Question

Consider the following minterm expression for \( F \): \[ F(P, Q, R, S) = \Sigma(0, 2, 5, 7, 8, 10, 13, 15) \] \(\text{The minterms 2, 7, 8, and 13 are don't care terms. The minimal sum of products form for F is}\)

• A. \( \overline{Q}S + QS \)
• B. \( \overline{Q}S + QS \)
• C. \( \overline{Q}RS + Q\overline{R}S + QR\overline{S} + QRS \)
• D. \( \overline{P}QS + PQS + PQ\overline{S} + P\overline{Q}S \)

Hint:

When simplifying Boolean expressions with don't care terms, group the terms strategically to minimize the number of product terms.

Answer 1

The Correct Option is B

To minimize the given minterms, we use the don't care terms (2, 7, 8, and 13) to simplify the Boolean expression. By grouping the terms appropriately, we can reduce the expression to:
\[ \overline{Q}S + QS \] This is the minimal sum of products form for \( F \). Thus, the correct answer is \( \boxed{\overline{Q}S + QS} \).