GATE CSE 2015 Set 2 | Question: 7

Question

The minimum number of $\text{JK}$ flip-flops required to construct a synchronous counter with the count sequence $(0, 0, 1, 1, 2, 2, 3, 3, 0, 0, \ldots)$ is _______.

Comments

I have basic doubt here

what is sequence here ?

is it

0, 0, 1, 1, 2, 2, 3, 3, 0, 0 (in this case 4 FF needed )

or

0, 0, 1, 1, 2, 2, 3, 3 (in this case three FF needed)

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@mehul vaidya same doubt occuring here,

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For 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3,... we will require 4 FF. Right?

Answer 1

Found something interesting. Guys at MadeEasy were able to do this with 2 flip flops using an additional clock.

Although I would like to clarify that the answer in the official sheet is 3.

 

Comments

that's why writers on GATE OVERFLOW are much better than made easy/ace/any other coaching institute's writers.

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This is not a classic example of a synchronous counter. Although we could do that but it will become advance level.

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gmrishikumar Couldn't deny it, this is actually very interesting.
 

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i am not able to understand this solution can anyone plz explain me this ?

Answer 2

The patter can be generated by a mod 8 counter so the answer is 3.

Comments

how?? plz explain

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Pls explain it...

Answer 3

This series is equivalent to designing mod-8 counter and considering only the two most significant bits.

000, 001, 010, 011, 100, 101, 110, 111

Hence, 3 FFs are required.

Answer 4

2 should be correct because using some extra gates along with Flip-Flops we can count this sequence.

Comments

Can you kindly elaborate what kind of ckt can be used along with flip-flops to obtain above sequence ? As per my understanding, a frequency divider ckt (divide by 2) can be used, but then it will require one more flipflop along with two output flipflops. Hence 3 flipflops in total. Is there any other method which uses less than 3 flipflops?

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I think as GATE AUTHORITY mentioned the counter as synchronous counter then we can go for the Clock frequency sampling policy(changing its period length).. By this we can accomplish the task with 2 flip flop... BUT MAY BE ITS WRONG.