A theorem on SPDT switching circuits

Abstract

It is first demonstrated that networks of SPDT (Single Pole Double Throw) switches can be represented abstractly with a Boolean algebra in much the same way as networks of SPST (Single Pole Single Throw) switches have been treated by Shannon, provided a certain set of network wiring rules is established. A theorem is then proved which shows that all networks represented in this way can be handled as though each network were itself a single SPDT switch. Proof of a corollary then allows discussion of techniques of network construction. The component minimization problem is also discussed and several detailed examples are given.