RADIX-16 SIGNED-DIGIT DIVISION

For use in the context of a linearly scalable arithmetic architecture supporting high/variable precision arithmetic operations (integer or fractional), a two-stage algorithm for fixed point, radix-16 signed-digit division is presented. The algorithm uses two limited precision radix-4 quotient digit selection stages to produce the full radix-16 quotient digit. The algorithm requires a two-digit estimate of the (initial) partial remainder and a three-digit estimate of the divisor to correctly select each successive quotient digit. The normalization of redundant signed-digit numbers requires accommodation of some fuzziness at one end of the range of numeric values that are considered normalized. A set of general equations for determining the ranges of normalized signed-digit numbers is derived. Another set of general equations for determining the precisions of estimates of the divisor and dividend required in a limited precision SRT model signed-digit division are derived. These two sets of equations permit design tradeoff analyses to be made with respect to the complexity of the model division. The specific case of a two-stage radix-16 signed-digit division is presented. The staged division algorithm used can be extended to other radices as long as the signed-digit number representation used has certain properties. © 1990 IEEE