Fully Redundant Decimal Arithmetic

Hardware implementation of all the basic radix-10 arithmetic operations is evolving as a new trend in the design and implementation of general purpose digital processors. Redundant representation of partial products and remainders is common in the multiplication and division hardware algorithms, respectively. Carry-free implementation of the more frequent add/subtract operations, with the byproduct of enhancing the speed of multiplication and division, is possible with redundant number representation. However, conversion of redundant results to conventional representations entails slow carry propagation that can be avoided if the results are kept in redundant format for later use as operands of other arithmetic operations. Given that redundant decimal representations, contrary to redundant binary, do not necessarily require extra storage, we are motivated to develop a framework for fully redundant decimal arithmetic, where all operands and results belong to the same redundant decimal number system and can be stored and later used as operands of further decimal operations. In this paper, we present a new faster decimal signed digit add/sub unit and show how it can be efficiently used in the design of decimal multipliers and dividers, where all operands and results are represented with the same redundant digit set [-7, 7].