Mapping of Reed-Muller coefficients and the minimisation of exclusive OR-switching functions

A new geometric format, the bj coefficient map, is here introduced, the entries in which are the {0, l} coefficient values of the Reed-Muller Exclusive-OR expansions by which any given combinatorial function may be expressed. Although similar in format to the classic Karnaugh map, the bj map entries do not represent the function output in the same manner as do the minterm entries plotted on a Karnaugh map. It is shown that this coefficient map structure may readily be used to generate any required Exclusive-OR realisation of a given function, and provides a deeper insight into the coefficient relationships which arise when input variables are complemented in any Exclusive-OR expansion.