The boolean expression $$Z = \overline{A}\, \overline{B} \overline{C} D + \overline{A} B C \overline{D} + A \overline{B} \overline{C} D + A B \overline{C} \overline{D}$$​ can be minimized to?

Correct option is B

All terms share a common literal $$\overline{D}$$​, which is factored out. The remaining expression simplifies using Boolean identities, leading to:

​$$Z = \overline{A} B \overline{D} + \overline{B} C D + A B C \overline{D}$$​​

Important Key Points:

1. Common literal factoring (e.g. $$\overline{D}$$​,) is the first simplification step.
2. Use Boolean identities like$$X + X' = 1 \text{ and } X + 0 = X$$​ for simplification.
3. Grouping terms by common variables helps in compacting expressions.

Knowledge Booster:

• Option A: Contains term$$\overline{A} B C$$​, which is not present in the original expression.
• Option C: Includes incorrect simplification like$$\overline{B D}$$​, which doesn’t logically follow from grouping.
• Option D: Contains AB, which is overly generalized and cannot be derived from any valid group in the original.