International Journal of applied mathematics and computer science

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Paper details

Number 1 - March 2011
Volume 21 - 2011

Hierarchical residue number systems with small moduli and simple converters

Tadeusz Tomczak

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.

digital arithmetic, digital circuits, residue number system, VLSI