A novel Reverse Converter design for new Five moduli set RNS

Residue Number System (RNS) is widely used in various applications such as design of cryptoprocessor, digital filters etc. For better performance of these RNS systems conversion module should be fast enough. This paper presents a new reverse converter architecture for a novel five moduli set Residue Number System (RNS) {2ⁿ - 1, 2ⁿ, 2ⁿ + 1, 2^{n + 1} - 1, 2^{n - 1} - 1} for even values of n. It exploits the special properties of the numbers of the form 2ⁿ ± 1, and extends the dynamic range of the present triple moduli {2ⁿ - 1, 2ⁿ, 2ⁿ + 1} based systems. The proposed moduli set has a dynamic range that can represent upto 5n - 1 bit numbers while keeping the moduli small enough and the converter efficient considering computation required. In our new Five moduli set Reverse Converter design we use both the Chinese Remainder Theorem (CRT) and Mixed Radix Conversion (MRC) techniques.