High-Speed Binary-to-Residue Converter Design Using 2-Bit Segmentation of the Input Word


Gdańsk University of Technology, 11/12 Gabriela Narutowicza Street, 80-233 Gdańsk, Poland, e-mail: robert.smyk@pg.edu.pl


The University of Applied Sciences in Elbląg, 1 Wojska Polskiego Street, 82-300 Elbląg, Poland


In this paper a new approach to the design of the high-speed binary-to-residue converter is proposed that allows the attaining of high pipelining rates by eliminating memories used in modulo m generators. The converter algorithm uses segmentation of the input binary word into 2-bit segments. The use and effects of the input word segmentation for the synthesis of converters for five-bit moduli are presented. For the number represented by each segment, the modulo m reduction using a segment modulo m generator is performed. The use of 2-bit segments substantially reduces the hardware amount of the layer of input modulo m generators. The generated residues are added using the multi-operand modulo m adder based on the carry-save adder (CSA) tree, reduction of the number represented by the output CSA tree vectors to the 2m range and fast two-operand modulo m additions. Hardware amount and time delay analyses are also included.

Binary-to-residue conversion, residue number system, FPGA
Download full text in pdf: 

This article is an open access article distributed under a Creative Commoms Attribution (CCBY 4.0) licence


Alia, G., Martinelli, E., 1990, Short Note: VLSI Binary-Residue Converters for Pipelined Processing, The Computer Journal, Vol. 33, No. 5, pp. 473–475.

Avižienis, A., 1964, A Set of Algorithms for a Diagnosable Arithmetic Unit, Jet Propulsion Laboratory, California Institute of Technology, USA.

Avižienis A., 1971, Arithmetic Codes: Cost and Effectiveness Studies for Applications in Digital System Design, IEEE Trans. Comput., Vol. C-20, pp. 1322–1331.

Cardarilli, G.C., Nannarelli, A., Re, M., 2007, Residue Number System for Low-power DSP Applications, Conference Record of the Forty-First Asilomar Conference on Signals, Systems and Computers, IEEE, pp. 1412–1416.

Czyżak, M., 2004, High-Speed Binary-to-Residue Converter with Improved Architecture, 27th International Conference on Fundamentals of Electrotechnics and Circuit Theory, Gliwice-Niedzica, pp. 431–436.

Czyżak, M., 2013, Digital Structures for High-Speed Signal Processing, Politechnika Gdańska, pp. 94–95.

Czyżak, M., Smyk R., 2008, High-Speed FPGA Pipelined Binary-to-Residue Converter, Poznan University of Technology, Academic Journals Electrical Engineering, No. 58, pp. 65–72.

Huang, K., 1979, Computer Arithmetic:  Principles, Architecture, and Design, John Wiley & Sons.

Luan, Z., Chen, X., Ge, N., Wang, Z., 2014, Simplified Fault-Tolerant FIR Filter Architecture Based on Redundant Residue Number System, Electronics Letters, Vol. 50, No. 23, pp. 1768–1770.

Miller, D.D., Altschul, R.E., King, J.R., Polky, J.N., 1986, Analysis of the Residue Class Core Function of Akushskii, Burcev, and Pak. In Residue Number System Arithmetic: Modern Applications in Digital Signal Processing, pp. 390–401.

Piestrak, S.J., 1994a, Design of High-Speed Residue-to-Binary Number System Converter Based on Chinese Remainder Theorem, Proceedings IEEE International Conference on Computer Design: VLSI in Computers and Processors, pp. 508–511.

Piestrak, S.J., 1994b, Design of Residue Generators and Multioperand Modulo Adders Using Carry-Save Adders, IEEE Trans. Comp., Vol. 43, pp. 68–77.

Premkumar, A.B., 2002, A Formal Framework for Conversion from Binary to Residue Numbers, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, Vol. 49, No. 2, pp. 135–144.

Szabo, N.S., Tanaka, R.J., 1967, Residue Arithmetic and its Applications to Computer Technology, New York, McGraw-Hill.

Robert Smyk

Citation pattern: Smyk R., Czyżak M., High-Speed Binary-to-Residue Converter Design Using 2-Bit Segmentation of the Input Word, Scientific Journal of Gdynia Maritime University, No. 124, pp. 42-56, 2022

BibTeX     EndNote