A new efficient memoryless residue to binary converter

Abstract

An algorithm is described which converts the moduli (2/sup k/+1, 2/sup k/, 2/sup k/-1) residue numbers into their binary equivalent. A hardware implementation for this algorithm was constructed using binary adders only. The proposed algorithm and its implementation have the following advantages: (1) it enables an extremely wide fixed-point dynamic range, since its upper bound is not limited by a memory size; (2) it requires only four binary adders, two of which are operating in parallel; consequently, its conversion speed is higher than any similar reported converter, and its integrated circuit implementation would occupy less area; and (3) novel compact forms of the multiplicative inverses for the above moduli set are introduced.