### 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) |
---|---|

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

**Radix 2 division with over-redundant quotient selection.** / Srinivas, Hosahalli R.; Parhi, Keshab K; Montalvo, Luis A.

Research output: Contribution to journal › Article

*IEEE Transactions on Computers*, vol. 46, no. 1, pp. 85-92. https://doi.org/10.1109/12.559806

}

TY - JOUR

T1 - Radix 2 division with over-redundant quotient selection

AU - Srinivas, Hosahalli R.

AU - Parhi, Keshab K

AU - Montalvo, Luis A.

PY - 1997/12/1

Y1 - 1997/12/1

N2 - 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.

AB - 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.

KW - Division

KW - Division without prescaling

KW - Over-redundant representation

KW - Radix 2 redundant arithmetic

KW - Signed digit arithmetic

KW - Two-digit quotient selection

UR - http://www.scopus.com/inward/record.url?scp=0031348556&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031348556&partnerID=8YFLogxK

U2 - 10.1109/12.559806

DO - 10.1109/12.559806

M3 - Article

AN - SCOPUS:0031348556

VL - 46

SP - 85

EP - 92

JO - IEEE Transactions on Computers

JF - IEEE Transactions on Computers

SN - 0018-9340

IS - 1

ER -