670 



THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 



that, if a contact is touched by a rotor when the shaft is in position number j, 

 then this contact remains untouched for all other positions of the shaft. 



Networks built from two-position switches are analyzed with the aid of 

 Boolean Algebra. It is possible to construct an algebra which is appropriate 

 for selector switch circuits. A detailed account of this algebra has been 

 given by H. Piesch.^ 



The state of a switch with p positions can be associated with a switching 

 variable x which ranges over the values 1, 2, • • • , />. Then "a; = ^" means 

 the same as ''the switch is in its k^^ position." The state of a two- terminal 

 network, using M switches with pi j - • - , and pM positions, is a hindrance 

 function f{xi , • • • , Xm) of the M switching variables Xi , • • - , Xm with Xi 



-^. 



SHAFT 



Fig. 1 — Selector switch. 



ranging from 1 to pi . As usual / = 1 means the circuit is open and / = 

 means the circuit is closed. Then/(ii;i , • • • , Xm) + g{xi , • • • , Xm) is the func- 

 tion representing the series connection of two networks whose functions are 

 f and g while f{xi , • • • , Xm) g{xi , • • • , Xm) represents the networks/ and g 

 in parallel. 



The circuit which consists of just a rotor which touches a contact in its 

 i^ position has hindrance function 



fl if X7^ i 

 Ciix) = \ 



[0 \i X = i 



»H. Piesch, Archivfiir ELectrotechnik, 33, pp. 674, 686 and pp. 733-746 (1939). 



