Memory Requirements in a Telephone Exchange 



By CLAUDE E. SHANNON 



{Manuscript Received Dec. 7, 1949) 



1. Introduction 



A GENERAL telephone exchange with N subscribers is indicated sche- 

 matically in Fig. 1. The basic function of an exchange is that of setting 

 up a connection between any pair of subscribers. In operation the exchange 

 must "remember," in some form, which subscribers are connected together 

 until the corresponding calls are completed. This requires a certain amount 

 of internal memory, depending on the number of subscribers, the maximum 

 calling rate, etc. A number of relations will be derived based on these con- 

 siderations which give the minimum possible number of relays, crossbar 

 switches or other elements necessary to perform this memory function. 

 Comparison of any proposed design with the minimum requirements ob- 

 tained from the relations gives a measure of the efficiency in memory utili- 

 zation of the design. 



Memory in a physical system is represented by the existence of stable 

 internal states of the system. A relay can be supplied with a holding con- 

 nection so that the armature will stay in either the operated or unoperated 

 positions indefinitely, depending on its initial position. It has, then, two 

 stable states. A set of N relays has 2^ possible sets of positions for the arma- 

 tures and can be connected in such a way that these are all stable. The total 

 number of states might be used as a measure of the memory in a system, 

 but it is more convenient to work with the logarithm of this number. The 

 chief reason for this is that the amount of memory is then proportional to 

 the number of elements involved. With N relays the amount of memory is 

 then M = log 2^ = A'' log 2. If the logarithmic base is two, then log2 2=1 

 and M = N. The resulting units may be called binary digits, or more 

 shortly, bits. A device with M bits of memory can retain M different "yes's" 

 or "no's" or M different O's or I's. The logarithmic base 10 is also useful in 

 some cases. The resulting units of memory will then be called decimal 

 digits. A relay has a memory capacity of .301 decimal digits. A 10 X 10 

 crossbar switch has 100 points. If each of these points could be operated 

 independently of the others, the total memory capacity would be 100 bits 

 or 30.1 decimal digits. As ordinarily used, however, only one point in a 

 vertical can be closed. ,Vith this restriction the capacity is one decimal 

 digit for each vertical, or a total of ten decimal digits. The panels used in a 



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