GATE 2021 IN – Question 46

Digital Electronics · Sequential logic and counters · 2 marks · Multiple choice

The synchronous circuit contains JK and T flip-flops with outputs A and B, respectively, $J_A=A^\prime+B^\prime$, $K_A=A+B$, and $T_B=A$. Starting at $AB=00$, its state sequence is ______.

Diagram for GATE 2021 IN question 46

$00\to01\to10\to11\to00\to\cdots$
$00\to10\to01\to11\to00\to\cdots$
$00\to10\to11\to01\to00\to\cdots$
$00\to01\to11\to00\to\cdots$

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Show answer and explanation

Correct answer: (B) $00\to10\to01\to11\to00\to\cdots$

Explanation

Use A+=JA A′+KA′ A and B+=B⊕A, evaluating both from the same old state. From 00, JA=1,KA=0 gives 10. From 10 the JK toggles A and the T toggles B, giving 01. From 01 A sets and B holds, giving 11. From 11 A resets and B toggles, returning to 00.

Thus **00→10→01→11→00, B**.