Q.Explain don't care condition.

A don't-care condition is an input combination that either never occurs or whose output value is of no consequence; it is marked X (or d) in the truth table or K-map. …

[!TLDR]

A don't-care (X) is an input combination that cannot occur or whose output is irrelevant; it may be taken as 0 or 1 during K-map grouping to get a simpler expression.

In many real systems certain input combinations either never appear or produce an output that nobody uses. For such combinations the designer does not care what the output is; these are called don't-care conditions and are written as X (or d) in the truth table and Karnaugh map.

The great advantage of don't-cares is the freedom they give during minimisation. When grouping cells in a K-map, each X may be regarded as a 1 if that lets a larger group form (fewer, simpler terms), or as a 0 if it is not helpful. This flexibility often yields a considerably simpler final expression than would be possible without them. …