Logic relizations based on reed-muller canonical forms Ph.D. Thesis

Abstract

The thesis is concerncd v/ith a study of Recd-Mullor Canonical (FMC) forms and the associated logic realizations. Tv/o nonexhaustive procedures for obtaining minimal PS'IC forms have been reviewed, One of them has boen modified to obta.in improved upper bounds on the number of M C forms to be de rived for choosing the minimal ones. It has been shov/n that the. task of obtaining minim8.1 R4C forms is further simplified for some special types of switching functions. Some alternatives to the R4C networks for reaJLizing sv/itching functions that achieve a reduction in both the number of levels and the number of gates have been proposed. A straight forv/ard factoring techniq.ue for obtaining multi-level AND-EOR circuits has been suggested. A generalization of the HiC forms to multi-valued logic has been obtained and several results regarding the M C forms have been generalized to the multi-valued case, A rectangular universal cellular array based on the M C forms for realizing any sv/itching function has been proposed. An algebraic generalization of the well known q-function array to multi-valued logic has been ob tained. The problem of fault diagnosis in R4C netv/orks and multi-level AND-EOR realizations has been investigated.