Given the Boolean expression F(A, B, C, D) = Σ(0, 1, 2, 3, 8, 9, 10, 11), what…
2025
Given the Boolean expression F(A, B, C, D) = Σ(0, 1, 2, 3, 8, 9, 10, 11), what is the simplified expression using the algebraic method?
- A.
B'
- B.
AB + AC + AD + BC + BD + CD
- C.
AB + CD
- D.
ABCD + ABC'D + AB'CD + ABCD
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Correct answer: A
Step 1: The given minterms are 0, 1, 2, 3, 8, 9, 10, 11. These correspond to the binary values where A=0 for the first four terms and A=1 for the last four terms. Step 2: For A=0, the minterms are 0, 1, 2, 3. These can be grouped as B'C'D' + B'C'D + B'CD' + B'CD = B'. Step 3: For A=1, the minterms are 8, 9, 10, 11. These can be grouped as AB'C'D' + AB'C'D + AB'CD' + AB'CD = AB'. Step 4: Combine the two groups: B' + AB'. Step 5: Factor out B': B'(1 + A) = B'. Thus, the simplified expression is B'.