<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml">In this paper, a new class of Hierarchical Residue Number Systems (HRNSs) is proposed, where the numbers are represented as a set of residues modulo factors of 2<italic>k</italic> ± 1 and modulo 2<italic>k</italic>. The converters between the proposed HRNS and the positional binary number system can be built as 2-level structures using efficient circuits designed for the RNS (2<italic>k</italic> - 1, 2<italic>k</italic>, 2<italic>k</italic> + 1). This approach allows using many small moduli in arithmetic channels without large conversion overhead. The advantages resulting from the use of the proposed HRNS depend on the possibility of factorisation of moduli 2<italic>k</italic> ± 1.</abstract>

In this paper, a new class of Hierarchical Residue Number Systems (HRNSs) is proposed, where the numbers are represented as a set of residues modulo factors of 2k ± 1 and modulo 2k. The converters between the proposed HRNS and the positional binary number system can be built as 2-level structures using efficient circuits designed for the RNS (2k - 1, 2k, 2k + 1). This approach allows using many small moduli in arithmetic channels without large conversion overhead. The advantages resulting from the use of the proposed HRNS depend on the possibility of factorisation of moduli 2k ± 1.

Hierarchical residue number systems with small moduli and simple converters

Institute of Computer Engineering, Control and Robotics, Wrocław University of Technology, Janiszewskiego 11/17, 50-372 Wrocław, Poland

International Journal of Applied Mathematics and Computer Science

{"article-title":"Hierarchical residue number systems with small moduli and simple converters"}

In this paper, a new class of Hierarchical Residue Number Systems (HRNSs) is proposed, where the numbers are represented as a set of residues modulo factors of...

Hierarchical residue number systems with small moduli and simple converters

Published Online: Mar 28, 2011

Page range: 173 - 192

DOI: https://doi.org/10.2478/v10006-011-0013-2

Keywords
digital arithmetic, digital circuits, residue number system, VLSI

This content is open access.

Hierarchical residue number systems with small moduli and simple converters

Published Online: Mar 28, 2011

Page range: 173 - 192

DOI: https://doi.org/10.2478/v10006-011-0013-2

Keywordsdigital arithmetic, digital circuits, residue number system, VLSI

This content is open access.

Keywords
digital arithmetic, digital circuits, residue number system, VLSI