Hierarchical residue number systems with small moduli and simple converters

Authors:
Tadeusz Tomczak
Affiliations:
Institute of Computer Engineering, Control and Robotics, Wrocław University of Technology, Janiszewskiego 11/17, 50-372 Wrocław, Poland
Venue:
International Journal of Applied Mathematics and Computer Science - Semantic Knowledge Engineering
Year:
2011

Citing 12
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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 ï戮驴 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 ï戮驴 1.