Official PYQ · 2017Set 2 · Q42Sequential CircuitsMCQ1 mark

GATE CS 2017 Set 2 Q42 — Sequential Circuits

The next state table of a $2-$ bit saturating up-counter is given below.

$\begin{array}{cc|cc} Q_1 & Q_0 & Q_1^+ & Q_0^+ \\ \hline 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 0 \\ 1 & 0 & 1 & 1 \\ 1 & 1 & 1 & 1 \end{array}$

The counter is built as a synchronous sequential circuit using $T$ flip-flops. The expressions for $T_1$ and $T_0$ are

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Answer: B

To find the expressions for the flip-flop inputs $T_1$ and $T_0$ , we use the characteristic equation of a $T$ flip-flop, which is given by:

T = Q \oplus Q^+

Using this relation, we can determine the values of $T_1$ and $T_0$ for each state transition:

$Q_1$	$Q_0$	$Q_1^+$	$Q_0^+$	$T_1 = Q_1 \oplus Q_1^+$	$T_0 = Q_0 \oplus Q_0^+$
0	0	0	1	$0 \oplus 0 = 0$	$0 \oplus 1 = 1$
0	1	1	0	$0 \oplus 1 = 1$	$1 \oplus 0 = 1$
1	0	1	1	$1 \oplus 1 = 0$	$0 \oplus 1 = 1$
1	1	1	1	$1 \oplus 1 = 0$	$1 \oplus 1 = 0$

From the table, $T_1$ is high only when $Q_1 = 0$ and $Q_0 = 1$ .

T_1 = \bar{Q_1}Q_0

From the table, $T_0$ is high for the states $00$ , $01$ , and $10$ , and low only when $Q_1 = 1$ and $Q_0 = 1$ . This represents a NAND operation:

T_0 = \overline{Q_1 Q_0} = \bar{Q_1} + \bar{Q_0}

Thus, the correct expressions are:

T_1 = \bar{Q_1}Q_0, \quad T_0 = \bar{Q_1} + \bar{Q_0}

This matches Option B.

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Published 10 Oct 2026

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