284 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1952 



THEORY OF A MINIMUM RELAY COUNTER 



The counting circuit under consideration does not contemplate the 

 use of any circuit elements other than relays that react to the beginning 

 or end of a pulse. Therefore it must establish a distinct combination of 

 relays operated or released during and between successive pulses. The 

 minimum number of ordinary "two-position" relays, R, reciuired to 

 count P pulses can be obtained from the expressions (1) 2P < 2^^ if 

 the counter is to lock up during, or recycle after, the last pulse or (2) 

 2P < 2'^ — 1 if the counter is to lock up after the last pulse. 



The usual counting circuit used for determining the number of pulses 

 in a dial train is required to count ten pulses, however there are certain 

 advantages in regard to trouble indications if the counter counts eleven 

 pulses. In either case the minimum number of relays necessary, accord- 

 ing to the preceding formulae, is five. It should be noted that the ease 

 with which this minimum number can be attained depends upon whether 

 the input is derived from a single, double or transfer contact source. 



DETERMINATION OF OPERATING SEQUENCE 



Having determined that the minimum number of relays necessary is 

 five, the first step in design is to develop an operating sequence pattern 

 from the resulting 2^ or 32 possible relay combinations. These combina- 

 tions may be utilized in any order deemed desirable to obtain the 23 dis- 

 tinct combinations needed to differentiate between eleven pulses (22 for 

 the eleven makes and breaks plus an all-relays-normal combination). In 

 this phase of the design switching algebra is not involved. The optimum 

 sequence to meet a particular set of requirements can only be determined 

 by repeated trials guided by an intimate knowledge of objectives. 



Initial studies, made by Joseph Michal, of various possible sequence 

 patterns for a five relay circuit, including those having a three relay 

 "ring" followed by tw^o auxiliary relays and those having a two relay 

 pulse divider followed by three auxiliary relays, resulted in the conclu- 

 tion that the latter approach was the most fruitful. The secjuence pat- 

 tern adopted is shown in detail in Table I. The pattern is extended 

 through 12 pulses, and it can be seen that the nature of the sequence is 

 such that this employs all 32 combinations of the 5 relays. Several of 

 these are transient and occur during part of a pulse or inter-pulse inter- 

 val. Examination of the tail end of the sequence indicates that it will be 

 simpler to design on the basis of a full 12 pulses than attempt to block 

 at the end of the 11 pulses specified by the I'cquirements. If trouble con- 



