Complex Binary Number System

At the IEEE SoutheastCon 2000 held at Nashville, Tennessee, a research paper entitled "Towards implementation of a binary number system for complex numbers" presented at the conference had started my journey in pursuit of equal opportunity representation for complex numbers in the realm of computing. Given that these numbers play an important role in engineering applications such as digital signal processing and image processing, one would assume that they are treated with much respect in computer science and engineering but, alas, it was found that, instead of treating them as a dignified pair of real and imaginary components, a villainous "divide-and-conquer" technique is used in computer arithmetic to deal with these numbers. In this treatment of complex numbers, a complex number is broken-up into its real and imaginary parts and then operations are carried out on each part as if it was a part of the real arithmetic. At the end, the overall result of the complex operation is obtained by the accumulation of the individual results. In other words, addition of two complex numbers requires two separate additions (one for the real parts and one for the imaginary parts) while multiplication of the same two complex numbers requires four individual multiplications, one subtraction, and one overall addition. This can be effectively reduced to just one complex addition or only one multiplication and addition respectively for the given cases if each complex number is represented as single unit instead of two sub-units of real and imaginary components.