GATE 2017 CS (CS2) – Question 52

Digital Logic · Sequential Circuits · 2 marks · Multiple choice

A synchronous two-bit saturating up-counter has transitions 00→01,01→10,10→11,11→11. With T flip-flops, find T₁,T₀.

$T_1=Q_1Q_0,\quad T_0=\bar Q_1\bar Q_0$
$T_1=\bar Q_1Q_0,\quad T_0=\bar Q_1+\bar Q_0$
$T_1=Q_1+Q_0,\quad T_0=\bar Q_1+\bar Q_0$
$T_1=\bar Q_1Q_0,\quad T_0=Q_1+Q_0$

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Correct answer: (B) $T_1=\bar Q_1Q_0,\quad T_0=\bar Q_1+\bar Q_0$

Explanation

For a T flip-flop, $T=Q\oplus Q^+$. Q₁ toggles only for current state 01, giving T₁=Q̄₁Q₀. Q₀ toggles in 00,01,10 but stays in 11, giving T₀=¬(Q₁Q₀)=Q̄₁+Q̄₀. This is B.

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