BOOLEAN ALGEBRA AND CIRCUIT DE.SIGN 



291 



times bo drawn in bridge form with a consequent saving of contacts. 

 One method is to manipulate the expression into a form whicli is known 

 to be the series-parallel {M[ui\alent of a bridge. However, following 

 usual algebraic procedures it is often difficult to recognize where this is 

 possible. In the present case a method developed by (J. K. Frost (not 

 yet published) was used effectively. This resulted in the l)ridge circuit of 

 Fig. 3b which has the series-parallel eciuivalent : 



/((') = [(' + {D' -f E'){D + E)][A' + 7? + (L>' + E'){1) + K)] 



[C + A']{C + B] 



By use of theorem (3b) this is seen to be ecjuivalent to the pi-evious 

 expression for /(('). 



For the D relay which only operates and releases once in the entire 

 cycle 



g{D) = (.1 + R + C + E') 



r{D) = {A + B + C + E) 

 h{D) = {A -^ B + C + E)' 

 = A'B'C'E' 

 and /(D) = (A + 5 + C + E'){D -f A'B'C'E'). 



A B D E 



J~ 



X" 



J~ 



[a) 



Q 



D + 



E- 



r 



(b) 



'i 



(c) 



rtn, 



b. 



(D) 



'^ 



J- 



a 



(d) 



D-- 



E-- 



x-^ 



J C ABE 



; — i— X * X — X— (- 



(E) 



HI 



tL 



(D) 



^"^ 



X" 



cHll^ 





(e) 



!-" 



'i 



Fig. 3 — Internal control of counting circuit. 



