Systematic analysis of bounds on power consumption in pipelined and non-pipelined multipliers

The paper presents a systematic theoretical approach for the analysis of bounds on power consumption in Baugh-Wooley, binary tree and Wallace tree multipliers. This is achieved by first developing state transition diagrams (STDs) for the sub circuits making up the multipliers. The STD is comprised of states and edges, with the edges representing a transition (switching activity) from one state to another in the sub circuit. Then, maximum (minimum) energy values associated with the edges constituting the STDs are used to derive the zipper (lower) bound in both non pipelined and p-bit level pipelined multipliers. It is shown that as p is decreased, the upper bound approaches the lower bound. Moreover, based on the theoretical analysis we conclude that the upper bound in a Baugh-Wooley multiplier has a cubic dependence on the word length, while that in a binary tree multiplier has a quadratic dependence on the word length.