# I have a problems with K-Map minimization

Discussion in 'Electronics Homework Help' started by alK, May 17, 2012.

1. ### alK

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May 17, 2012
Hello!

I'd solved the K-Map, but my professor makes me look for the most minimal form, telling me that my minimization is not minimal form. I can't understand why this minimization is not most minimal. Anybody can explain me what I am doing wrong?

K-Map

Last edited: May 17, 2012
2. ### alK

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May 17, 2012
Oops, theK-Map picture was not attached. How to be?

3. ### alK

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May 17, 2012
Where I can store it?
How can I store it on the forum?
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Picture hosting preblem solved.
K-Map minimization problem is still actual

Last edited: May 17, 2012
4. ### alK

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May 17, 2012
Is there any recomended picture hosting to store images?
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Picture hosting problem solved, K-Map proble is still active.

Last edited: May 17, 2012
5. ### (*steve*)¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥdModerator

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Jan 21, 2010
You can upload small images to this site.

Check out the attach icon in the editor (looks like a paper-clip). You may need to press "advanced" to see it.

6. ### alK

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May 17, 2012
Thank you, Steve, for help
Currently I solved the image hosting problem, but Kmap solving problem is still actual

25,505
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8. ### alK

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May 17, 2012
No problems, you can't know all. Thanks for help!

9. ### alK

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May 17, 2012
I tried to make copy of image that holded on this site.
It seems to be working.

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10. ### timothy48342

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Nov 28, 2011
Glad to see you got the image posting issue worked out.

Someone might be able to find a way to minimize it just from the formula.

One thing I noticed also is that there are a whole lot less zeros than ones. The purple rectangles isolate the ones along with the don't care's away from the zeros. What about drawing rectangles to isolate the zeros and don't cares away from the ones. I would think that would give you less purple rectangles as a starting point. You would have to remember that your dealing with the false condition and do a not to the result appropriately, but still seems like it would start out closer to a short final formula.

--tim

11. ### (*steve*)¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥdModerator

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Jan 21, 2010
My guess is this:

That's my guess, but this is the very first Karnaugh map I've ever drawn, so trust me about as far as you can throw me.

Perhaps you can write the logic for yours and mine and see who's is simpler?

And maybe someone who really knows will give a good answer

p.s. I learned all I know about these things from this video about 5 minutes ago. (So blame the video for any errors )

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12. ### gorgon

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Jun 6, 2011
Have you got the equations or the truth table of the signals in question? I also wonder about all the '-' squares, are they 'don't care' or what?

If this is the case I would think that an inverse solution is what the professor is seeking. You have far less '0's than '1's in the diagram. But all depends on the equations.

TOK

Last edited: May 17, 2012
13. ### timothy48342

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Nov 28, 2011
Yes the "-" is a "don't care"

I was thinking the same thing as gorgon about taking advantage of the inbalance between the number of 1's and 0's. However I have to take that back. Here's why.
The final truth formula will a series of terms. Each term OR'd together. Within each term will be one or more expressions AND'ed together.
For instance we might have Q = (A AND B) OR ((NOT A) AND C) OR (NOT C)
That is 3 terms.

If we were concentrating on the 0's we might have ended up with that as a FALSE formula we would still have to NOT it. So the truth of Q would be:
Q = NOT((A AND B) OR ((NOT A) AND C) OR (NOT C))
But that "NOT" at the beginning can't stay there. When we force this into the proper form of TERM OR TERM OR ... that "NOT" might make things real messy. It might or it might not, but the point is we don't know, so just starting out with isolating the 1's rather than the 0's is the way to go.

About the request to the OP to post his answer... I asked for that, too, but now I have to take that back as well. I think the image that the OP posted IS HIS ANSWER. The next step after doing a Karnaugh Map would be to write the truth expression. (Q=...) Each grouping in the K-map will be an term in that expression, but in this step I think the assignment is to just circle the best groupings.

Steve! Nice what you did with the one red block wrapping around all 4 corners. And you got it to 5 groups.

I think I see one more way to simplify it. If your purple group is shifted down by one row, it will snag the 1 in the top row. And then the blue group can be eliminated.

Down to 4 groupings.
-t

14. ### alK

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May 17, 2012
'-' - don't cares
I need to find minimal form as sum of products (minimize by 1)

15. ### alK

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May 17, 2012
Thank you
Red's are good, and it's an idea that I'd missed, but blue is wrong cause coverage must cover cells in order of 2^N.

16. ### alK

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May 17, 2012
That is a lot of mistakes in my first solution - I've lost some obvious things.

Thank *steve* with reds - I found that idea that the coverages can be merged. Better solution that was accepted:

Thanks for help!!

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17. ### alK

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May 17, 2012
Solution was found then I tried to write the formula. Some inputs obvious present in terms in direct form and in inverse form, and they must be merged

18. ### (*steve*)¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥdModerator

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Jan 21, 2010
Check out what Timothy said about dropping one group down by one to eliminate another group.

And my blue is 8 cells, that's 2^3... bit it is the one which can be totally eliminated.

Hey, this Karnaugh mapping is interesting.

Say, alK, why don't you help educate me by explaining what these things are used for?

19. ### alK

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May 17, 2012
Timothy is not right, it is impossible to make it, because it will produce error.

The same thing, blue is bad aligned. Can you write the term for this coverage?

I'm studing k-mapping too

20. ### (*steve*)¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥdModerator

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Jan 21, 2010
Really? Seems correct to me.

(X5 AND NOT X4) AND ((X1 AND X3) OR NOT (X2 OR X3))

X5 AND NOT (X2 OR X3)