# 5 Variable Karnaugh Map

#### jegues

Joined Sep 13, 2010
733
See figure attached for problem statement, as well as my attempt.

This is my first time attempting a 5 variable K-map, but I followed the tutorial on the site and this is what I came up with.

Can anyone see any problems with my simplified SOP? Or my K-map in general?

I'm not sure if this is right, but I'd like to know before I proceed with the simplified POS expression, as well as trying to simplify it even further using functional decomposition.

Thanks again!

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#### Georacer

Joined Nov 25, 2009
5,182
D is for Don't Care, right?

I used a software to check on your answer and it replied:
$$\bar{x_2}\bar{x_3}{x_4}\bar{x_5}+\bar{x_1}\bar{x_2}x_3 x_5 +x_2x_3x_4\bar{x_5}+x_1x_2x_3x_4+x_1\bar{x_2}\bar{x_3}x_4+\bar{x_2}x_3\bar{x_4}$$

I guess one of us is wrong. Here is the PrintScreen (well, the Snagit):

I haven't read your method on solving a 5-variable Carnot map. Personally I have never done so. So I suggest you revise your method. Propably you must have misunderstood something.

#### jegues

Joined Sep 13, 2010
733
D is for Don't Care, right?

I used a software to check on your answer and it replied:
$$\bar{x_2}\bar{x_3}{x_4}\bar{x_5}+\bar{x_1}\bar{x_2}x_3 x_5 +x_2x_3x_4\bar{x_5}+x_1x_2x_3x_4+x_1\bar{x_2}\bar{x_3}x_4+\bar{x_2}x_3\bar{x_4}$$

I guess one of us is wrong. Here is the PrintScreen (well, the Snagit):View attachment 22985

I haven't read your method on solving a 5-variable Carnot map. Personally I have never done so. So I suggest you revise your method. Propably you must have misunderstood something.

Hmph. I read the method right off this site, maybe I misunderstood something.

Can someone give me a better idea of where I went wrong?

If I don't know what I did wrong, then I don't know what to do different next time.

Thanks again.

#### t_n_k

Joined Mar 6, 2009
5,447
I had a go following the AAC layout for the map ...

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#### Georacer

Joined Nov 25, 2009
5,182
Yes, tnk found the same solution as me, but he did a transformation of the variables (unintentionaly). I 'm not sure if this is ok. Only if you rename your variables from the beginning the solutions will match.

In any case, we have ensured that your application of the Carnot map was the problematic spot.

#### jegues

Joined Sep 13, 2010
733
Yes, tnk found the same solution as me, but he did a transformation of the variables (unintentionaly). I 'm not sure if this is ok. Only if you rename your variables from the beginning the solutions will match.

In any case, we have ensured that your application of the Carnot map was the problematic spot.

I'm trying to do another Karnot map attempt but I dont know which squares represent which minterms, I could look at the binary value for each one and place a 1 there but that takes a long time.

Is there a quick way to see what minterms are where?

EDIT: Nevermind I can see it now on tnk's map

Thank you! I was finally able to obtain the same answer.

I had placed my 1's and x's in the wrong place on my map, but now I know where each minterm goes so I can do it.

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#### t_n_k

Joined Mar 6, 2009
5,447
Hi Georacer,

I believe I followed the convention outlined here ..

My pdf attachment also includes a verification of the minterms for SOP notation.

I've included a check for your equation which doesn't tally with the above convention. I think you may have transformed the variables.

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#### Georacer

Joined Nov 25, 2009
5,182
It seems I am so sloppy these days I can't read my own notes. I had created a text file RIGHT NEXT to the .exe, specifying explicitly that the correct order of the variables is EABCD, since the 5-variable version of the software is faulty (hey, it's a freeware).

So, yes, all the cudos to you.

P.S. I just discovered that it is spelled Karnaugh and not Carnot. It was a shocking discovery for a spelling maniac like me.

#### t_n_k

Joined Mar 6, 2009
5,447
Hi Georacer,

You should see some of my 'Bloopers'!

In the end it was all about which variable was the least significant bit. As you pointed out in an earlier post the method was fine. Looks like the OP has the problem under control - which is a good outcome.

#### Georacer

Joined Nov 25, 2009
5,182
So we can give ourselves a pat in the back and get us a beer!

#### t_n_k

Joined Mar 6, 2009
5,447
So we can give ourselves a pat in the back and get us a beer!
Yes indeed - Cheers!