Towards implementation of a binary number system for complex numbers

These days computer operations involving complex numbers are most commonly performed by dealing with the real and imaginary parts separately and then accumulating their individual results to get the final result of the operation. This divide-and-conquer 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 various available complex bases 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.