Journal Article


Séamas McGettrick
Chris J. Bleakley
Anne O'Donnell



fermat numbers error correction mixed radix conversion choice residue number systems arithmetic delay error detection

Area-Delay Efficient Arithmetic Mixed-Radix Conversion for Fermat Moduli (2011)

Abstract Mixed Radix Conversion is an essential feature of error detection and correction in Redundant Residue Number Systems. Fermat numbers are a popular choice as moduli in these systems. However, Fermat numbers are typically implemented using Diminished–1 arithmetic which necessitates special consideration of zero in arithmetic operations. Furthermore, the sequential nature of Mixed Radix Conversion leaves it prone to considerable delay due to carry propagation in adders at each stage. In this paper, Diminished-1 arithmetic in carry save form is used to give significant reductions in area and delay compared to previously proposed hardware architectures. The percentage area reduction was found to range from 13% to 41% and that of delay from 19% to 49% for bit widths from 8 to 28 bits.
Collections Ireland -> University College Dublin -> School of Computer Science
Ireland -> University College Dublin -> Computer Science Research Collection

Full list of authors on original publication

Séamas McGettrick, Chris J. Bleakley, Anne O'Donnell

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Chris Bleakley
University College Dublin
Total Publications: 105