An advanced recursive algorithm for low-cost implementation of matrix multipliers

Of late, with adders (subtractors) and shifts replacing multipliers, the complexity of multiplication is dominated by the number of adders (subtractors) used to implement the multipliers. In this paper an advanced recursive common subexpression elimination (CSE) algorithm based on the Binary representation of the coefficients is proposed. The recursive algorithm maximizes the selection of frequently occurring common subexpressions (CSs) thereby reducing the number of adders required to implement the matrix multiplication and hence reduces the cost of implementation considerably. Design examples show that the proposed method offers an average adder reduction of about 28% over the best known CSE method and the percentage reduction increases with the order of multiplication, higher the order greater the reduction.