Using both Binary and Residue Representations for Achieving Fast Converters in RNS

Abstract

In this paper, a new method is introduced for improving the efficiency of the Residue Number System, which uses both binary and residue representations in order to represent a number. A residue number system uses the remainder of the division in several different modules. Conversion of a number to smaller ones and carrying out parallel calculations on these numbers greatly increase the speed of the arithmetic operations. But as a result of using the non-weighted system, the performance of some calculations such as comparison and reverse conversion is extraordinarily difficult as compared with binary representation. We can use the benefits of both representations in the novel system and this scheme has a simple implementation for reverse/forward conversion.

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