GENERALIZED HYBRID ARITHMETIC CANONICAL EXPANSIONS FOR COMPLETELY SPECIFIED QUATERNARY FUNCTIONS

A novel representation of completely specified quaternary functions, c alled 'hybrid arithmetic canonical expansion' is shown. The new expans ion is based on both standard and GF(4) algebra. The transform matrix of the expansion is defined by an arbitrary set of linearly independen t functions in GF(4). The introduced expansion is generalised by apply ing to it the concept of polarity. The way of obtaining the coefficien t vector of the expansion from some coefficient vector in known polari ty is introduced. Generalised hybrid arithmetic polynomial expansions for known basis functions from quaternary Reed-Muller transforms are s hown. The idea of binary and ternary independent function is extended to the quaternary case and the new expansion for such a transform matr ix is also presented. The generalised hybrid arithmetic expansion is c anonical for completely specified quaternary functions. Finally, imple mentation of the generalised hybrid arithmetic expansion in the form o f a suitable universal logic module is introduced.