Dont care condition-Karnaugh map
Suppose you have four inputs (\$Q_A\$, \$Q_B\$, \$Q_C\$, and \$Q_D\$) and four outputs (\$T_A\$, \$T_B\$, \$T_C\$, and \$T_D\$) that depend upon these inputs in the following way:

$$\begin{array}{rl}
\begin{smallmatrix}\begin{array}{r|cccc}
T_D&amp;\overline{Q_B}\:\overline{Q_A}&amp;\overline{Q_B}\: Q_A&amp;Q_B \:Q_A&amp;Q_B \:\overline{Q_A}\\
\hline
\overline{Q_D}\:\overline{Q_C}&amp;1&amp;1&amp;x&amp;x\\
\overline{Q_D}\:Q_C&amp;x&amp;x&amp;1&amp;x\\
Q_D\: Q_C&amp;0&amp;0&amp;0&amp;0\\
Q_D\:\overline{Q_C}&amp;0&amp;x&amp;0&amp;x
\end{array}\end{smallmatrix}
&amp;
\begin{smallmatrix}\begin{array}{r|cccc}
T_C&amp;\overline{Q_B}\:\overline{Q_A}&amp;\overline{Q_B}\: Q_A&amp;Q_B \:Q_A&amp;Q_B \:\overline{Q_A}\\
\hline
\overline{Q_D}\:\overline{Q_C}&amp;0&amp;1&amp;x&amp;x\\
\overline{Q_D}\:Q_C&amp;x&amp;x&amp;x&amp;x\\
Q_D\: Q_C&amp;0&amp;1&amp;1&amp;0\\
Q_D\:\overline{Q_C}&amp;0&amp;1&amp;1&amp;0
\end{array}\end{smallmatrix}\\\\
\begin{smallmatrix}\begin{array}{r|cccc}
T_B&amp;\overline{Q_B}\:\overline{Q_A}&amp;\overline{Q_B}\: Q_A&amp;Q_B \:Q_A&amp;Q_B \:\overline{Q_A}\\
\hline
\overline{Q_D}\:\overline{Q_C}&amp;1&amp;0&amp;x&amp;x\\
\overline{Q_D}\:Q_C&amp;x&amp;x&amp;x&amp;x\\
Q_D\: Q_C&amp;1&amp;x&amp;0&amp;1\\
Q_D\:\overline{Q_C}&amp;1&amp;0&amp;0&amp;1
\end{array}\end{smallmatrix}
&amp;
\begin{smallmatrix}\begin{array}{r|cccc}
T_A&amp;\overline{Q_B}\:\overline{Q_A}&amp;\overline{Q_B}\: Q_A&amp;Q_B \:Q_A&amp;Q_B \:\overline{Q_A}\\
\hline
\overline{Q_D}\:\overline{Q_C}&amp;1&amp;1&amp;x&amp;x\\
\overline{Q_D}\:Q_C&amp;x&amp;x&amp;x&amp;x\\
Q_D\: Q_C&amp;1&amp;1&amp;1&amp;1\\
Q_D\:\overline{Q_C}&amp;1&amp;1&amp;1&amp;1
\end{array}\end{smallmatrix}
\end{array}$$

The \$x\$ in the above tables just means "don't care" or, put another way, "doesn't matter whether it is a 1 or a 0 in this case."

This often happens when there are circumstances which don't occur (or should not occur), anyway. And since it won't happen, you don't care about the output value in that case.

For example, suppose you wanted to make a "decade counter" that went from 0 to 9 and then back to 0, again. This counter requires four output bits because 9 is "1001" and that needs four bits. But you will never output "1100" (12) because the counter will never count that high. So the internal logic that helps the counter perform its function may have cases where the situation won't occur and, therefore, you don't care since it won't happen.

Anyway, take the above set of four tables and lets assign "convenient values" where we think it will help simplify the final logic:

$$\begin{array}{rl}
\begin{smallmatrix}\begin{array}{r|cccc}
T_D&amp;\overline{Q_B}\:\overline{Q_A}&amp;\overline{Q_B}\: Q_A&amp;Q_B \:Q_A&amp;Q_B \:\overline{Q_A}\\
\hline
\overline{Q_D}\:\overline{Q_C}&amp;1&amp;1&amp;1&amp;1\\
\overline{Q_D}\:Q_C&amp;1&amp;1&amp;1&amp;1\\
Q_D\: Q_C&amp;0&amp;0&amp;0&amp;0\\
Q_D\:\overline{Q_C}&amp;0&amp;0&amp;0&amp;0
\end{array}\end{smallmatrix}
&amp;
\begin{smallmatrix}\begin{array}{r|cccc}
T_C&amp;\overline{Q_B}\:\overline{Q_A}&amp;\overline{Q_B}\: Q_A&amp;Q_B \:Q_A&amp;Q_B \:\overline{Q_A}\\
\hline
\overline{Q_D}\:\overline{Q_C}&amp;0&amp;1&amp;1&amp;0\\
\overline{Q_D}\:Q_C&amp;0&amp;1&amp;1&amp;0\\
Q_D\: Q_C&amp;0&amp;1&amp;1&amp;0\\
Q_D\:\overline{Q_C}&amp;0&amp;1&amp;1&amp;0
\end{array}\end{smallmatrix}\\\\
\begin{smallmatrix}\begin{array}{r|cccc}
T_B&amp;\overline{Q_B}\:\overline{Q_A}&amp;\overline{Q_B}\: Q_A&amp;Q_B \:Q_A&amp;Q_B \:\overline{Q_A}\\
\hline
\overline{Q_D}\:\overline{Q_C}&amp;1&amp;0&amp;0&amp;1\\
\overline{Q_D}\:Q_C&amp;1&amp;0&amp;0&amp;1\\
Q_D\: Q_C&amp;1&amp;0&amp;0&amp;1\\
Q_D\:\overline{Q_C}&amp;1&amp;0&amp;0&amp;1
\end{array}\end{smallmatrix}
&amp;
\begin{smallmatrix}\begin{array}{r|cccc}
T_A&amp;\overline{Q_B}\:\overline{Q_A}&amp;\overline{Q_B}\: Q_A&amp;Q_B \:Q_A&amp;Q_B \:\overline{Q_A}\\
\hline
\overline{Q_D}\:\overline{Q_C}&amp;1&amp;1&amp;1&amp;1\\
\overline{Q_D}\:Q_C&amp;1&amp;1&amp;1&amp;1\\
Q_D\: Q_C&amp;1&amp;1&amp;1&amp;1\\
Q_D\:\overline{Q_C}&amp;1&amp;1&amp;1&amp;1
\end{array}\end{smallmatrix}
\end{array}$$

This greatly simplifies things. Now the logic is:

$$\begin{align*}
T_A &amp;= 1\\
T_B &amp;= \overline{Q_A}\\
T_C &amp;= Q_A\\
T_D &amp;=\overline{Q_D}
\end{align*}$$

We could have made the above equations far, far more complicated had we picked, say, random choices for \$x\$. But we instead used intelligent choices and, in doing so, reduced the required logic needed to achieve the outputs.

These "don't care" values don't always make things simpler. Sometimes, they aren't located in places that allows you to conveniently simplify the logic. But they often do help out. You just need to look at the table to see if you can find a simplifying pattern when you have the freedom to choose values for them in the tables you are faced with.