GATE CSE 2016 Set 1 | Question: 8

Question

We want to design a synchronous counter that counts the sequence $0-1-0-2-0-3$ and then repeats. The minimum number of $\text{J-K}$ flip-flops required to implement this counter is _____________.

Comments

@Shaik Masthan

If the sequence was 0 - 1 - 0 - 2 - 3 .... then we would require 3 FFs right????

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Please update this. The answer is 3 or 4 as per the official key.

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anwer is 4 ,  the sequence has 3 distinct numbers 1,2,3 to store that 2 bit is required and the zeros are 3 distinct zeros as 0-1,0-2,0-3 they are not the same , therefore for 3 distinct zeros you need 2 more bits to store them .

final answer is 2+2 = 4 bits means 4 FF .

as 1 ff stores 1 but of info

Answer 1

We need four JK flipflops.
$0\to 1\to0\to2\to0\to3$
$0000\to0001\to0100\to0010\to1000\to0011$

There are $6$ states and $3$ of them correspond to same states.

• To differentiate between $0,1,2,3$ we need $2$ bits.
• To differentiate between $3$ $0's$ we need another $2$ bits.

So, total $4\text{-bits}\to 4\;\text{FFs}$

Edit:
whether using extra combinational logic for output is allowed in a counter?
Page No. $10/11$ http://textofvideo.nptel.iitm.ac.in/117105080/lec23.pdf or archive

Now, if you see the counters, now a counter we can define in this way the counter is a degenerate finite state machine, where the state is the only output. So, there is no other primary output from this machine, so the counter is defined like that.

ALSO

Page No. $3$ http://textofvideo.nptel.iitm.ac.in/117106086/lec24.pdf or archive

Counter you know what counter it is, that’s what we want we count the output of counter what is the particular count what is the current count that is the output of a count so no external output. The counter is a case of a state machine in which there are no external inputs, no external outputs. 

Page No. $10$ http://textofvideo.nptel.iitm.ac.in/117106086/lec24.pdf or archive

At $35:30$ www[dot]youtube[dot]com/watch?v=MiuMYEn3dpg

Here In Counter, we cannot use external variable, that purpose will be served by FF's only
We have four distinct states $0,1,2,3$ so, $2 FF$ for them for $3\;0's$ to distinguish we need $2$ more $\text{FFs}$ http://www.youtube.com/watch?v=MiuMYEn3dpg

$4\;\text{FF}$ required.

Comments

links are not working

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At 35:30 www[dot]youtube[dot]com/watch?v=MiuMYEn3dpg

Why use [dot] in youtube link and making it non-clickable link?

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@abhilashpanicker29

Can you design such a counter with 4 JK FFs and post pictures of it? I am not able to visualize what you are trying to convey

Answer 2

I am using two AND gates and a NOT gate along with 3 flip flops.

there are 6 unique states. lets assume there is a  synchronous counter the generates below sequence:

100->001->101->010->110->011->100.

Let output of 3 flip flops be S1, S2 , S3. Take them through below circuit  

S1	S2	S3	A	B	C
1	0	0	1	0	0
0	0	1	0	0	1
1	0	1	1	0	0
0	1	0	0	1	0
1	1	0	1	0	0
0	1	1	0	1	1

if we take B C as final output we can generate 0->1->0->2->0->3. 

So I think it is possible with 3 flip flops.

Requesting comments.

Comments

http://nptel.ac.in/courses/117105080/23
OR
https://www.youtube.com/watch?v=2gqsf9N9N_Y

Lec 23 - Digital Systems Design by Prof.D.Roychoudhury, Department of Computer Science and Engineering,IIT Kharagpur

Watch from 26:45... 
Or you can go through the transcribed text here
http://textofvideo.nptel.iitm.ac.in/117105080/lec23.pdf

I am attaching a part from the pdf..
 

 

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it will be 4 FF only.

we can't take any equation to represent the sequence its only binary states of FF's and decimal representation of them.

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how did u make the combinational circuit, just by logic or any standard approach?

Answer 3

IISC Answered it as either 3 or 4 . Both are correct . As seen , 2 bits are required to differentiate 3 Zeros hence 4 bits = 4FF

Also , someone may think it as 6 states and hence 2^3 = 8 >=6 Hence 3 is also correct .

Please note that these questions are repeatedly getting asked . We have to understand that only distinct states can be designed since we dont have dont care input in excitaion table. and hence we should not get confused. First make the states dinsinct with minimum bits. Similar question was asked in GATE 2015 . Please check .

Comments

Shouldn't the answer be 3 then? Since they have asked for minimum number of JK FF required.

Answer 4

2 flip flops are required

Comments

You are right there are only 4 states that is (0,1,2,3) it can be achieved using 2 JK flip flop and some gates.