# GATE CSE 2021 Set 1 | Question: 28

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Consider a $3$-bit counter, designed using $T$ flip-flops, as shown below:

Assuming the initial state of the counter given by $\text{PQR}$ as $000$, what are the next three states?

1. $011,101,000$
2. $001,010,111$
3. $011,101,111$
4. $001,010,000$

recategorized ago

P Q R
0 0 0
0 1 1
1 0 1
0 0 0

If P is 0, then Q will toggle in next clock cycle.

If Q is 0, then R will toggle in next clock cycle.

If R is 1, then P will toggle in next clock cycle.

Using these rules, the transition is shown in the table.

Option A

From the given 3 state T flip flop the next input sequence are as follows:

• $T_P=R$
• $T_Q=\bar P$
• $T_R=\bar Q$
 Initial State Current input Next State P Q R $T_P$ $T_Q$ $T_R$ $P^+$ $Q^+$ $R^+$ 0 0 0 0 1 1 0 1 1 0 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 0 0

in T flip flop for low input (0)the next state is $Q_n$(current state), for high input(1) it toggle/complement the present state($\bar Q_n$)

$011,101,000$ option A is corret.

ANS IS A.

011, 101, 000.

INITIAL VALUE OF PQR = 000.

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