Fast tabular technique for fixed-polarity Reed-Muller logic with inherent parallel processes

Abstract

We have developed a fast tabular technique for Boolean to fixed-polarity Reed–Muller logic conversion. The idea is derived from the popular tabular technique but the processes of generating new terms and cancelling pairs are vastly different. The feature of bit-by-bit operation in the tabular technique has also been changed. In our technique, an index table is used to capture the number of occurrences of initial and new terms. This instant updating process eliminates the time-consuming step of cancelling pairs and makes the method much more efficient than the tabular technique. In addition, the fast tabular technique possesses inherent parallelism since different minterms can be processed concurrently and added to the index table independently. Our method is applicable to any number of variables and is suitable for manual computations as well as computer programming. Some comparison results are given, and we believe our technique has achieved the best time and space complexities so far.