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Find the contents of the flip-flop $Q_2, Q_1$ and $Q_0$ in the circuit of figure, after giving four clock pulses to the clock terminal. Assume $Q_2Q_1Q_0=000$ initially.

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Best answer
36 votes
36 votes

Initial $Q_2=0, Q_1=0, Q_0=0$

Clock $1:$

  • $Q_2=1$  $[J =$ ( old $Q_0)'=1, K=1,$ New $Q2=$ Complement of old $Q2=1]$
  • $Q_1 =0$  $[D =$old $Q_2=0,$ new $Q1= D =0]$
  • $Q_0=0$  $[T=$ old $Q1=0,$ New $Q_0 = $old $Q_0 =0]$


Clock $2:$

  • $Q_2=0$   $[J =$ ( old $Q_0)'=1, K=1,$ New $Q2=$ Complement of old $Q2=0]$
  • $Q_1 =1$   $[  D =$old $Q_2=1,$ new $Q1= D =1]$
  • $Q_0=0$  $[ T=$ old $Q_1=0,$ New $Q_0 = $old $Q_0 =0]$


Clock $3:$

  • $Q_2=1$  $[J =$ ( old $Q_0)'=1, K=1,$ New $Q_2=$ Complement of old $Q2=1]$     
  • $Q_1 =0$  $[D =$ old $Q_2=0,$ New $Q_1= D =0]$
  • $Q_0=1$  $[T= $ old $Q1=1,$ New $Q_0 =$ complement of old $Q_0 =1]$


Clock $4:$

  • $Q2=0$  $[J =($old $Q_0)'=0, K=1$, new $Q_2=$ Reset$=0]$
  • $Q1 =1$  $[D =$old $Q_2=1$, new $Q_1= D =1]$
  • $Q0=1$  $[T= $old $Q_1=0$, new $Q_0 = $old $Q_0 =1]$


After $4$ clock pulses $Q2Q1Q0$ is $011$

Note : for JK flipflops, $Q_{(t+1)} = JQ' +K'Q$, for D flipflops, $Q_{(t+1)} = D$, and for T flipflops $Q_{(t+1)}= T\oplus Q $ Where $Q_{(t+1)}$ represent new value of $Q.$

edited by
13 votes
13 votes

The below table clearly demonstrates how after 4th cycle it will be 011 state. 

Answer:

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