n-1, 2n, 2n+1)

Abstract

High-speed signed-digit (SD) architectures for weighted-to-residue (WTOR) and residue-to-weighted (RTOW) number conversions with the moduli set (2n, 2n-1, 2n+1) are proposed. The complexity of the conversion has been greatly reduced by using compact forms for the multiplicative inverse and the properties of modular arithmetic. The simple relationships of WTOR and RTOW number conversions result in simpler hardware requirements for the converters. The primary advantages of our method are that our conversions use the modulo m signed-digit adder (MSDA) only and that the constructions are simple. We also investigate the modular arithmetic between binary and SD number representation using circuit designs and a simulation, and the results show the importance of SD architectures for WTOR and RTOW number conversions. Compared to other converters, our methods are fast and the execution times are independent of the word length. We also propose a high-speed method for converting an SD number to a binary number representation.