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A Novel Division Algorithm for the Residue Number System
August 1992 (vol. 41 no. 8)
pp. 1026-1032

A novel general algorithm for signed number division in the residue number system (RNS) is presented. The parity checking technique used for sign and overflow detection in this algorithm is more efficient and practical than conventional methods. Sign magnitude arithmetic division is implemented using binary search. There is no restriction to the dividend and the divisor (except zero divisor), and no quotient estimation is necessary before the division is executed. Only simple operations are needed to accomplish this RBS division. All these characteristics have made the algorithm simple, efficient, and practical for implementation on a real RNS divider.

[1] W. K. Jenkins and B. J. Leon, "The use of residue number systems in the design of finite impulse response digital filters,"IEEE Trans. Circuits Syst., vol. CAS-24, pp. 191-201, Apr. 1977.
[2] F. J. Taylor, "A VLSI residue arithmetic multiplier,"IEEE Trans. Comput., vol. C-31, pp. 540-546, June 1982.
[3] N. S. Szabo and R. I. Tanaka,Residue Arithmetic and Its Application to Computer Technology. New York: McGraw-Hill, 1967.
[4] W. A. Chren, Jr., "A new residue number system division algorithm,"Comput. Math. Appl., vol. 19, no. 7, pp. 13-29, 1990.
[5] M. J. Flynn and S. Waser,Introduction to Arithmetic for Digital Systems Designers. CBS College Publishing, 1982, pp. 215-222.
[6] D. K. Banerji, T. Y. Cheung, and V. Ganesan, "A high-speed division method in residue arithmetic, " inProc. 5th IEEE Symp. Comput. Arithmetic, 1981, pp. 158-164.
[7] E. Kinoshita, H. Kosako, and Y. Kojima, "General division in the symmetric residue number system,"IEEE Trans. Comput., vol. C-22, pp. 134-142, Feb. 1973.
[8] Y. A. Keir, P. W. Cheney, and M. Tannenbaum, "Division and overflow detection in residue number systems,"IRE Trans. Electron. Comput., vol. EC-11, pp. 501-507, Aug. 1962.
[9] M.-L. Lin, E. Leiss, and B. McInnis, "Division and sign detection algorithm for residue number systems,"Comput. Math. Appl., vol. 10, no. 4/5, pp. 331-342, 1984.
[10] D. D. Miller, J. N. Polky, and J. R. King, "A survey of Soviet developments in residue number theory applied to digital filtering," inProc. 26th Midwest Symp. Circuits Syst., Aug. 1983.
[11] T. V. Vu, "Efficient implementations of the Chinese remainder theorem for sign detection and residue decoding,"IEEE Trans. Comput., vol. C-34, no. 7, pp. 646-651, July 1985.
[12] D. E. Atkins and S.-C. Ong, "Time-component complexity of two approaches to multioperand binary addition,"IEEE Trans. Comput., vol. C-28, pp. 918-926, Dec. 1979.

Index Terms:
sign detection; sign magnitude arithmetic division; division algorithm; residue number system; signed number division; parity checking; overflow detection; binary search; algorithm theory; digital arithmetic; dividing circuits; number theory; search problems.
M. Lu, J.-S. Chiang, "A Novel Division Algorithm for the Residue Number System," IEEE Transactions on Computers, vol. 41, no. 8, pp. 1026-1032, Aug. 1992, doi:10.1109/12.156545
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