In this part, we will introduce a third important application of Boolean algebra, the algebra of circuits, involving two-state  (bistable) devices. The simplest example of such a device is a switch or contact. The theory introduced holds equally well for such two-state devices as rectifying diodes, magnetic cores, transistors, various types of electron tubes, etc. The nature of the two states varies with the device and includes conducting versus nonconducting, closed versus open, charged versus discharged, magnetized versus nonmagnetized, high-potential versus low-potential, and others.

The algebra of circuits is receiving more attention at present, both from mathematicians and from engineers, than either of the two applications of Boolean algebra which we considered in the previous chapters. The importance of the subject is reflected in the use of Boolean algebra in the design and simplification of complex circuits involved in electronic computers, dial telephone switching systems, and many varied kinds of electronic control devices.

The algebra of circuits fits into the general picture of Boolean algebra as an algebra with two elements 0 and 1. This means that except for the terminology and meaning connecting it with circuits, it is identical with the algebra of propositions considered as an abstract system. Either of these Boolean algebras is much more restricted than an algebra of sets.  The latter concept is so general, in fact, that every Boolean algebra may be interpreted as an algebra of sets.