A Radix-10 Digit-Recurrence Division Unit: Algorithm and Architecture (original) (raw)
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IEEE Transactions on Computers, 1997
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 mostsignificant 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.
Very-high radix division with prescaling and selection by rounding
IEEE Transactions on Computers, 1994
A division algorithm in which the quotient-digit selection is performed by rounding the shifted residual in carrysave form is presented. To allow the use of this simple function, the divisor (and dividend) is prescaled to a range close to one. The implementation presented results in a fast iteration because of the use of carry-save forms and suitable recodings. The execution time is calculated and several convenient values of the radix are selected. Comparison with other dividers for radices 2' to 2" is performed using the same assumptions. I k T e m-Computer arithmetic, high radix division, presesling, selection by rounding, redundant representation. All operations (except the scaling of the divisor) are performed using a carry-save representation, thus avoiding time-consuming assimilations. A. Related Work We mention division algorithms that are characterized by features similar to our approach. Svoboda [17] developed a radix-10 division scheme with scaling of divisor (and div