Abstract: The residue number system (RNS) is popular in high performance computation applications because of its carry-free nature. The challenges of RNS systems design lie in the moduli set selection and in the reverse conversion from residue representation to weighted representation. In this paper, we proposed a fully parallel reverse conversion algorithm for the moduli set {rn - 2, rn - 1, rn}, based on simple mathematical relationships. Also an efficient hardware realization of this algorithm is presented. Our proposed converter is very faster and results to hardware savings, compared to the other reverse converters.
Abstract: In this paper, a new reverse converter for the moduli set {2n, 2n–1, 2n–1–1} is presented. We improved a previously introduced conversion algorithm for deriving an efficient hardware design for reverse converter. Hardware architecture of the proposed converter is based on carry-save adders and regular binary adders, without the requirement for modular adders. The presented design is faster than the latest introduced reverse converter for moduli set {2n, 2n–1, 2n–1–1}. Also, it has better performance than the reverse converters for the recently introduced moduli set {2n+1–1, 2n, 2n–1}