Does Variable Order in Karnaugh Maps Affect SOP Solutions?

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Discussion Overview

The discussion revolves around the impact of variable order in Karnaugh Maps (K-maps) on Sum of Products (SOP) solutions. Participants explore whether different arrangements of variables lead to different results in K-map representations and the implications for truth tables.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant questions if the arrangement of variables (x1x2 horizontal and x3x4 vertical versus x2x1 and x4x3) affects the resulting SOP expressions derived from K-maps.
  • Another participant asserts that the drawing method is irrelevant as long as the labeling is consistent, suggesting that the interpretation of the labels is what matters.
  • There is a concern raised about obtaining different answers from the two K-map configurations, indicating a potential misunderstanding in filling out the maps.
  • A participant emphasizes that if the maps are filled in correctly, they should represent the same functions, regardless of the variable arrangement.
  • Questions arise about how to start the truth table and whether the minterms are fixed, indicating uncertainty in the mapping process.
  • One participant suggests that the expression for one of the K-maps should be corrected to properly reflect the variables involved.

Areas of Agreement / Disagreement

Participants express differing views on whether the arrangement of variables affects the K-map results, with some asserting it does not matter while others highlight discrepancies in the outputs. The discussion remains unresolved regarding the correct approach to filling out the K-maps and the implications for truth tables.

Contextual Notes

There are limitations in understanding how to properly fill in the K-maps based on variable arrangement and the implications for truth tables, which remain unclear among participants.

EternityMech
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Is there a difference between drawing one that goes x1x2 horizontal and x3x4 vertical or one that goes x2x1 and x4x3?

suppose you are doing a SOP and u got Epsilon(m0,m2,m8,m12)

then for the first map u get f=x3'x4' but the other diagram gives f=x2'x1'

does it matter or is it all the same?
 
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In my experience, it is irrelevant how you draw the map; what matters is that you label it correctly based on your drawing and then consistently follow the labels.

So, you if you had two columns you could label the first one A (implying that the second r is NOT-A) or you could label the second one A (implying that the first one is NOT-A). It doesn't matter.
 
but you are getting two different answers.
 
I have no idea what you are talking about.
 
which one is correct?

A:
[PLAIN]http://img41.imageshack.us/img41/7519/73372374.jpg

B:
[PLAIN]http://img684.imageshack.us/img684/7462/73298056.jpg i guess the problem is how do u write the truthtable u start with x4 or with x1 on the right side...
 
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Your maps describe totally different functions, so NATURALLY they are different in the Karnaugh map. You don't seem to understand how to fill in the maps if you are trying to map the same thing in both versions.

If filled in correctly, both versions would show the same functions.
 
phinds said:
Your maps describe totally different functions, so NATURALLY they are different in the Karnaugh map. You don't seem to understand how to fill in the maps if you are trying to map the same thing in both versions.

If filled in correctly, both versions would show the same functions.

yes but the problem is how do u start the truthtable? are the m's fixed or not?
 
What do you mean "yes but" ? "Yes but" says to me that you understand that you made a mistake. Fix the mistake and your question goes away.
 
look the question is:

create a K-map of SOP E m(0,4,8,12)

how would the map look like A or B and are the ms fixed
 
  • #10
EternityMech said:
create a K-map of SOP E m(0,4,8,12)

Sorry, I don't have a clue what that means. I use Kmaps for boolean expressions like

A and NOT B and C and NOT D
 
  • #11
EternityMech said:
which one is correct?

A:
[PLAIN]http://img41.imageshack.us/img41/7519/73372374.jpg

B:
[PLAIN]http://img684.imageshack.us/img684/7462/73298056.jpg


i guess the problem is how do u write the truthtable u start with x4 or with x1 on the right side...

Your expression for the second one should be

\overline{X}_2\ \overline{X}_1
instead of having the bar over the whole thing. Then they are both correct. While you can put the variables in in any order, I would suggest putting them in the same order that you would write a binary number, with the least significant bit on the right. I would have called the variables y_3y_2y_1y_0 and in that order.
 
Last edited by a moderator:

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