Abstract: For designing high speed digital systems, it considered so many factors, among those the Number System, what it uses plays a crucial role. The Residue number system provides the inherent properties such as Carry-free operations, Parallelism and Fault Tolerance. While designing RNS, the selection of choice of moduli set plays a key role. The 3n-bit dynamic range RNS moduli set {2n-1,2n, 2n+1} is the most famous RNS moduli set because of its simple and well formed balanced moduli. However, the arithmetic operations with respect to the modulus 2n+1 are complex and dynamic range is not sufficient for applications that require larger dynamic range. The 4n-bit dynamic range four moduli set minimize the dynamic range, asymmetric moduli channel length and long conversion delay. In this paper review on, a special five moduli set (2n-1, 2n, 2n+1, 2n+1-1, 2n-1-1) for even n . It exploits the special properties of the numbers of the form 2n 1, and extends the dynamic range of present triple moduli {2n-1, 2n ,2n+1} based systems. It has dynamic range that can represent up to 5n-1 bits while keeping the moduli small enough and converter efficient. In this review paper reverse converter design is done with the Chinese Remainder Theorem (CRT) and the results are compared with the Mixed Radix Conversion theorem and also with three and four moduli sets.

Keywords: Residue Number System (RNS), Chinese Remainder Theorem (CRT), Dynamic Range (DR), Mixed Radix Conversion.