### Abstract

In digit on-line arithmetic, operands are introduced a digit at a time. After the first few operand digits have been introduced, the result begins to appear a digit at a time. This feature of digit on-line arithmetic allows a significant amount of overlapping of arithmetic operations. Digit on-line arithmetic can sometimes produce unnormalized results. This can present a problem for the divide and square root algorithms. If the divisor and radicand are highly unnormalized, these algorithms will not produce the correct results. Two advances in overcoming this problem are presented. First, several techniques for producing results that are closer to being normalized are developed. Second, it is shown that normalized results are not necessary for divide and square root to work properly. Combining these results yields algorithms that will always give the correct results.

Original language | English (US) |
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Title of host publication | Proceedings - 7th Symposium on Computer Arithmetic, ARITH 1985 |

Editors | Kai Hwang |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 20-27 |

Number of pages | 8 |

ISBN (Electronic) | 0818606320 |

DOIs | |

State | Published - Jan 1 1985 |

Event | 7th IEEE Symposium on Computer Arithmetic, ARITH 1985 - Urbana, United States Duration: Jun 4 1985 → Jun 6 1985 |

### Publication series

Name | Proceedings - Symposium on Computer Arithmetic |
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### Conference

Conference | 7th IEEE Symposium on Computer Arithmetic, ARITH 1985 |
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Country | United States |

City | Urbana |

Period | 6/4/85 → 6/6/85 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Software
- Theoretical Computer Science
- Hardware and Architecture

### Cite this

*Proceedings - 7th Symposium on Computer Arithmetic, ARITH 1985*(pp. 20-27). [6158979] (Proceedings - Symposium on Computer Arithmetic). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ARITH.1985.6158979

}

*Proceedings - 7th Symposium on Computer Arithmetic, ARITH 1985.*, 6158979, Proceedings - Symposium on Computer Arithmetic, Institute of Electrical and Electronics Engineers Inc., pp. 20-27, 7th IEEE Symposium on Computer Arithmetic, ARITH 1985, Urbana, United States, 6/4/85. https://doi.org/10.1109/ARITH.1985.6158979

**Improved normalization results for digit on-line arithmetic.** / Zaccone, Richard J.; Barlow, Jesse Louis.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Improved normalization results for digit on-line arithmetic

AU - Zaccone, Richard J.

AU - Barlow, Jesse Louis

PY - 1985/1/1

Y1 - 1985/1/1

N2 - In digit on-line arithmetic, operands are introduced a digit at a time. After the first few operand digits have been introduced, the result begins to appear a digit at a time. This feature of digit on-line arithmetic allows a significant amount of overlapping of arithmetic operations. Digit on-line arithmetic can sometimes produce unnormalized results. This can present a problem for the divide and square root algorithms. If the divisor and radicand are highly unnormalized, these algorithms will not produce the correct results. Two advances in overcoming this problem are presented. First, several techniques for producing results that are closer to being normalized are developed. Second, it is shown that normalized results are not necessary for divide and square root to work properly. Combining these results yields algorithms that will always give the correct results.

AB - In digit on-line arithmetic, operands are introduced a digit at a time. After the first few operand digits have been introduced, the result begins to appear a digit at a time. This feature of digit on-line arithmetic allows a significant amount of overlapping of arithmetic operations. Digit on-line arithmetic can sometimes produce unnormalized results. This can present a problem for the divide and square root algorithms. If the divisor and radicand are highly unnormalized, these algorithms will not produce the correct results. Two advances in overcoming this problem are presented. First, several techniques for producing results that are closer to being normalized are developed. Second, it is shown that normalized results are not necessary for divide and square root to work properly. Combining these results yields algorithms that will always give the correct results.

UR - http://www.scopus.com/inward/record.url?scp=85032072761&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85032072761&partnerID=8YFLogxK

U2 - 10.1109/ARITH.1985.6158979

DO - 10.1109/ARITH.1985.6158979

M3 - Conference contribution

AN - SCOPUS:85032072761

T3 - Proceedings - Symposium on Computer Arithmetic

SP - 20

EP - 27

BT - Proceedings - 7th Symposium on Computer Arithmetic, ARITH 1985

A2 - Hwang, Kai

PB - Institute of Electrical and Electronics Engineers Inc.

ER -