RNS Overflow Detection by Operands Examination

Abstract

In this paper, a novel scheme for detecting overflow in Residue Number System (RNS) is presented. A generalized scheme for RNS overflow detection is introduced, followed by a simplified Operands Examination Method for overflow detection for the moduli set . The proposed method detects overflow in RNS addition of two numbers without pre-computing their sum .Moreover, when compared with the best known similar state of the art designs, the proposed scheme requires lesser hardware, eruder htr izre heit epr and is faster.

A Novel RNS Overflow Detection and Correction Algorithm for the Moduli Set {2^n-1,2^n,2^n+1}

“…From (6), let and be two RNS numbers such that their sum is . Which implies from (6) that: Furthermore, if (13) holds true then (10) can be rewritten as…”

“…Theoretical analysis from Table 1 shows that the proposed scheme has less delay and complexity without compromising on accuracy compared to [4] which is the current best state of the art and has a correction component. The proposed scheme is also faster than [6] which was the best state of the art before [4]. Even though, the hardware complexity of the proposed scheme is higher than that in [6], the proposed scheme uses three comparators and a single AND gate whilst [6] uses six comparators and three AND gates which are not included in the comparison.…”

“…Over the past few years, researchers have made considerable efforts to design overflow detection schemes to handle both odd and even dynamic ranges schemes which do not rely on the traditional techniques such as CRT and Mixed Radix Conversion (MRC) for full reverse conversion, recently proposed RNS overflow detection algorithms still rely on the later [4], and other costly and time consuming procedures such as base extension, group number and sign detection as in [5], [6] and [7]. The scheme in [6] is demonstrated to be better than those in [4] and [5] in terms of both area and delay.…”

A Fault Tolerant Scheme for Detecting Overflow in Residue Number Microprocessors

“…The scheme in [5] evaluated the sign of the sum of two numbers and and used it to detect overflow but adopted a residue-to-binary converter proposed by [10]. The scheme in [11] presented a scheme by an Operands Examination Method for overflow detection for the moduli set ( ) during RNS addition. All these schemes either relied on complete reverse conversion process as in the case of [5], or other costly and time consuming procedures such as base extension, group number and sign detection as in [9] and [11].…”

“…The scheme in [11] presented a scheme by an Operands Examination Method for overflow detection for the moduli set ( ) during RNS addition. All these schemes either relied on complete reverse conversion process as in the case of [5], or other costly and time consuming procedures such as base extension, group number and sign detection as in [9] and [11]. In this paper, an additive overflow detection and correction scheme for the moduli set * +, which has odd dynamic range is presented.…”