Logic Properties of Transistor Circuits:Analysis of Relay-Contact Networks.

Analysis of Relay-Contact Networks

Let us analyze a relay contact network. “Analysis of a network” means the description of the logic performance of the network in terms of a logic expression [1].

where the last term, x2x2x3x5, may be eliminated, since it is identically equal to 0 for any value of x2.

Procedure 33.1 yields the transmission of the given network because all the tie sets correspond to all the possibilities for making f equal 1. For example, the first term, x1x6x2x5, in Eq. 33.1 becomes 1 for the combination of variables x1 = x6 = x5 = 1 and x2 = 0. Correspondingly, the two terminals a and b of the network in Figure 33.5 are connected for this combination.

This expression looks different from Eq. 33.1, but they are equivalent, since we can get identical truth tables for both expressions.

Procedure 33.2 yields the transmission of a relay contact network because all the cut sets correspond to all possible ways to disconnect two terminals, a and b, of a network; that is, all possibilities of making f equal 0. Any way to disconnect a and b which is not a cut set constitutes some cut set plus additional unnecessary open contacts, as can easily be seen.

The disjunction inside each pair of parentheses in Eq. 33.2 corresponds to a different cut set. A disjunction that contains the two different literals of any variable (e.g., (x2 ∨ x3 ∨ x2) in Eq. 33.2 contains two literals, x2 and x2, of the variable x2) is identically equal to 1 and is insignificant in multiplying out f. Therefore, every cut set that contains the two literals of some variable need not be considered in Procedure 33.2.