Radix 2 division with over-redundant quotient selection

Abstract

In this paper we present a new radix 2 division algorithm that uses a recurrence employing simple 3-to-2 digit carry-free adders to perform carry-free addition/subtraction for computing the partial remainders in radix 2 signed-digit form. The quotient digit, during any iteration of the division recursion, is generated from the two most-significant radix 2 digits of the partial remainder and independent of the divisor in over-redundant radix 2 digit form (i.e., with digits which belong to the digit set {-2, -1, 0, +1, +2}). The over-redundant quotient digits are then converted to the conventional radix 2 digits (belonging to the set {-1, 0, +1}) by using a reduction technique. This division algorithm is well suited for IEEE 754 standard operands belonging to the range (1, 2) and is slightly faster than previously proposed radix 2 designs (such as the radix 2 SRT), which do not employ input scaling, since the quotient selection for such algorithms is a function of more than two most-significant radix 2 digits of the partial remainder. In comparison with the designs that employ input scaling, the proposed design although slightly slower saves hardware required for scaling purposes.