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BELL SYSTEM TECHNICAL JOURNAL 



panel type exchange are another form of memory device. If the commutator 

 in a panel has 500 possible levels, it has a memory capacity of log 500; 8.97 

 bits or 2.7 decimal digits. Finally, in a step-by-step system, 100-point selec- 

 tor switches are used. These have a memory of two decimal digits. 



Frequently the actual available memory in a group of relays or other 

 devices is less than the sum of the individual memories because of artilicial 

 restrictions on the available states. For technical reasons, certain states are 

 made inaccessible — if relay A is operated relay B must be unoperated, etc. 

 In a crossbar it is not desirable to have more than nine points in the same 

 horizontal operated because of the spring loading on the crossarm. Con- 

 straints of this type reduce the memory per element and imply that more 

 than the minimum requirements to be derived will be necessary. 



Fig. 1 — General telephone exchange. 



2. Memory Required for any S Calls out of N Subscribers 



The simplest case occurs if we assume an isolated exchange (no trunks 

 to other exchanges) and suppose it should be able to accommodate any pos- 

 sible set of 5 or fewer calls between pairs of subscribers. If there are a total 

 of .V subscribers, the number of ways we can select m pairs is given by 



N{N - DCY - 2) • • • (.Y - 2m + 1) 



N\ 



I'^mliN - 2m) 



(1) 



The numerator N{N — 1) • • • {N — 2m + 1) is the number of ways of 

 choosing the 2m subscribers involved out of the N. The m\ takes care of 

 the permutations in order of the calls and 2"' the inversions of subscribers 

 in pairs. The total number of possibilities is then the sum of this for m — 

 0, l,---,.S;i.e. 



N\ 



In 2'"m\{N - 2m) I 



(2) 



The exchange must have a stabk- iiUcrnal stale corresponding to each of 

 these possibilities and must have, therefore, a memory capacity M where 



M = log Z 



AM 

 2"'m\{N - 2m) \' 



(3) 



