Graphical method for the conversion of minterms to Reed-Muller coefficients and the minimisation of exclusive-OR switching functions

A graphical method extended from a folding technique developed by Wu et al. is used to convert the minterms of a switching function to the coefficients of its Reed-Muller polynomial with fixed polarity. The conversion starts from a Karnaugh map and results in a Reed-Muller coefficient map. An algorithm which attempts to find a minimal exclusive-OR realisation for the switching function in mixed polarity by grouping the Reed-Muller coefficient map is presented. The graphical method of converting minterms to Reed-Muller coefficients and the minimisation algorithms are also applied to incompletely specified functions.