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answer is D but I'm getting A. pls tell where am I going wrong?

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Check my approach  aditi19 . I'm getting the same.

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answer key is wrong then? :P
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Sorry I have taken the NOR gate earlier.

It should be option D itself :).

if x=1 then  $0\rightarrow 1\rightarrow 3\rightarrow 0\rightarrow 1\rightarrow 3\rightarrow 0\rightarrow 1\rightarrow 3............$

if x=0 then  $0\rightarrow 1\rightarrow 3\rightarrow1\rightarrow 3\rightarrow 1\rightarrow 3\rightarrow$

one thing we should note is that

after a few clock cycle

means at x=0     after few clock cycle  it will move from 1 to 3 ,3 to 1,1 to 3 .........................

by Boss (10.6k points)

$$D_a = Q_a{\oplus }Q_b\\ D_b = (Q_a.x)'$$

$$Q_a$$ $$Q_b$$ $$Q_a^+$$ $$Q_b^+$$ $$D_a$$ $$D_b$$
0 0 0 1 0 1
0 1 1 1 1 1
1 0 1 x' 1 x'
1 1 0 x' 0 x'

CASE 1: When X = 1,

Only three states are possible for this case.

CASE 2: When X = 0,

Only two states are possible. for this case.

Therefore, OPTION D is Correct.

by Junior (785 points)