Redundant complex number systems

This paper presents redundant complex number systems (RCNSs)-new complex number representations for high-speed arithmetic circuits. RCNS is a positional number system that has a complex radix rj and a digit set {-α,…,0,…,α}, where r⩾2 and [(r² -1)/2]⩽α⩽r²-1. The use of complex radix rj allows additions and multiplications of complex numbers to be done without treating real part and imaginary part separately. Also the redundancy in the number representation enables carry-free addition as well as binary-tree multiple-operand addition. This paper discusses the basic arithmetic algorithms of RCNSs and their implementations