GATE CSE 2005 | Question: 64

Question

Consider the following circuit:

The flip-flops are positive edge triggered $D$ $\textsf{FF}$s. Each state is designated as a two-bit string $Q_0Q_1$. Let the initial state be $00.$ The state transition sequence is

• A.   
• B.
• C.
• D.

Comments

After first state (0,0) q0 complement =1 and q1complement=1
next value for q0 is complement so its 1 which is also value for xor and another input is 1 which is value of q1complement so result of xor for (1,1) is 0 there for q1 is 0 and state becomes(1,0) how are you people getting 1,1

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(D) is the correct choice!

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what will happen if we take states as q1 qo instead of qo ,q1 in while creating the table

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@svas7246 It will become 00 → 11 → 10 → 01 → 00 if we take states as q1 qo instead of qo ,q1 in while creating the table.

Answer 1

Clearly, $Q_{0}$ alternates in every clk cycle as $Q_{0}'$ is fed as input and it is D flipflop.

$Q_{1}$ becomes $1$ if its prev value and current $Q_{0}$ differs (EXOR). 

So, the sequence of transitions will be $: 00 \rightarrow 11 \rightarrow 01 \rightarrow 10 \rightarrow 00$, (D) choice. 

Comments

your statement : "Q₁ becomes 1 if its prev value and current Q₀ differs (EXOR)." is wrong i guess as q1 becomes 1 if complement of its prev value and current Qo differs  

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how to know about the sequence

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 @Arjun sir,

$Q_1$ becomes $1$ if its prev value and current $Q_0$ differs (EXOR).   

 Shouldn't it be $Q_1$ becomes $1$ if the complement of its previous value and previous $Q_0$ differs (EXOR). ?

Answer 2

Very clearly, Option D.

Answer 3

answer - D

Comments

it is given a in ace pyq