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

This 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 upper (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.