SYNTHESIS OF SWITCHING CIRCUITS 



n-2 



91 



i;(^)2^'2^'*""' 



< {n - 3) — 2 2 

 and the ratio of this to 2" — > as n — > <» . 



Fig. 20 — Use of separability to reduce number of elements. 



Fig. 21 — Use of separability of two sets of variables. 



In case such a functional separabiUty occurs, the general design method 

 described above can be used to advantage in many cases. This is typified 

 by the circuit of Fig. 20. If the separability is more extensive, e.g. 



/ = gOhiXx ■ ■ ■ Xs), h2(Xs+y ■ ■ ■ X,), Z.+i , • • • , X„) 



the circuit of Fig. 21 can be used, using for '7/2" either hi or ht , whichever 

 requires the least number of elements for realization together with its 

 negative. 



We will now consider a second type of functional relation which often 

 occurs in practice and aids in economical realization. This type of relation 

 may be called group invariance and a special case of it, functions symmetric 



