# Simple Karnaugh Map Question

Discussion in 'Homework Help' started by jegues, Dec 9, 2010.

1. ### jegues Thread Starter Well-Known Member

Sep 13, 2010
735
45
I'm confused about an aspect of Karnaugh maps.

When we have a map like indicated in the figure attached, how do we group appropriately?

I've always tried to group every 0 in the largest group possible, regardless whether or not the other 0's in the same group have been grouped already.

This will create redundant terms, correct?

How do I identify this and eliminate them?

The expression I come up with, with my groupings is,

$(x_{2} + x_{0})(x_{2} + x_{1})( \bar{x_{3}} + x_{0})(x_{1} + \bar{x_{0}} + x_{3})$

Thanks again!

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2. ### blah2222 Well-Known Member

May 3, 2010
574
36
That's fine, might be more intuitive to do the Sum of Products (all the 1's, if the blanks are all 1's with no don't cares).

F = x1x0 + x0'x2x3' + x0x2x3

3. ### Georacer Moderator

Nov 25, 2009
5,151
1,266
If you group the 1s (assuming that they are the rest of the squares), you need only 3 groups with less overlay, but with smaller groups.

I don't think overlaying hurts. If I grouped the 0s I would do it the same way you did.

4. ### zgozvrm Active Member

Oct 24, 2009
115
2
That's correct! You want to get the fewest number of groups that contain all the 0's (or 1's). If a "straggler" can be grouped in a small group or a large group, use the large group.