Simplify the following using K-map : \(F (A, B, C, D) = Σ (0, 1, 2, 8, 9, 12,…
2018
Simplify the following using K-map :\(F (A, B, C, D) = Σ (0, 1, 2, 8, 9, 12, 13) \\
d (A, B, C, D) = Σ (10, 11, 14, 15)\)
\(d\) stands for don’t care condition
- A.
\(A+\bar{B} \bar{D} +BC\) - B.
\(A+\bar{B} \bar{D} + \bar{B} \bar{C}\) - C.
\(\bar{A} + \bar{B} \bar{C}\) - D.
\(\bar{A} + \bar{B} \bar{C} + \bar{B} \bar{D}\)
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Correct answer: B
Given minterms: 0, 1, 2, 8, 9, 12, 13. Don't-cares: 10, 11, 14, 15.
K-map grouping and rationale:
Group all cells with A=1 (including don't-cares) to form the implicant A. This covers minterms 8, 9, 12, 13 (and uses don't-cares 10, 11, 14, 15 to complete the block).
Group the four cells where B=0 and C=0 to form B' C'. This covers minterms 0, 1, 8, 9 and does not include any zero cells.
Group the four cells where B=0 and D=0 to form B' D'. This covers minterms 0, 2, 8 and the don't-care 10, and is a valid implicant.
Combining these prime implicants covers all required minterms without including any forbidden zeros.
Final simplified expression: F = A + B' C' + B' D'
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