In 1937 a research assistant at Massachusetts Institute of Technology, Claude E. Shannon, was studying for his degree of master of science. He was enrolled in the Department of Electrical Engineering. He was interested in automatic switching circuits and wondered why an algebra should not apply to them. He wrote his thesis on the answer to this question and showed that: (1) There is an algebra that applies to switching circuits. (2) It is the algebra of logic. A paper, based on his thesis, was published in 1938 in the _Transactions of the American Institute of Electrical Engineers_ with the title “A Symbolic Analysis of Relay and Switching Circuits.” [Illustration: FIG. 1. Switches in series.] For a simple example of what Shannon found out, suppose that we have two switches, 1, 2, in series (see Fig. 1). When do we get current flowing from the source to the sink? There are 4 possible cases and results (see Table 9). Table 9 SWITCH 1 IS CLOSED SWITCH 2 IS CLOSED CURRENT FLOWS Yes Yes Yes No Yes No Yes No No No No No Now what does this table remind us of? It is precisely the truth table for “AND.” It is just what we would have if we wrote down the truth table of the statement “Switch 1 is closed AND switch 2 is closed.” [Illustration: FIG. 2. Switches in parallel.] [Illustration: FIG. 3. Switch open—current flowing.] Suppose that we have two switches 1, 2 in parallel (see Fig. 2). When do we get current flowing from the source to the sink? Answer: when either one or both of the switches are closed. Therefore, this circuit is an exact representation of the statement “Switch 1 is closed or switch 2 is closed.” Suppose that we have a switch that has two positions, and at any time must be at one and only one of these two positions (see Fig. 3). Suppose that current flows only when the switch is open. There are two possible cases and results (see Table 10). Table 10 SWITCH 1 IS CLOSED CURRENT FLOWS Yes No No Yes This is like the truth table for “NOT”; and this circuit is an exact representation of the statement “Switch 1 is NOT closed.” (_Note_: These examples are in substantial agreement with Shannon’s paper, although Shannon uses different conventions.) We see, therefore, that there is a very neat correspondence between the algebra of logic and automatic switching circuits. Thus it happens that: 1. The algebra of logic can be used in the calculation of some electrical circuits. 2. Some electrical circuits can be used in the calculations of the algebra of logic. This fact is what led to the next step. LOGICAL-TRUTH CALCULATION BY MACHINE