On the Area Required by VLSI Circuits

A technique is developed and used to derive lower bounds on the area required by a VLSI circuit by taking into account the amount of information that has to be memorized in the course of the computation. Simple arguments show, in particular, that any circuit performing operations such as cyclic shift and binary multiplication requires an area at least proportional to its output size. By extending the technique, it is also possible to obtain general tradeoffs between the area, the time, and the period (a measure of the pipeline rate) of a circuit performing operations like binary addition. The existence of VLSI designs for these operations shows that all the lower bounds are optimal up to some constant factor.