AN EFFICIENT OVERFLOW DETECTION AND CORRECTION SCHEME IN RNS ADDITION THROUGH MAGNITUDE EVALUATION

Abstract

Number Systems are media for representing numbers; the popular ones being the Weighted Number Systems (WNS), which sometimes propagate carries during arithmetic computations. The other category, Un-Weighted Number Systems, of which the Residue Number System (RNS) belongs, do not carry weights but have not yet found widespread usage in general purpose computing as a result of some challenges; one of the main challenges of RNS is overflow detection and correction. The presence of errors in calculated values due to such factors as overflow means that systems built on this number system will continue to fail until serious steps are taken to resolve the issue. In this paper, a scheme for detecting and correcting overflow during RNS addition is presented. The proposed scheme used mixed radix digits to evaluate the magnitude of the addends in order to detect the occurrence of overflow in their sum. The scheme also demonstrated a simplified technique of correcting the overflow in the event that it occurs. An analysis of the hardware requirements and speed limitations of the scheme showed that it performs considerably better in relation to similar state of art schemes.