i\r-TERMlNAL SWITCHING CIRCUITS 



687 



it. This is so regardless of how large K is. If the rotor of a selector switch 

 is connected to such a node, the chance is great that none of the other 

 branches at the node are operated by this same switching variable. Hence 

 we suspect that a typical switching network requires almost as mnay rotors 

 as contacts. 



Acknowledgment 



The author has discussed this switching problem with B. D. Holbrook, A. 

 W. Horton, J. Riordan, and C. E. Shannon and has received valuable com- 

 ments and ideas from them. He is also indebted to A. E. Joel and W. Keister 

 for their suggestions for improving the readability of the manuscript. 



Table I 



APPENDIX 



To illustrate how the network synthesis method operates in a typical 

 case consider a three-terminal network using three switches x, y, z. Switches 

 X and y have two positions and 1, and z has four positions 1, 2, 3, 4. A 

 three- terminal switching function fix, y, z) is defined by means of the first 

 four columns of Table I. The sixteen entries in column four represent the 

 states of the terminals which the network must produce for the correspond- 

 ing switch settings given in the columns labelled x^ y, z. In column four, 

 parentheses are used to group terminals which are connected together; for 

 example /(I, 0, 4) is the state in which terminals 1 and 2 are connected 

 together and 3 is left free. 



A network with switching function f{xj y, z) will be designed by connect- 

 ing two- terminal networks between the pairs of terminals 1, 2; 2, 3; and 1,3. 

 The hindrance functions of these three two-terminal networks will be called 



