This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
A Systematic Method for Division with High Average Bit Skipping
January 1990 (vol. 39 no. 1)
pp. 127-130

It is shown that, if a division is described by AQ=C, where A is the divisor, Q is the quotient, and C is the dividend, then the bit variables involved in a set of equations, each of which determines a leading bit of C, gives an approximation for Q that an be used in a SRT division scheme. The results of an exhaustive statistical simulation, using all possible combinations of two pairs of integers 12 b in length, in normalized form, representing A and C are presented to validate the method.

[1] R. Stefanelli, "A suggestion for a high-speed parallel binary divider,"IEEE Trans. Comput., vol. C-21, no. 1, pp. 42-55, Jan. 1972.
[2] K. Hwang,Computer Arithmetic: Principles, Architecture, and Design. New York: Wiley, 1979.
[3] O. L. MacSorley, "High-speed arithmetic in binary computers,"Proc. IRE, vol. 49, no. 1, pp. 67-91, Jan. 1961.
[4] C. V. Freiman, "Statistical analysis of certain binary division algorithms,"Proc. IRE, vol. 49, no. 1, pp. 91-103, Jan. 1961.
[5] C. S. Wallace, "A suggestion for a fast multiplier,"IEEE Trans. Comput., vol. EC-13, pp. 14-17, Feb. 1964.
[6] J. J. F. Cavanagh,Digital Computer Arithmetic Design and Implementation. New York: McGraw-Hill, 1984, pp. 117-122.
[7] N. R. Scott,Computer Number Systems&Arithmetic. Englewood Cliffs, NJ: Prentice-Hall, 1985, ch. 5.
[8] J. E. Robertson, "A new class of digital division methods,"IEEE Trans. Comput., vol. C-7, pp. 218-222, Sept. 1958.
[9] D. E. Atkins, "Higher-radix division using estimates of the divisor and partial remainders,"IEEE Trans. Comput., vol. C-17, no. 10, pp. 925-934, Oct. 1968.
[10] L. Dadda, "Some schemes for parallel multipliers,"Alta Frequenza, vol. 34, pp. 349-356, Mar. 1965.
[11] K. D. Tocher, "Techniques of multiplication and division for automatic binary computers,"Quart. J. Mech. Appl. Math., vol. XI, pt. 3, pp. 364-384, 1958.
[12] J. B. Wilson and R. S. Ledley, "An algorithm for rapid binary division,"IRE Trans. Electron. Comput., vol. EC-10, pp. 662-670, 1961.

Index Terms:
systematic method; division; high average bit skipping; approximation; statistical simulation; normalized form; digital arithmetic.
Citation:
D.M. Mandelbaum, "A Systematic Method for Division with High Average Bit Skipping," IEEE Transactions on Computers, vol. 39, no. 1, pp. 127-130, Jan. 1990, doi:10.1109/12.46287
Usage of this product signifies your acceptance of the Terms of Use.