2-LEVEL LOGIC-CIRCUITS USING EXOR SUMS OF PRODUCTS

Two-level logic is most often implemented as an inclusive-OR sum of pr oduct terms, e.g. with PLAs. Using exclusive-OR (EXOR) sums may simpli fy 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 implem entation structures, it has not been possible to translate these theor etical advantages into practical benefits. In this paper solutions for the two main problems associated with the use of EXOR sums are presen ted. On the one hand we describe a new method to minimise functions us ing two-level EXOR sums of products, on the other hand we present an i mplementation structure called the XPLA to map the minimisation result s to efficient circuit layouts. We show, for a set of benchmark exampl es, that the minimisation algorithm results in representations with co nsiderably smaller product term counts than previous EXOR minimisation algorithms or sum-of-product minimisation algorithms. We also show, a lthough the EXOR operator is more expensive to implement in today's te chnologies, that XPLA implementations can be considerably more compact than PLAs in some cases, and give increased testability.