# Application of Boolean algebra to electrical switching circuit problems

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Since 1847 the time of the first published paper on mathematical logic by George Boole, Boolean algebra has grown to be a rigorous and useful part of mathematics. The theorems of the algebra can be logically developed from a few initially assumed postulates. It is interesting to note that the algebra is a specialised lattice and a restricted type of a ring. There are also Boolean algebras of higher orders than one. The algebra needed to specify the relationship between relay and switch contacts of a contact circuit is isomorphic to Boolean algebra. Hence, with the proper restrictions on the range of variables and a defining of the operations with respect to switching circuit requirements, a switching algebra can be developed from Boolean algebra. This switching algebra is used as an aid in solving the two central switching circuit problems of network synthesis and network simplification. Combinational contact networks, to which switching algebra can be applied, consist of series-parallel and non-series-parallel networks. By using Ingenious devices switching algebra can be used as an aid in solving sequential network problems. If certain restrictions are made switching algebra can be applied to circuits using other circuit elements than relay or switch contacts. Some of these other circuit elements are vacuum and gas tubes, rectillers, transistors, and magnetic cores. Thus Boolean or switching algebra can be used as an aid in the design of computers and logic machines.