GATE 2024 EC – Question 42

Digital Circuits · Sequential Circuits · 2 marks · Multiple choice

The sequence of states ($Q_1Q_0$) of the given synchronous sequential circuit is ______.

$00\to10\to11\to00$
$11\to00\to10\to01\to00$
$01\to10\to11\to00\to01$
$00\to01\to10\to00$

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Correct answer: (B) $11\to00\to10\to01\to00$

Explanation

From the figure, $T_1=Q_1+\overline{Q_0}$ and $T_0=Q_1+Q_0$; a T flip-flop toggles when its input is 1. State 00: $T_1=1,T_0=0\Rightarrow10$. State 10: $T_1=1,T_0=1\Rightarrow01$. State 01: $T_1=0,T_0=1\Rightarrow00$. State 11: $T_1=1,T_0=1\Rightarrow00$. So the sequence is $11\to00\to10\to01\to00$.