AN EFFICIENT RNS SCALER FOR A CERTAIN MODULI SET

Abstract

Residue Number System (RNS) has been widely used in special purpose processors because of its interesting inherent features such as carry free addition; borrow free subtraction, digit by digit multiplication without partial product, and error detection and correction capabilities. However, RNS has not found a widespread usage in general purpose processors due to the following RNS disadvantages: sign detection, magnitude comparison, overflow detection, conversion, division etc. In this thesis. we present an effective RNS scaler for moduli set {220 +l, 2°, i2°-l}. Scaler has always been conceived as a performance bottlenecks due to the inefficient inter-modulo operation. The existing scaling algorithms have small dynamic range. In order to accommodate application requiring larger dynamic range, we propose scaling algorithm for the three moduli set {220 +l, 2°, 220-1}. The complexity of inter-modulo operation has been dealt with by a new formulation of scaling an integer in RNS domain by one of its moduli. Chinese remainder theorem and the number theoretic properties have been exploited for this moduli set. The proposed scheme results into an architecture that does not require any read-only memory. Another advantage of this proposal is that, the scaled integer in normal binary representation is also produced as a byproduct of this process which saves the residue-to -binary converter when the binary representation of scaled integer is also required. Theoretically speaking, this proposal outperforms the known state of the art scalers in terms of area and delay.