RNS-to-Binary Converters for Two Four-Moduli Sets {2n-1,2n,2n+1,2n+1-1} and {2n-1,2n,2n+1,2n+1+1}

In this paper, reverse converters for two recently proposed four-moduli sets {2@@un@ - 1,2@@un@,2@@un@ + 1,2@@un@+1 - 1} and {2@@un@ - 1, 2@@un@, 2@@un@ + 1, 2@@un@+1 + 1} are described. The reverse conversion in the three-moduli set {2@@un@ - 1,2@@un@,2@@un@ + 1} has been optimized in literature. Hence, the proposed converters are based on two new moduli sets {(2@@un@(2@@u2n@-1)),2@@un+1@-1} and {(2@@un@(2@@u2n@-1)), 2@@un+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 {2@@un@ - 1, 2@@un@, 2@@un@ + 1, 2@@un@+1 + 1} is slightly complicated due to the difficulty in performing reduction modulo (2@@un+1@+1) as compared with modulo (2@@un+1@-1). The proposed conversion techniques are compared with earlier realizations described in literature with regard to conversion time as well as area requirements.