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Addition in signed digit number systems

Published: 01 January 1978 Publication History

Abstract

The paper studies a general class of signed number representation systems. Among the members of that class, it selects the number representation systems that allow one to build multisummand ripple carry-like adders enjoying simultanesouly the properties of saturation, expandability and symmetry.

References

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Lehman M., Highspeed multiplication. IRE.TEC. EC-6, pp. 204-205, 1957
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Booth A. D., A signed binary multiplication technique. Quart. J. Mech. and appl. math., 4, part 2, p.236, 1951.
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Davio M. and Bioul G., Fast parallel multiplication. Philips Res. Repts, 32, pp. 43-70, 1977.
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Avizienis A., Signed digit number representation for fast parallel arithemtic. IRE TEC, EC-10, 3, pp. 389-399, 1951.
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Flores I., The Logic of Computer Arithmetic. Prentice Hall. Englewood Cliffs, N.J., 1963.
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Szabo N. S. & Tanaka R. I., Residue arithmetic and its application to computer technology, Mc Graw Hill, N.Y., 1967.
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Banerji D. K., Residue arithmetic in computer design. Ph.D. Thesis. Univ. of Waterloo, Ontario, 1971.
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Knuth D. E., The art of computer programming. vol.2, Seminumerical Algorithms. Addison Wesley. Reading Mass. 1969.
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Loomis H. H., Data representation . In "Introduction to computer architecture" (H. Stone Ed.) S. R.A. Chicago 1975.
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Shannon C. E., A symmetrical notation of number. Amer. Math. Month., 57, p.90, 1950.
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Wadel L. B., Negative base number systems. IEEE TEC, EC-6, p.123, June 1957.
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Agrawal D. P., Some aspects of fast arithmetic computing circuits. Ph.D. Thesis, nr. 206, Dept. of Electrical Engineering, E.P.F. Lausanne, 1975.
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Knuth D. E., An imaginary number system. Comm. ACM, 3, pp. 245-247, 1960.
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Lannlng W. C., General algorithms for direct radix conversion. Computer Design, pp. 61-73, June 1975.
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De Regt M. P., Negative radix arithmetic Computer Design, May-Dec. 1967, Jan. 1968.
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Zohar S., Negative radix conversion IEEE TC, C-19, March 1970.
[17]
Lanning W. C., Negative radix transformation algorithms, Information and Control, 34, pp. 271-285, 1977.
[18]
Davio M., Deschamps J.P., Addition in signed digit number systems, MBLE Research Lab., Rept. R361, Nov. 1977.
[19]
Davio M., Deschamps J.P., Thayse A., Discrete and Switching functions. McGraw Hill, To appear, spring 1978.

Cited By

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  • (1981)On Classes of Positive, Negative, and Imaginary Radix Number SystemsIEEE Transactions on Computers10.1109/TC.1981.167578830:5(312-317)Online publication date: 1-May-1981
  • (1980)Complex Number Arithmetic with Odd- Valued LogicIEEE Transactions on Computers10.1109/TC.1980.167563129:7(604-611)Online publication date: 1-Jul-1980

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Published In

cover image ACM Conferences
MVL '78: Proceedings of the eighth international symposium on Multiple-valued logic
January 1978
298 pages

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IEEE Computer Society Press

Washington, DC, United States

Publication History

Published: 01 January 1978

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Cited By

View all
  • (1981)On Classes of Positive, Negative, and Imaginary Radix Number SystemsIEEE Transactions on Computers10.1109/TC.1981.167578830:5(312-317)Online publication date: 1-May-1981
  • (1980)Complex Number Arithmetic with Odd- Valued LogicIEEE Transactions on Computers10.1109/TC.1980.167563129:7(604-611)Online publication date: 1-Jul-1980

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