60 



BELL SYSTEM TECHNICAL JOURNAL 



NETWORK 



» 0^0 • 



a 0^0 • 





HINDRANCE FUNCTION 



(PERMANENTLY CLOSED CIRCUIT) 



1 (PERMANENTLY OPEN CIRCUIT) 

 X (MAKE CONTACT ON RELAY X) 

 X' (BREAK CONTACT ON RELAY X) 

 X + Y (SERIES CONNECTION) 



XY (PARALLEL CONNECTION) 



-• w [x + y(z+ X')] 



Fig. 1 — Hindrance functions for simple circuits. 



expression corresponding to a two-terminal network. This expression will 

 involve the various relays whose contacts appear in the network and will be 

 called the hindrance or hindrance function of the network. The last net- 

 work in Fig. 1 is a simple example. 



Boolean expressions can be manipulated in a manner very similar to 

 ordinary algebraic expressions. Terms can be rearranged, multiplied out, 

 factored and combined according to all the standard rules of numerical 

 algebra. We have, for example, in Boolean Algebra the following identities^ 



+ Z = X 



OX = 



\-X = X 



X -\-Y = Y + X 



XY = YX 



X + (F + Z) = (X -f F) + Z 



X(YZ) = iXY)Z 



X{Y -h Z) = XY -\- XZ 



The interpretation of some of these in terms of switching circuits is shown 



in Fig. 2. 



There are a number of further rules in Boolean Algebra which allow 



