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Consider a sequential digital circuit consisting of $\mathrm{T}$ flip-flops and $\mathrm{D}$ flip-flops as shown in the figure. $\text{CLKIN}$ is the clock input to the circuit. At the beginning, $\text{Q1, Q2}$ and $\text{Q3}$ have values $0,1$ and $1,$ respectively.

Which one of the given values of $\text{(Q1, Q2, Q3)}$ can $\text{NEVER}$ be obtained with this digital circuit?

  1. $(0,0,1)$
  2. $(1,0,0)$
  3. $(1,0,1)$
  4. $(1,1,1)$
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From the given $3$ state counter made from $T$ flipflops and $D$ flipflops, the next input sequence are as follows:

  • $T_0=\overline Q_2$
  • $D_1=Q_0$
  • $T_2=Q_1$
Initial State Current input Next State
$Q_0$ $Q_1$ $Q_2$ $T_0$ $D_1$ $T_1$ $Q_0^+$ $Q_1^+$ $Q_2^+$
0 1 1 0 0 1 0 0 0
0 0 0 1 0 0 1 0 0
1 0 0 1 1 0 0 1 0
0 1 0 1 0 1 1 0 1
1 0 1 0 1 0 1 1 1
1 1 1 0 1 1 1 1 0
1 1 0 1 1 1 0 1 1

we can see from the above table given counter count sequence like $011\rightarrow 000\rightarrow 100\rightarrow 010\rightarrow 101\rightarrow 111\rightarrow 110$. The state $001$ is missing.

Option (A) is correct.

Answer:

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