A New Moduli Set for Residue Number System: {rn 2,rn 1,rn}

In this paper a new moduli set {r
ⁿ
-2,r
ⁿ
-1,r
ⁿ
} is introduced where r = 2k + 1 and k= 1,2,3,... . This moduli set includes pair wise relatively prime moduli, so it offers the maximum possible dynamic range. For this moduli set, the related circuits are simply realized in the Multiple Valued Logic (MVL) and arithmetic in this moduli set enjoys very high speed operations and simple reverse/forward conversion (RNS to MVL/MVL to RNS). After introducing the new moduli set, we design its related circuits and converters. Finally, we compare the results to those of similar moduli sets and show that our moduli set significantly improves the time complexity while offers greater dynamic range.