An Application of Boolean Algebra to 

 Switching Circuit Design 



BY ROBERT E. STAEHLER 



(Manuscript received January 10, 1952) 



This paper discusses the application of switching (Boolean) algebra to the 

 development of an all-relay dial pulse counting and translating circuit em- 

 ploying the minimum number of relays. An attempt is made to outline what 

 appears to be the most promising method of obtaining beneficial residts from, 

 the use of the algebra in the design of practical switching circuits. 



INTRODUCTION 



The demands made upon telephone switching systems in regard to im- 

 provements in handhng capacity, speed, flexibihty and economy are con- 

 tinually increasing. In order to meet design objectives enabling the 

 fulfillment of these demands, switching circuits have of necessitj^ become 

 more and more complex and intricate. As certain types of relay switch- 

 ing circuits increase in complexity, the problem of control and output 

 contact network design becomes more and more laborious and time con- 

 suming. This is especially true in those circuits in which an attempt has 

 been made to achieve the ultimate in efficiency and economy in that the 

 number of relays used therein approaches the absolute minimum neces- 

 sary to provide the required number of distinct output combinations. 

 In this type of near-minimum combinational or sequential relay circuit 

 there are numerous parallel control and output contact paths which 

 thread through the same relays repeatedly, thereby causing the indi- 

 vidual relay contact loads to become relatively large. Thus the designer's 

 problem becomes that of first de^'eloping a workable control and output 

 contact network and then manipulating and minimizing contacts within 

 that network so that the maximum number of contacts used on any one 

 relay is within that permissible on any commercially available relay 

 having the necessary speed characteristics. 



Even in those combinational and sequential relay circuits which ai'e 

 not near-minimum and therefore probably have fairly light individual 

 relay contact loads, there are, of course, advantages to be gained by 

 using the least number of contacts possible. Although the initial cost per 

 additional contact (assuming that a few added contacts per relay will 

 not impair the relay speed or space characteristics to an extent that the 

 circuit recjuirements are not met) is almost negligible, there are other 



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