Design of RNS Converters for moduli sets with Dynamic Ranges up to 6n-bit

Abstract

The RNS has been considered as an interesting area for researchers in recent year. This paper presents memoryless and area efficient RNS converters for moduli set with dynamic ranges up to 6n-bit. Residue number system (RNS) has mainly targeted parallelism and larger dynamic ranges. In this paper, we start from the moduli sets {2, 2 1, 2 + 1, 2 – 2 + 1, 2 + 2 + 1} with dynamic range of 5n-bit and propose vertical extension in order to improve the parallelism and increase the dynamic range. The vertical extension increase the value of the power of 2 modulus in the five-moduli set. The Chinese remainder theorem is applied in this paper to derive an efficient reverse converter. This paper also proposed a conventional binary to RNS representation called RNS Forward conversion. The RNS forward converter is more efficient in terms of area, delay and power. Synthesis results suggest that the proposed vertical extension in RNS reverse converter allow reducing the area-delay product in comparison with the related state-of-the-art. KeywordsChinese Remainder theorem, Forward converter, Residue Number system, Reverse converter