A High Dynamic Range 3-Moduli-Set with Efficient Reverse Converter

TL;DR

This paper introduces a new high dynamic range 3-moduli residue number system and its efficient binary converter, demonstrating improved performance and area efficiency over existing converters for various bit ranges.

Contribution

Proposes a novel 3-moduli set and its residue to binary converter with simple hardware, outperforming existing converters in speed and area for high dynamic ranges.

Findings

Faster conversion for 8-bit, 16-bit, 32-bit, 64-bit ranges.

Better performance and area utilization compared to existing reverse converters.

Hardware implementation mainly uses CSA and Modular Adder.

Abstract

-Residue Number System (RNS) is a valuable tool for fast and parallel arithmetic. It has a wide application in digital signal processing, fault tolerant systems, etc. In this work, we introduce the 3-moduli set {2^n, 2^{2n}-1, 2^{2n}+1} and propose its residue to binary converter using the Chinese Remainder Theorem. We present its simple hardware implementation that mainly includes one Carry Save Adder (CSA) and a Modular Adder (MA). We compare the performance and area utilization of our reverse converter to the reverse converters of the moduli sets {2^n-1, 2^n, 2^n+1, 2^{2n}+1} and {2^n-1, 2^n, 2^n+1, 2^n-2^{(n+1)/2}+1, 2^n+2^{(n+1)/2}+1} that have the same dynamic range and we demonstrate that our architecture is better in terms of performance and area utilization. Also, we show that our reverse converter is faster than the reverse converter of {2^n-1, 2^n, 2^n+1} for dynamic ranges like 8-bit, 16-bit, 32-bit and 64-bit however it requires more area.