Information transfer and area-time tradeoffs for VLSI multiplication

The need to transfer information between processing elements can be a major factor in determining the performance of a VLSI circuit. We show that communication considerations alone dictate that any VLSI design for computing the 2 n -bit product of two n -bit integers must satisfy the constraint AT 2 ≥ n 2 /64 where A is the area of the chip and T is the time required to perform the computation. This same tradeoff applies to circuits which can shift n -bit words through n different positions.