Consider a 3-bit counter, designed using T flip-flops, as shown below: Assuming the initial state of the counter given by PQR as 000, what are the next three states?

From the circuit diagram, the inputs to the three T flip-flops are given by:

• $T_P = R$

• $T_Q = P^{\prime}$

• $T_R = Q^{\prime}$

The next state of a T flip-flop is determined by the characteristic equation:

Given the initial state $(P, Q, R) = (0, 0, 0)$:

1. Clock Pulse 1:

   • Inputs: $T_P = R = 0$, $T_Q = P^{\prime} = 1$, $T_R = Q^{\prime} = 1$

   • Next state:

     $$P_{next} = 0 \oplus 0 = 0$$

     $$Q_{next} = 0 \oplus 1 = 1$$

     $$R_{next} = 0 \oplus 1 = 1$$

   • State becomes $011$.

2. Clock Pulse 2:

   • Inputs: $T_P = R = 1$, $T_Q = P^{\prime} = 1$, $T_R = Q^{\prime} = 0$

   • Next state:

     $$P_{next} = 0 \oplus 1 = 1$$

     $$Q_{next} = 1 \oplus 1 = 0$$

     $$R_{next} = 1 \oplus 0 = 1$$

   • State becomes $101$.

3. Clock Pulse 3:

   • Inputs: $T_P = R = 1$, $T_Q = P^{\prime} = 0$, $T_R = Q^{\prime} = 1$

   • Next state:

     $$P_{next} = 1 \oplus 1 = 0$$

     $$Q_{next} = 0 \oplus 0 = 0$$

     $$R_{next} = 1 \oplus 1 = 0$$

   • State becomes $000$.

Thus, the sequence of the next three states is 011, 101, 000, which corresponds to option (A).