Tri-state map for the minimisation of exclusive-OR switching functions

A tri-state map is developed as a general format for Karnaugh maps, Reed-Muller coefficient maps and transition (partially polarised) maps. The polarisation statuses of the variables in transition maps and Reed-Muller coefficient maps are indicated by the labels on the tri-state maps. A variable in a tri-state map can exist in two of three different states: true, complemented or nonexistent. Karnaugh maps and positive-polarity or negative-polarity Reed-Muller coefficient maps are special cases, in which there are only two states. Minimisation of exclusive-OR switching functions can be carried out, not only on Reed-Muller coefficient maps, but also on Karnaugh maps or any of the transition maps.