### 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.

Original language | English (US) |
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Pages (from-to) | 85-92 |

Number of pages | 8 |

Journal | IEEE Transactions on Computers |

Volume | 46 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1 1997 |

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### Keywords

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

### Cite this

*IEEE Transactions on Computers*,

*46*(1), 85-92. https://doi.org/10.1109/12.559806