The New proposed Non Coprime moduli set using forward conversion in Residue Number System Mathematical Proof

In this paper a mathematical proof of the new Binary-to-RNS Non-Coprime moduli set in RNS [1] of the form { 2 n -2, 2 n , 2 n + 2 } is presented. The modulies 2 n -2, 2 n + 2 are known to be called conjugates of each other and has been discussed in previous literature [1 -4]. Co-prime moduli sets are known to offer these benefits: 1) Large dynamic ranges. II) Fast RNS arithmetic. III) Simple and efficient RNS processing hardware. IV) Efficient weighted-to-RNS and RNS-to-Weighted converters. When comparing the Non-Coprime ones to them the DR (Dynamic Range) is the dominant. The dynamic range achieved by the set above is defined by the least common multiple ( LCM ) of the moduli and the non-coprime set was carefully chosen to do the mathematical calculations upon. This new non-coprime moduli set is unique and the only one of its shape. .