Two-level logic circuits using EXOR sums of products

Two-level logic is most often implemented as an inclusive-OR sum of product terms, e.g. with PLAs. Using exclusive-OR (EXOR) sums may simplify the representation and manipulation of Boolean functions and result in more easily testable implementations requiring fewer product terms. However, due to the lack of relevant algorithms and efficient implementation structures, it has not been possible to translate these theoretical advantages into practical benefits. Solutions for the two main problems associated with the use of EXOR sums are presented. On the one hand the authors describe a new method to minimise functions using two-level EXOR sums of products, on the other hand they present an implementation structure called the XPLA to map the minimisation results to efficient circuit layouts. They show, for a set of benchmark examples, that the minimisation algorithm results in representations with considerably smaller product term counts than previous EXOR minimisation algorithms or sum-of-product minimisation algorithms. They also show, although the EXOR operator is more expensive to implement in today´s technologies, that XPLA implementations can be considerably more compact than PLAs in some cases, and give increased testability.