Minimizing and mapping sequential circuits

SHANNON'S original paper suggesting a modification of the classical Boolean algebra of symbolic logic to a form of switching algebra led to the development among switching and computer designers of many special techniques.1‾3 Recent interest in the field is rapidly developing methods well within the reach of the occasional switching engineer who finds a moderately complex relay circuit necessary to the operation or sequencing of another design. Reference is made to these papers for a brief summary of the binary nomenclature and operators of switching algebra.4,5 The approach suggested here assures the designer that he is manipulating an adequate number of relays, and provides a pictorial work sheet that keeps track of all contact positions. The work sheet permits easy recognition of possible holding circuit difficulties. Negation is proposed as the switching-algebra operator to denote shunt contacts, and is consistent with the mapping procedure.