A higher-radix division with simple selection of quotient digits

Abstract

A higher-radix division algorithm with simple selection of quotient digits is described. The proposed scheme is a combination of the multiplicative normalization used in the continued-product algorithms and the recursive division algorithm. The scheme consists of two parts: in the first part, the divisor and the dividend are transformed into the range which allows the quotient digits to be selected by rounding partial remainders to the most significant radix-r digit in the second part. Since the selection requires only the most significant part of the partial remainder, limited carry-propagation adders can be used to form the partial remainders. The divisor and dividend transformations are performed in three steps using multipliers of the form 1 + s k r−k as in the continued product algorithm. The higher radix of the form r = 2k, k=2,4,8,…, can be used to reduce the number of steps while retaining the simple quotient selection rules.