Can KMAP Fully Minimize This SOP Expression?

  • MHB
  • Thread starter shamieh
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  • #1
shamieh
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I used a KMAP and got this as my expression

Is there any way I can minimize this? Maybe I'm just not seeing it. I thought the whole point of a KMAP was to minimize the expression?

Some how the answer is this:

If anyone is interested I had to design a circuit with output f with 4 inputs. I'm supposed to be showing the simplest sum of product expression for f. My f row for my truth table was this:
1
0
0
0

1
1
0
0

1
1
1
0

1
1
1
1Thanks in advance
 
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  • #2
shamieh said:
I used a KMAP and got this as my expression



...

Some how the answer is this:
You can turn the three-variable minterms into two-variable ones, namely, remove from and from .
 
  • #3
Evgeny.Makarov said:
You can turn the three-variable minterms into two-variable ones, namely, remove from and from .
Well I can't combine them because they don't differ by two variables correct? So what minimization "tool" should I use? Should I factor something? I mean how do you just "get rid of them". See what I'm saying? What method I should I be using? Sorry if I sound ignorant.
 
  • #4
When you remove a variable from a three-variable minterm, its representation in the Karnaugh map grows from 2 to 4 cells. However, if the added two cells are already covered by other minterms, then the Boolean function does not change.

In this case, the minterm represents two cells in the middle of column 3 (). When you remove , the result is the complete column 3. But the top cell of column 3 is already covered by , and the bottom cell of column 3 is covered by . So removing from does not change the function. A similar thing happens with turning into .

When reading off a minimal formula from a Karnaugh map, the temptation is always to break the cells corresponding to 1 into disjoint regions. But this results in smaller regions and therefore larger minterms. Instead, one must make regions as large as possible by using the fact that overlap is allowed.
 
  • #5
Awesome explanation! Thanks so much. So it looks like I probably missed a overlapping grouping I could of put together then - thus getting not exactly the complete minimization.
 

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