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The multiplicative inverse numbers are needed for converting the numbers in a residue number system (RNS) into a weighted number. In this paper, a new hardware algorithm is presented by use of a radix-two signed-digit (SD) arithmetic for the multiplicative inverse calculation modulo mi = (2p-1), where mi is a modulus in the RNS. The calculation of an multiplicative inverse number can be implemented only by carry-free SD additions. An efficient serial residue-to-weighted number converter with the number inversion circuit is also proposed. By circuit design and simulation, the proposed converter using SD arithmetic has high speed performance compared to that based on binary arithmetic.