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#1 2008-09-15 15:32:21

mikau
Member
Registered: 2005-08-22
Posts: 1,504

Karnaugh Maps

Karnaugh maps are not covered in my discrete math text, but my teacher is required to teach them in accordance with an agreement with the computer science department.

Further, my teacher stated that he hates Karnaugh maps, and only went over them briefly because he has to. And I only grasped so much of his lecture.

I can sort of see the logic behind it, but i don't understand the exact rules for how to connect the 1's in the map. Wikipedia says: "the groups may be 4 boxes in a line, 2 boxes high by 4 boxes long, 2 boxes by 2 boxes"
they don't seem to include single 1's in this description. What about if you have something like this:

1 0 1 0
0 1 0 1

is it illegal to connect (1, 0, 1) in the top row, or do you just need the number of 1's to be a power of 2? do the groupings have to consist entirely of 1's?

another question, the map that looks like this:
1 1 1 1
0 1 1 0

can be grouped in many ways. How do you know when you've got the one that most simplifies the resulting boolean expression?

Note thats three question. cool


A logarithm is just a misspelled algorithm.

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#2 2008-09-19 07:44:22

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

Re: Karnaugh Maps

If there are 3  1's in a row,
then you group them with
2 overlapping 2  1's.
For 101, you can just have
two single circles.
But the XOR gate, which is
not the norm can smaller this equation,
but usually you just use
SOP and POS equations.

Last edited by John E. Franklin (2008-09-19 07:45:05)


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