An RNS Comparator via Dynamic Range Partitioning: The Case of {2^n - 1, 2^n, 2^(n+1) -1}

An RNS Comparator via Dynamic Range Partitioning: The Case of {2^n - 1, 2^n, 2^(n+1) -1}

Zeinab Torabi, Armin Belghadr

Abstract

It is common to speed-up addition, subtraction and multiplication via Residue Number Systems (RNS). The key advantage of the RNS is its limited carry propagation scheme, which is due to breaking down the long-word operations into a number of independent small-word parallel operations. Applications with repeated use of addition and multiplication have mostly benefited from RNS, while lack of efficient realizations for other operations does not allow for wider range of applications. Comparison, as a basic building block for other difficult RNS operations such as division, has been subject of numerous studies. Comparison via dynamic range partitioning has been shown to be the most successful implementation for the 3-moduli set {2^n - 1, 2^n, 2^n + 1} . In this paper, we proposed an efficient RNS comparator for the moduli set {2^n - 1, 2^n, 2^(n+1) -1} via dynamic range partitioning technique. Synthesis results reveal 27.5% delay, 64% area, 59.7% power dissipation and 71% energy consumption reduction for the proposed design against straightforwardcomparator (i.e. reverse conversion followed by binary comparator).

Keywords

Computer Arithmetic, Residue Number System, Difficult Operations, Dynamic Range Partitioning, Comparison