Improved memoryless RNS forward converter based on the periodicity of residues

• Published in: IEEE transactions on circuits and systems. II, Express briefs Vol. 53; no. 2; pp. 133 - 137
• Main Authors: Premkumar, A.B., Ang, E.L., Lai, E.M.-K.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.02.2006; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adders; Architecture; Arithmetic; Circuits; Conversion; Converters; Digital signal processing; Dynamic range; Forward and reverse converters; Hardware; Logic design; Memory architecture; periodicity property; processing elements; Registers; residue number system (RNS); Residues; Serials; Tables; Transformations
• ISSN: 1549-7747; 1558-3791
• DOI: 10.1109/TCSII.2005.857090

The residue number system (RNS) is suitable for DSP architectures because of its ability to perform fast carry-free arithmetic. However, this advantage is over-shadowed by the complexity involved in the conversion of numbers between binary and RNS representations. Although the reverse conversion (RNS to binary) is more complex, the forward transformation is not simple either. Most forward converters make use of look-up tables (memory). Recently, a memoryless forward converter architecture for arbitrary moduli sets was proposed by Premkumar in 2002. In this paper, we present an extension to that architecture which results in 44% less hardware for parallel conversion and achieves 43% improvement in speed for serial conversions. It makes use of the periodicity properties of residues obtained using modular exponentiation.