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Abstract
For years complex numbers have been treated as distant relatives of real numbers despite their widespread applications in the fields of electrical and computer engineering. These days computer operations involving complex numbers are most commonly performed by applying divide-and-conquer technique whereby each complex number is separated into its real and imaginary parts, operations are carried out on each group of real and imaginary components, and then the final result of the operation is obtained by accumulating the individual results of the real and imaginary components. This technique forsakes the advantages of using complex numbers in computer arithmetic and there exists a need, at least for some problems, to treat a complex number as one unit and to carry out all operations in this form. In this paper, we have analyzed and proposed a (–1–j)-base binary number system for complex numbers. We have discussed the arithmetic operations of two such binary numbers and outlined work which is currently underway in this area of computer arithmetic.
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References
- BLEST, D. and JAMIL, T. Efficient division in a binary representation for complex numbers. Proceedings of the IEEE Southeastcon 2001. Clemson, South Carolina. 30 March-1 April 2001. USA.
- GEPPERT, L. 1999. The 100-million Transistor IC. IEEE Spectrum. 36: 7: 23-60.
- JAMIL, T., HOLMES, N., and BLEST, D. 2000. Towards implementation of a binary number system for complex numbers. Proceedings of the IEEE SoutheastCon 2000. Nashville, Tennessee. 7-9 April 2000. USA
- KNUTH, D.E. 1960. An Imaginary Number System. Communications of the ACM. 3: 245-247.
- PENNEY, W. 1964. A Numeral System with a Negative Base. Mathematics Student Journal. 11(4): 1-2.
- PENNEY, W. 1965. A Binary System for Complex Numbers. Journal of the ACM. 12(2): 247-248.
- STEPANENKO, V.N. 1996. Computer Arithmetic of Complex Numbers. Cybernetics and System Analysis. 32(4): 585-591.
References
BLEST, D. and JAMIL, T. Efficient division in a binary representation for complex numbers. Proceedings of the IEEE Southeastcon 2001. Clemson, South Carolina. 30 March-1 April 2001. USA.
GEPPERT, L. 1999. The 100-million Transistor IC. IEEE Spectrum. 36: 7: 23-60.
JAMIL, T., HOLMES, N., and BLEST, D. 2000. Towards implementation of a binary number system for complex numbers. Proceedings of the IEEE SoutheastCon 2000. Nashville, Tennessee. 7-9 April 2000. USA
KNUTH, D.E. 1960. An Imaginary Number System. Communications of the ACM. 3: 245-247.
PENNEY, W. 1964. A Numeral System with a Negative Base. Mathematics Student Journal. 11(4): 1-2.
PENNEY, W. 1965. A Binary System for Complex Numbers. Journal of the ACM. 12(2): 247-248.
STEPANENKO, V.N. 1996. Computer Arithmetic of Complex Numbers. Cybernetics and System Analysis. 32(4): 585-591.