A complex-number multiplier using radix-4 digits

This paper describes the design of a 16×16 complex-number multiplier developed as part of the arithmetic datapath of a complex-number digital signal processor. The complex-number multiplier internally uses binary signed digits for fast multiplication and compact layout. It employs the traditional three-multiplication scheme while minimizing the logic and delay associated with the three extra pre-multiplication binary additions which that scheme requires. The minimization comes from producing the redundant binary sum for each of the pre-multiplication binary additions with minimal hardware, and then recoding the redundant sums as radix-4 multiplier operands. The radix-4 operands halve the number of summands to be added in each of the three real multiplier units. Furthermore, an additional factor of two reduction in the number of summands is effectuated by our coding scheme for representing binary signed digits. The result is a fast and compact complex-number multiplier