Radix 2 division with over-redundant quotient selection

Hosahalli R. Srinivas, Keshab K. Parhi, Luis A. Montalvo

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12 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)85-92
Number of pages8
JournalIEEE Transactions on Computers
Issue number1
StatePublished - 1997


  • Division
  • Division without prescaling
  • Over-redundant representation
  • Radix 2 redundant arithmetic
  • Signed digit arithmetic
  • Two-digit quotient selection


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