### Abstract

The authors propose an extension to the popular {2

^{n}-1, 2^{n}, 2^{n}+1} moduli set by adding a fourth modulus 2^{n+1}+1. This extension leads to higher parallelism while keeping the forward conversion and modular arithmetic units simple. The main challenge of efficient reverse conversion is met by three techniques described for the first time. Firstly, we reverse convert linear combinations of moduli hence reducing the number of non-zero bits in the Booth encoded multiplicands from n to merely 2. Secondly, it is shown that division by 3, if introduced at the right stage, can be implemented very efficiently and can, in turn, reduce the cost of the converter. To implement VLSI efficient modulo reduction, we propose two techniques-multiple split tables (MST) and a modified division algorithm (MDA). It is shown that the MST can reduce exponential ROM requirements to quadratic ROM requirements while the MDA can reduce these further to linear requirements. As a result of these innovations, the proposed reverse converter uses simple shift and add operations and needs a lookup with only 6 entries. The delay of the converter is approximately 10n+13 full adder delays and the area cost is quadratic in nOriginal language | English |
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Pages | 168-175 |

Number of pages | 8 |

Publication status | Published - Apr 1999 |

Event | 14th IEEE Symposium on Computer Arithmetic - Adelaide, Australia Duration: 14 Apr 1999 → 16 Apr 1999 |

### Conference

Conference | 14th IEEE Symposium on Computer Arithmetic |
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Country | Australia |

City | Adelaide |

Period | 14/04/99 → 16/04/99 |

## Fingerprint Dive into the research topics of 'A reverse converter for the 4-moduli superset {2<sup>n</sup>-1, 2 <sup>n</sup>, 2<sup>n</sup>+1, 2<sup>n+1</sup>+1}'. Together they form a unique fingerprint.

## Cite this

Bhardwaj, M., Srikanthan, T., & Clarke, C. T. (1999).

*A reverse converter for the 4-moduli superset {2*. 168-175. Paper presented at 14th IEEE Symposium on Computer Arithmetic, Adelaide, Australia.^{n}-1, 2^{n}, 2^{n}+1, 2^{n+1}+1}