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When I have an expression such as: $f(x_1,x_2,x_3)= \sum m(1,4,7)+ D(2,5)$

What do I do with the part D(2,5)? Do I make a second k-map just for that term and OR(+) it to the expression or should I just put the terms (2,5) in the original k-map and find the expression that way?


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up vote 2 down vote accepted

In principle, you should make 4 different K-maps trying all possible $0$ and $1$ combinations in the places of don't cares and see which K-map minimization gives the simplest expression.

In practice, it is cumbersome to carry out the principle. So we put a star in the K-map, in the place of don't cares and try to do the computation faster.

The answer to your problem is $f(x_1,x_2,x_3) = x_1\overline{x_2} + x_3\overline{x_2} + x_1x_3$. Among the two don't cares, the don't care $5$ helps, but the don't care $2$ does not help.


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You should use one Karnaugh map with don't cares inputs $x$ as it is shown on picture bellow:

enter image description here

So minimized function is $f(X_1,X_2,X_3)=(X_1\land \neg X_2)\lor (X_1\land X_3)\lor (\neg X_2\land X_3)$

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+1 for the graphic, thank you – Nick Sep 30 '11 at 18:49

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