Manipulation and Optimization techniques for Boolean logic

AlJassani, B.A., Urquhart, N., Almaini, A.E.A. (2010). Manipulation and Optimization techniques for Boolean logic. IET Computers and Digital Techniques , 4, (3), 227-239.


ISBN:
ISSN: 1751-8601

Abstract

In this study, new techniques and algorithms are presented for the derivation and optimisation of mixed
polarity Reed Muller (MPRM) and mixed polarity dual Reed Muller (MPDRM) functions. The first algorithm is used
for bidirectional conversion between fixed polarity dual Reed Muller (FPDRM) and MPDRM and to derive any
polarity from another polarity. The second algorithm is used to generate reduced MPDRM expressions from
FPDRM using a new procedure based on tabular techniques. The third algorithm is proposed for bidirectional
conversion between sum of products (SOP)/product of sums (POS) and MPRM/MPDRM forms, respectively. It
can also be used to derive any mixed polarity from another MPRM/MPDRM. The last algorithm is to find
optimal MPRM/MPDRM among 3n different polarities using genetic algorithm (GA) for large functions but
without generating all the polarity sets. The proposed algorithms are efficient in terms of memory size and
CPU time and can be used for large functions. Experimental results are given using a personal computer with
an Intel CPU of 2.4 GHz and 2 GB RAM. All algorithms are implemented using Cþþ and fully tested with
benchmark examples.
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Authors

Neil Urquhart
Lecturer
n.urquhart@napier.ac.uk
+44 131 455 2655

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