RNS-to-Binary Converters for New Three-Moduli Sets {2k−3, 2k−2, 2k−1} and {2k+1, 2k+2, 2k+3}

Abstract

In this paper, mixed radix conversion (MRC)-based residue number system (RNS)-to-binary converters for two new three-moduli sets {2[Formula: see text], 2[Formula: see text], 2[Formula: see text]} and {2[Formula: see text], 2[Formula: see text], 2[Formula: see text]} which are derived from the moduli set {2[Formula: see text], 2[Formula: see text], 2[Formula: see text]} are presented. These have the advantage of having one modulus of the form 2[Formula: see text] or 2[Formula: see text] simplifying computations in one residue channel. The proposed reverse converters are evaluated and compared with state-of-the-art reverse converters proposed in literature for other three-moduli sets regarding hardware requirement and conversion time.

Design of an Efficient Reverse Converter for Moduli Sets

“…The proposed converter has shown less delay than the reported design [Phalguna et al (2018)] and consumes less area Teghipour et al (2015). Delay and area for the new moduli sets have been calculated…”

“…The development of a large modular expansion tree is required. Apart from the architecture that was presented in [Phalguna et al (2018)], the CRT approach can be used to design the converters for special moduli sets. After all, the inner products of the Chinese Remainder Theorem (CRT) are large moduli.…”

Performance Analysis of Hardware Implementations of Reverse Conversion from the Residue Number System

“…The architecture of computing systems operating in RNS generally consists of forward conversion of positional numbers into RNS [3], computation of the main problem using modular addition [4], multiplication [5], number comparison and sign determination [6] operations, reconversion from RNS to positional number system [7][8][9][10][11][12][13][14]. Furthermore, if addition, subtraction, multiplication in RNS have a parallel structure with numbers of small dimensions, then the operations of sign determination, comparison, conversion from RNS to the positional number system require the calculation of the positional characteristic of the number, which is computationally complex.…”