Comparison of graphical and subexpression methods for design of efficient multipliers

Relationships are examined between two traditional strategies used to design "multiplier blocks": graphical methods and common subexpression elimination (CSE), four applications: single multipliers, multiplier blocks (several products of a single multiplicand), FIR filters and matrix multipliers are compared. A new representation shows how graphical designs can be extracted from CSE designs. Algorithms for both approaches are compared. A new graphical algorithm for FIR filter design and new results for CSE in the multiple product case are presented so comparison can be made for all applications. We conclude that for simpler problems, graphical methods are best, while CSE works better for the more complex problems.