Does Variable Order in Karnaugh Maps Affect SOP Solutions?

  • Thread starter EternityMech
  • Start date
In summary: 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.
  • #1
EternityMech
95
0
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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  • #2
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.
 
  • #3
but you are getting two different answers.
 
  • #4
I have no idea what you are talking about.
 
  • #5
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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  • #6
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.
 
  • #7
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?
 
  • #8
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.
 
  • #9
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

[tex]\overline{X}_2\ \overline{X}_1[/tex]
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 [itex]y_3y_2y_1y_0[/itex] and in that order.
 
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1. What are Karnaugh diagrams and how are they used in science?

Karnaugh diagrams, also known as K-maps, are graphical tools used to simplify logical expressions and aid in the design and analysis of digital circuits. They are commonly used in the field of computer science and electrical engineering.

2. How do you create a Karnaugh diagram?

A Karnaugh diagram is created by arranging the inputs and outputs of a logical expression in a grid-like format, with each square representing a possible combination of inputs. The squares are then filled in with 1s and 0s based on the truth table of the expression.

3. What are the benefits of using Karnaugh diagrams?

Karnaugh diagrams are useful for simplifying complex logical expressions, reducing the number of gates needed in a digital circuit, and easily identifying any redundancies or errors in the design. They also provide a visual representation of the logic, making it easier to understand and troubleshoot.

4. Can Karnaugh diagrams be used for any type of logical expression?

Karnaugh diagrams are most commonly used for expressions with 2, 3, or 4 variables, but they can be used for expressions with any number of variables. However, as the number of variables increases, the diagram becomes more complex and less efficient.

5. Are there any limitations to using Karnaugh diagrams?

While Karnaugh diagrams are a powerful tool, they have some limitations. They can only be used for simplifying logical expressions with binary inputs and outputs. They also do not provide a unique solution, meaning there may be multiple possible ways to simplify the expression using the diagram.

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