Sign Detection and Signed Integer Comparison for the 3-Moduli Set {2^n±1,2^(n+k)}

Zeinab Torabi,Somaye Timarchi

doi:10.7494/csci.2021.22.3.3955

Zeinab Torabi, Somaye Timarchi

Open Access

https://doi.org/10.7494/csci.2021.22.3.3955

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Abstract

Comparison, division and sign detection are considered complicated operations in residue number system (RNS). A straightforward solution is to convert RNS numbers into binary formats and then perform complicated operations using conventional binary operators. If efficient circuits are provided for comparison, division and sign detection, the application of RNS can be extended to the cases including these operations.For RNS comparison in the 3-moduli set , we have only found one hardware realization. In this paper, an efficient RNS comparator is proposed for the moduli set which employs sign detection method and operates more efficient than its counterparts. The proposed sign detector and comparator utilize dynamic range partitioning (DRP), which has been recently presented for unsigned RNS comparison. Delay and cost of the proposed comparator are lower than the previous works and makes it appropriate for RNS applications with limited delay and cost.

Highlights

A number X in a residue number system (RNS) with k moduli {m1, m2, · · ·, mk} is represented by set of residues {x1, x2, · · ·, xk}, where xi = |X|mi denotes the remainder of integer division X/mi
In RNS, operations like addition, subtraction, and multiplication are performed in k parallel independent channels, which makes it a promising candidate for applications that use frequent add/multiply operations such as finite impulse response digital filters [4], data transmission [1], cryptography [18], and image processing [28]
As regarding the role of comparison in other complicated operations such as division, sign, and overflow detection, it is expected that a cost-effective and high-speed implementation of the comparison will assist in b improving other complicated operations

Summary

Introduction

A number X in a residue number system (RNS) with k moduli {m1, m2, · · ·, mk} is represented by set of residues {x1, x2, · · ·, xk}, where xi = |X|mi denotes the remainder of integer division X/mi. Since RNS is a non-weighted number system; comparison, division, sign, and overflow detection have difficulties. As regarding the role of comparison in other complicated operations such as division, sign, and overflow detection, it is expected that a cost-effective and high-speed implementation of the comparison will assist in b improving other complicated operations. The dynamic range of representing numbers in an arbitrary moduli set (i.e.,[0, M )) is partitioned into two nearly equal parts to provide negative numbers. Some other works compared signed numbers d from a different perspective in which the dynamic range included both positive and negative numbers [13, 20]

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Discussion

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