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Don’t care condition at K-MAP

Don’t care condition:

In two cases don’t care conditions can occur in Boolean function: 

1. When outputs do not matter for a set of the input sequences.

2. Input sequence that is never occurring or valid for such a Boolean function.

Example:

We consider a two variables truth table:

If we want to write a truth table of the above function.

In that case, 1 (01) is a don’t care term because for term 1 output is not defined, it may be 1 or 0. 

Because of in don’t care condition we can put either 1 or 0, we can use it at K-MAP to minimize Boolean function.

We use don't care conditions to form a grouping or larger grouping of the variables at K-MAP to minimize Boolean expression better way.

K-MAP of the above Boolean Function:

Here we have taken don’t care condition as 1 to make a group of variables.

From K-MAP:

Note: But we use don’t care terms to group variables when it is required otherwise we neglect it as the black cell. 

Another example where we see sometimes we use don’t care conditions if necessary.

K-MAP of above Boolean Function:

Here, one don’t care term  3 (11) is not grouped, as we will include don’t care terms only it is required to group variables for minimization.