Abstract
Most reverse conversions in Residue Number Systems (RNS) are based on the Chinese Remainder Theorem (CRT) and the Mixed Radix Conversion (MRC). The complexity of the circuitry of the CRT is high due to the large modulo-M operation. The MRC has a simple circuitry but it’s a sequential process in nature. The purpose of this research is to obtain an efficient reverse conversion method to reduce the computational overhead found in the conventional reverse conversion algorithms. In this paper, new algorithms for reverse conversion in RNS for four-moduli set and five-moduli set have been proposed and their correctness evaluated. Numerical evaluations to ascertain the correctness and simplicity of the algorithm have been presented. These algorithms have fewer multiplicative index operations than those in the conventional CRT and MRC. The large modulo-M operation has been eliminated which reduces the computational overhead.
Highlights
In recent times, digital processors based on Residue Number Systems (RNS) contribute significantly in many digital signal processing applications
The purpose of this research is to obtain an efficient reverse conversion method to reduce the computational overhead found in the conventional reverse conversion algorithms
The major problem with the Chinese remainder theorem based reverse conversion techniques is the need of a large modulo adder in the last stage
Summary
Digital processors based on RNS contribute significantly in many digital signal processing applications. The conversion process may be computational intensive in the circuitry and may introduce undue propagation delay and increase the area of the general architecture of the RNS system This can derail the importance of using RNS in digital processor applications. The major problem with the Chinese remainder theorem based reverse conversion techniques is the need of a large modulo adder in the last stage. This can derail the general performance of the RNS architecture because it increases the computational intensity of the conversion process. The new scheme seeks to increase the dynamic range in order to allow applications with huge numbers to be represented
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