Recoding algorithms for minimal signed-digit numbers in residue number system

In this paper, new algorithms for obtaining minimal radix-two signed-digit (SD) representations in a residue number system (RNS) are proposed. At first, we present a recoding algorithm to convert an arbitrary p-digit SD number representation to the (p+1)-digit minimal SD representation, in which there are a fewest number of nonzero digits. The recoding method can be used for the number conversion from a p-digit SD number to a minimal p-digit SD number representation in an RNS. Then we propose the recoding algorithms for some kinds of moduli. By giving randomly SD numbers with 64 and 128 digits, the nonzero digits are reduced in a deletion rate of 33%. We also implement the efficient converters for special moduli based on the proposed algorithms.