A Simple Circuit for Adding Complex Numbers

The important role of complex numbers in a wide range of engineering applications demands better and more efficient methods of handling arithmetic operations involving these numbers. Using base (-1+j), instead of base 2, to represent complex numbers in binary notation allows both real and imaginary parts of the number to be combined into single binary representation and facilitates reduction in the number of arithmetic operations. Design of a size-free adder circuit based on (-1+j)-base binary representation of complex numbers is presented in this paper. as follows: an-1(-1+j) n-1 +an-2(-1+j) n-2 +...+a1(-1+j) 1 + a0(-1+j) 0 where the coefficients an-1,an-2,an- 3,…,a2,a1,a0 are binary (either 0 or 1). This is analogous to the ordinary binary number system power series of: an-1(2) n-1 +an-2(2) n-2 +…+a1(2) 1 + a0 (2) 0 except that the bases are different. Using the algorithms, given in Ref.(4), we are able to represent a given complex number with single complex binary number as shown below: 2004 + j2004 = 1110100000001110111001100000base(-1+j) This can be verified by computing the power series (-1+j) 27 + (-1+j) 26 + (-1+j) 25 + (-1+j) 23 + (-1+j) 15 + (-1+j) 14 + (-1+j) 13 + (-1+j) 11 + (-1+j) 10 + (-1+j) 9 + (-1+j) 6 + (-1+j) 5 = 2004 + j2004