Synthesis of multilevel multiplexer circuits for incompletely specified multioutput Boolean functions with mapping to multiplexer based FPGA´s

The introduction of the multiplexer-based Actel FPGA series ACT resulted in an increased interest in multiplexer circuits. This paper introduces a level-by-level top-down minimization algorithm for them. The concept of a local transform is applied for the generalization of the ratio parameter method for M(1) multiplexer synthesis having one data select input and a spectral method for M(2) multiplexer synthesis to determine redundant multiplexer inputs for M(k) multiplexer circuits. The algorithm developed for multilevel synthesis of M(k) multiplexer circuits for incompletely specified multioutput Boolean functions takes advantage of the combination of spectral and Boolean methods. The obtained multiplexer circuit can be directly realized with FPGA´s like the Actel ACT series or the CLi 6000 series from Concurrent Logic. A simple heuristic is applied to map an M(1) multiplexer circuit to the Actel ACT1 family