Question Bank MCQ • 1 Mark Section 8: Electronics Digital Electronics

QB_PH_SEC8_002: Digital Electronics

Question Statement

Simplify the Boolean expression $Y = A \cdot B + A \cdot \bar{B} + \bar{A} \cdot B$. The minimal SOP form is
(A) $A + B$
(B) $A \cdot B$
(C) $\bar{A} + \bar{B}$
(D) $1$
Correct Answer
A
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Step-by-Step Derivation & Verification: 1. **Grouping Terms**: $Y = (A B + A \bar{B}) + \bar{A} B$ 2. **Factoring $A$**: $Y = A (B + \bar{B}) + \bar{A} B = A(1) + \bar{A} B = A + \bar{A} B$ 3. **Distributive Law Application**: $A + \bar{A} B = (A + \bar{A})(A + B) = (1)(A + B) = A + B$ 4. **Conclusion**: Minimal SOP representation is $A + B$. Option (A) is correct.
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