Difficulty: Easy
Correct Answer: B
Explanation:
Introduction / Context:Simplifying Boolean expressions reduces gate count, power, and delay. The expression AB + A'B is a common pattern that can be minimized using standard identities. Recognizing these patterns is essential in manual algebra and when checking tool results.
Given Data / Assumptions:
Concept / Approach:Use the Distributive and Absorption laws. Note that both product terms share B. Factor B, then apply the Complementarity law A + A' = 1. This often collapses the expression to a single literal or a simpler term.
Step-by-Step Solution:
Start with F = AB + A'B.Factor B: F = (A + A') * B.Use complementarity: A + A' = 1.Therefore F = 1 * B = B.Verification / Alternative check:Truth-table check: when B = 0, both AB and A'B are 0 → F = 0; when B = 1, either A or A' is 1 → AB + A'B = 1 → F = 1. This matches F = B for all A.
Why Other Options Are Wrong:
A + B: Overstates the function; when A=1, B=0 this yields 1, but original F=0.AB: Too restrictive; when A=0, B=1 original F=1 but AB=0.A'B: Only covers the A=0, B=1 case, not A=1, B=1 which also yields 1.Common Pitfalls:Forgetting to factor the common literal; misreading A'B as A + B; confusing A + A' (which equals 1) with A * A' (which equals 0).
Final Answer:B
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