286 THE BELL SYSTEM TECHMCAL JOURNAL, MARCH 1952 



uses all 32 of its available combinations. Its control and translating job 

 is complex enough to indicate the need for a considerable nimi})er of con- 

 tacts and hence the need for extensive contact manipulation to minimize 

 and distribute these contacts. 



It is apparent that a great deal of time would be necessary to accom- 

 plish this manipulation by inspection methods, therel^y indicating the 

 need for an additional tool such as switching algebra to assist the de- 

 signers in this task. 



ALGEBRAIC METHODS APPLIED TO CONTROL CIRCUIT 



The seciuence of operations of Table I is used as the starting point 

 in the application of the algebra. The exact calculations necessarj^ to 

 develop the control and translating circuit by this means are shown in 

 detail later. However, the indi\'idual steps in the solution might well be 

 outlined here. First, the design of the control and translating networks 

 will be regarded as separate problems. In theory these can be integrated 

 together, but the resultant network is likely to be so complex that under- 

 standing and maintenance of the circuit would suffer. Each of the two 

 netw^orks can be individually considered as a multi-terminal network of 

 the single input type. That is, the control network is an associated set of 

 contacts which connects a single ground input to the ^^dndings of five 

 relays, and the translating network is an associated set of contacts w'hich 

 connects a single ground input to the six output leads. Since switching 

 algebra is directly applicable to two-terminal networks rather than multi- 

 terminal networks, the approach to this particular problem is of neces- 

 sity somewhat indirect. 



The most satisfactory method of attack is to develop first a two- 

 terminal network for each of the output paths of the multi-terminal 

 network under consideration. The two-terminal networks can be ex- 

 pressed algebraically and manipulated into their simplest form by means 

 of the switching algebra theorems to be given later. The individual net- 

 works can then be inspected carefully, either in algebraic or circuit form, 

 with the objective of combining them in the most advantageous fashion. 

 It will be found, in general, that the simplest network configurations do 

 not readily combine and that further manipulation is necessary to obtain 

 an economical circuit. It is at this point that the algebra achieves its 

 greatest utility, since its application permits the simple and rapid chang- 

 ing of a given two-terminal network into a large variety of different 

 forms with mathematical assurance that circuit eciuivalence is main- 

 tained. Inspection of the networks in the several forms provides clues 



