GATE CSE 2014 | Set 3 | Question: 45

Question

The above synchronous sequential circuit built using JK flip-flops is initialized with $Q_2Q_1Q_0 = 000$. The state sequence for this circuit for the next $3$ clock cycles is

• A. $001, 010, 011$
• B. $111, 110, 101$
• C. $100, 110, 111$
• D. $100, 011, 001$

Comments

$J_2=\bar Q_1,K_2=Q_0,J_1=Q_2,K_1=\bar Q_2,J_0=Q_1,K_0=\bar Q_0$

it is a mod 5 counter whose sequence is :$000\rightarrow100\rightarrow110\rightarrow111\rightarrow011$

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Here is the Explanation 

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Answer 1

Option C

Answer 2

as simple as possible

Comments

perfect solution

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Better than most of the soultion over here..

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very very good solution, thank you

Answer 3

JK ff truth table---

j	k	Q
0	0	Q0
1	0	1
0	1	0
1	1	Q0’

Initially Q2Q1Q0=000 Present state FF input                   Next state

Q2	Q1	Q0	J2	K2	J1	K1	J0	K0	Q2	Q1	Q0
0	0	0	1	0	0	1	0	1	1	0	0
1	0	0	1	0	1	0	0	1	1	1	0
1	1	0	0	0	1	0	1	1	1	1	1

So ans is ( C) part.

Comments

@ bhuv 

It is Synchronous circuit.

In synchronous counter, all the flip-flops connected in the circuit are triggered by a common pulse signal and hence change states simultaneously, 

so when u solve this problem ,  solve simultaneously all of them then option c is coming as an answer . That means it is synchronous .

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@bikram sir

Yes, thnx for confirming. They discussed above that it is asynchronous. But I too have opinion that it is synchronous.

But is it not a necessary condition that a common clock pulse connected to all flip flops must be there, but this is achieved here indirectly. Is there any other variations possible like this to be synchronous ckt.

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@ bhuv

See the question, it says "The above synchronous sequential circuit .."

so that means we have to assume that this circuit is synchronous and proceed accordingly..

Answer 4

Although given answer is correct one thing worth to be noted here as it's "asynchronous circuit" and given "sign" of clock plus (-o>) which is "negative level trigger" {1-->0}
So when Q2 value change form 1-->0 Q1 gets complemented

Comments

it's synchronous

Answer 5

 

option c

Answer 6

SIMPLEST AND EASIEST WAY TO SOLVE THESE PATTERN QUESTIONS IS && CORRECT ANSWER IS -C✅