JOURNAL OF COMPUTERS (JCP)
ISSN : 1796-203X
Volume : 3    Issue : 2    Date : February 2008

Impact of Shift Operations on (-1+j)-Base Complex Binary Numbers
Tariq Jamil
Page(s): 63-71
Full Text:
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Abstract
Complex numbers play a very important role in various applications of electrical and computer
engineering. These days, arithmetic operations dealing with these numbers rely on a “divide-and-
conquer” technique wherein a complex number is broken into its real and imaginary parts and then,
after representing each part in binary number system, operation is carried out on each part as if part
of the real arithmetic. Thus, addition of two complex numbers requires two separate additions, and
their multiplication requires four individual multiplications, one subtraction and one addition. In
an effort to reduce the number of arithmetic operations within the realm of complex arithmetic, binary
number system with base (−1+j), called complex binary number system, has been proposed in the
literature which allows a complex number to be represented as single-unit instead of two separate
units as in the base-2 binary number system. In this paper, the effects of shift operations on
complex binary numbers have been examined and mathematical equations describing their
behavior have been obtained. Analysis of these equations leads to the conclusion that the impact of
shift operations on a complex binary number is, to a large extent, similar to typical multiply-by-2 (for
per-bit shift-left) and divide-by-2 (for per-bit shift-right) operations of traditional base-2 binary number.
Index Terms
complex number, complex binary number, shift-left, shift-right.