A theoretical analysis of square versus rectangular component multipliers in recursive multiplication

Previous discussions of recursive multiplication in the literature focus on how/why the scheme works and how a multiplier of a desired size can be built from given component multipliers or multiply-add modules. The form factors (square versus rectangular) for the component multipliers and the one to be synthesized, and how they affect the performance and cost of the resulting multiplier, have not been contemplated. We remedy this shortcoming by dealing with the general problem of synthesizing a possibly non-square k χ l multiplier from b × c component multipliers or multiply-add modules, demonstrating that in many cases, the use of rectangular components leads to speed and cost benefits.