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

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answer is D

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 .........................

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

$$Q_a$$ | $$Q_b$$ | $$Q_a^+$$ | $$Q_b^+$$ | $$D_a$$ | $$D_b$$ |
---|---|---|---|---|---|

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.**