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THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1953 



is made via levels, a level consisting of three intermediary switching 

 stages. The number of levels required is {2N^'^ — 1). Each level has 

 N^'^ inputs and the same number of outputs. The number of crosspoints 

 for a three-stage non-blocking array for A^^^^ inputs and A^^'^ outputs 

 can be obtained from equation (2) by substituting A^^^^ for N in that 

 equation. The total number of crosspoints required for the five-stage 

 array is: 



C(5) = (2N'^' - if SN''' + C2N'" - 1) 2N (3) 



= 16A^'^' - UN -f SN'^' (3a) 



The number of crosspoints required for several sizes of the five-stage 

 array is given in Table II. The results are compared to the square and 

 three-stage arrays. 



SEVEN-STAGE SWITCHING ARRAY 



A seven-stage switching array can be analyzed by considering paths 

 requiring five intermediary switching stages as paths via switching 

 aggregates. The number of such aggregates is {2N^''^ — 1). Each ag- 

 gregate has N^'* inputs and a like number of outputs. From equation (3) 

 the crosspoints for each aggregate can be obtained by substituting 



Fig. 4 — Five-stage switching array. 



