Question

What is the minimal sum of products form of $F(A, B, C, D) = AB + \overline{A}BC + \overline{A}B\overline{C}D$?

• A. \(AB + BC + BD\)
• B. \(A + B + C + D\)
• C. \(\overline{A} + \overline{B} + \overline{C} + D\)
• D. \(\overline{C} + \overline{A}C\overline{D} + A\)

Hint:

Use Boolean identities and common term grouping to simplify expressions in sum-of-products form.

Answer 1

The Correct Option is A

To minimize the expression \(AB + \overline{A}BC + \overline{A}B\overline{C}D\), we factor common terms and apply Boolean algebra identities.
Observe that all terms have either \(AB\), \(BC\), or \(BD\), so combining and applying distribution laws leads to the minimal form: \(AB + BC + BD\).