RNS-to-Binary Converters for Two Four-Moduli Sets $\{2^{n}-1,2^{n},2^{n}+1,2^{{n}+1}-1\}$ and $\{2^{n}-1,2^{n},2^{n}+1,2^{{n}+1}+1\}$
P. V. Ananda Mohan, A. Benjamin Premkumar · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · 2007
In this paper, reverse converters for two recently proposed four-moduli sets {2n- 1,2n,2n+ 1,2n+1 - 1} and {2n- 1, 2n, 2n+ 1, 2n+1 + 1} are described. The reverse conversion in the three-moduli set {2n- 1,2n,2n+ 1} has been optimized in literature. Hence, the proposed converters are based on two new moduli sets {(2n(22n-1)),2n+1-1} and {(2n(22n-1)), 2n+1+1} and use mixed radix conversion. The resulting designs do not require any ROM. Both are similar in their architecture except that the converter for the moduli set {2n- 1, 2n, 2n+ 1, 2n+1 + 1} is slightly complicated due to the difficulty in performing reduction modulo (2n+1+1) as compared with modulo (2n+1-1). The proposed conversion techniques are compared with earlier realizations described in literature with regard to conversion time as well as area requirements.