iV-TERMINAL SWITCHING CIRCUITS 



673 



If one expands f{xx , • • • , Xm) about Xi , • • • ,Xk one finds 



/ = II krfe) + ^5(^2) + • • • + e,{xk) 



(2) 



4-/(r, 5, ••• ,z, Xifc+i, ••• jOtTAf)] 



where the muhiple product is taken over the entire range of the variables 

 ^*i , • • • , ock . The different functions er{xi) + esix^) + • • • + ezipck) can all 

 be realized with one tree circuit as shown in Fig. 3. If the expansion had 

 been performed about all the variables X\y • • • ^Xm ^ identity (2) would 



e,(Xi) + ei(X2)- 

 e,(x,) + ei(X2)- 



.+ei(Xk) 



•+e2(XK) 



eptC^O + ep2(X2H...+ep^(Xk') 



Fig. 3— Tree. 



show that the desired function / could be synthesized by connecting one 

 terminal to the input lead of a tree and the other terminal to certain of 

 the tree's output leads. The number of contacts used would have been 

 about 2^"*"^ . The method which follows uses still fewer contacts. 



The network which we use to synthesize the function/ is shown in Fig. 4. 

 It consists of the tree of Fig. 3 with its output leads connected to the input 

 leads of a network on the right which is designed so that the hindrances 

 from its input leads to its output lead are the functions /(r, 5, • • • , z, Xk+i , 



