All About Circuits Forum Synchronous 3-Bit JK Flip-Flop Counter
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#1
08-21-2010, 09:57 PM
 ublu32 New Member Join Date: Aug 2010 Posts: 9
Synchronous 3-Bit JK Flip-Flop Counter

Hi,
I'm studying for exams soon and trying to do the following question;
Design a synchronous circuit using JK F/F to produce 0,3,5,6,1,7,4,2,0...(Binary)

My knowledge of this course is very basic I'm afraid so I'd appreciate any help I can get! I'm confused as to whether just flip-flops and AND gates is enough? Can somebody give me an idea of where to start or what I need to do, I'm really confused...!

Thanks guys!
#2
08-22-2010, 12:41 AM
 beenthere Senior Member Join Date: Apr 2004 Location: Missouri, USA (GMT -6) Posts: 15,815 Blog Entries: 10

Grab a data sheet for a 74LS161. That's a 4 bit synchronous counter with JK's inside. That will show how to make a counter.
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#3
08-22-2010, 03:14 AM
 ublu32 New Member Join Date: Aug 2010 Posts: 9

Ok, I've tried to figure this out and come up with this kind of circuit, but I'm not sure its right? Hopefully I'm on the right track though, could domebody have a look and let me know where I'm going wrong, obv the flip flops would all be connected to a clock, I just havent drawn it in....?
Attached Images
 JK.jpg (48.9 KB, 57 views)
#4
08-22-2010, 11:53 AM
 Georacer Super Moderator Join Date: Nov 2009 Location: Athens, Greece (GMT +2) Posts: 4,875

Please be more careful with what you write. If I'm correct you don't need a counter (0,1,2,3...) but a layout that will go through the sequence you mentioned (0,3,5,6,1,7,4,2), am I right? Do you have access to the textboot "Digital Design" of M. Mano? It will help a lot. Do you have any experience with FSM's (Finite State Machines)
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#5
08-22-2010, 12:25 PM
 ublu32 New Member Join Date: Aug 2010 Posts: 9

My apologies, I assumed that as it is counting but up and down it was a counter! As I said, my knowledge is pretty basic. This is a module which I must pass to get into my final year of a mechanical eng. degree. I missed most of this module due to illness so I'm struggling with this repeat exam as I'm pretty much on my own! I'm afraid I don't have access to this book at the minute, unless its available online perhaps?
#6
08-22-2010, 01:07 PM
 Georacer Super Moderator Join Date: Nov 2009 Location: Athens, Greece (GMT +2) Posts: 4,875

Let's start from the basics. You have numbers that reach up to 7, so you need 3 flip flops.
1. Build a table that will have the following columns: The first will be named "Current State". Fill it will all the binary numbers from 0 to 7. This column will be divided in three, one digit for each flip flop.
2. Next, create a column wich will be naded "Next State". Fill it with the binary number wich is next in your sequence, after the number in the same row in the previous column. Again, separate the digits to correspond to a flip flop.
What you have now is for each flip flop a table that describes all the previous states and all the next states.
3. Create another 6 columns, 2 for each ff. These will correspond to the J and K inputs. Fill them adequately so that from the "previous" column, you get the "next" column. Don't forget to use "X" (Don't care) terms. For example, for the FF1, if your "previous" state is 0 and you want to drive it to 1 you want J,K to be 1,X.
What you have now is essentially 6 truth tables, 2 for each FF, one for each input. These truth tables have 3 inputs, the current state of the FF's (the number you are at).
4. The logic function and the corresponding gate circuit you will extract, will then be inserted before each J and K terminal of the FF's to give you the complete circuit.
I am googling for a ready-made table as an example but still no luck.
Do you understand everything? Are you stuck at any step?
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I am a prisoner of high standards and low social skills
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I wish I was the best at what I would do, and what I would do wouldn't be pretty.
#7
08-22-2010, 01:15 PM
 ublu32 New Member Join Date: Aug 2010 Posts: 9

Thank you very much Georacer for your reply! This has cleared it up a great deal for. Before, for the present state i was starting from 0 and going down along the sequence, then had the next state as the following number in the sequence, which now appears to be wrong! I shall try it again, and maybe quickly post my attempt!
#8
08-22-2010, 01:18 PM
 Georacer Super Moderator Join Date: Nov 2009 Location: Athens, Greece (GMT +2) Posts: 4,875

Here, I found a paper with a lot of examples.
Try this http://myweb.dal.ca/gonzalej/Teaching/ECED2200/FSM.pdf
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I am a prisoner of high standards and low social skills
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I wish I was the best at what I would do, and what I would do wouldn't be pretty.
#9
08-22-2010, 02:13 PM
 ublu32 New Member Join Date: Aug 2010 Posts: 9

Ok, so trying to stick to your method you gave, I tried it and came up with this, but im not so sure its right?

Is it correct to go from P/S of lets say 000 to N/S 011 to give me 3, and then revert to P/S 001 to N/S 101 to give me 5 in the sequence? :-/

sorry, i know I must be greatly annoying! Really appreciate the help!

P.S - I also think J1 should be Q2'Q3 + Q2Q3'
Attached Images
 JK FLOP.png (33.4 KB, 57 views)

Last edited by ublu32; 08-22-2010 at 02:19 PM. Reason: mistake?
#10
08-22-2010, 02:42 PM
 Georacer Super Moderator Join Date: Nov 2009 Location: Athens, Greece (GMT +2) Posts: 4,875

I'm afraid it's not correct yet. For example in row #4 right to the binary 2, according to your sequence you need to place number 0 not 5.
Also be careful on how you fill a Carnot map. The correct way for a 3-variable table is shown in the attachment I include.
Study a little more on the Carnot Maps. This knowledge is never waisted.
Attached Images
 Truth Table.png (2.3 KB, 48 views) Carnot Map.png (1.4 KB, 42 views)
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I am a prisoner of high standards and low social skills
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I wish I was the best at what I would do, and what I would do wouldn't be pretty.

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