Simple Karnaugh Map Question

jegues

Joined Sep 13, 2010
733
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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blah2222

Joined May 3, 2010
582
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

Georacer

Joined Nov 25, 2009
5,182
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.

zgozvrm

Joined Oct 24, 2009
115
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.
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.