# GATE | GATE CS 2011 | Question 65

Consider the following circuit involving three D-type flip-flops used in a certain type of counter configuration. If at some instance prior to the occurrence of the clock edge, P, Q and R have a value 0, 1 and 0 respectively, what shall be the value of PQR after the clock edge?

(A)

000

(B)

001

(C)

010

(D)

011

Explanation:

P\’ = R Q\’ = (P + R)\’ R\’ = QR\’ Given that (P, Q, R) = (0, 1, 0), next state P\’, Q\’, R\’ = 0, 1, 1 ———————————————————————————————– D flip flop truth table

Initially (p,q,r) =(0,1,0) D for p=R D for q=NOT(p xor r) D for r= (not)r.q So Q(t+1) for(p,q,r) p=>r=0 so p=0 q=> NOT(p xor r) => 1      so q=1 r=>(not)r.q => 1         so r=1 (p, q, r) = (0, 1, 1) Alternative approach – Truth table of a D Flip-Flop- By looking at the circuit diagram, it is clear that the boolean expressions of P, Q, and R are- Here the subscript t refers to the current clock cycle, and the subscript (t+1) refers to the next clock cycle. [Tex]Q_{Q(t+1)} = Q_{t+1} = R_{t}\’ P_{t}\’  [/Tex] [Tex]\\begin{tabular}{|c|c|c|} \\hline D_{t} & Q_{t+1}\\\\ \\hline 0 & 0\\\\ \\hline 1 & 1\\\\ \\hline \\end{tabular}  [/Tex]This explanation is provided by Chirag Manwani

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