Optimizing logic design using Boolean transforms

Abstract

When a Boolean function is transformed by exclusive-OR with a suitably selected transform function, the new function is often synthesized with significantly reduced hardware. The transform function is separately synthesized and the original function is recovered as an exclusive-OR of the two functions. We select the transform to reduce the number of cubes in the function to be synthesized. The function is represented as a Shannon expansion about selected variables. A transform function is constructed such that a selected set of cofactors is complemented to minimize the overall number of cubes. Examples of single-output functions show an average area reduction of 19%. For a multiple-output function, transformations can be customized for each output.