Issue No. 01 - January (1997 vol. 46)

ISSN: 0018-9340

pp: 85-92

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/12.559806

ABSTRACT

<p><b>Abstract</b>—In this paper we present a new radix 2 division algorithm that uses a recurrence employing simple <it>3-to-2</it> 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 <it>reduction</it> 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.</p>

INDEX TERMS

Division, radix 2 redundant arithmetic, signed digit arithmetic, over-redundant representation, division without prescaling, two-digit quotient selection.

CITATION

Luis A. Montalvo, Hosahalli R. Srinivas, Keshab K. Parhi, "Radix 2 Division with Over-Redundant Quotient Selection",

*IEEE Transactions on Computers*, vol. 46, no. , pp. 85-92, January 1997, doi:10.1109/12.559806