What is the equivalent Boolean expression in product-of-sums form for the…
1996
What is the equivalent Boolean expression in product-of-sums form for the Karnaugh map given below?
- A.
BD' + B'D
- B.
(B+C'+D)(B'+C+D')
- C.
(B+D)(B'+D')
- D.
(B+D')(B'+D)
Attempted by 30 students.
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Correct answer: C
From the K-map, the 1-cells occur when B and D have different values: B = 0, D = 1 or B = 1, D = 0. Hence the function is B'D + BD', i.e. XOR of B and D.
However, the question asks for product-of-sums (POS) form, so we group the 0-cells. The 0-cells occur when B = D.
For B = 0 and D = 0, the corresponding maxterm is (B + D). For B = 1 and D = 1, the corresponding maxterm is (B' + D'). The variables A and C get eliminated during grouping because the pattern is independent of them.
Therefore, the equivalent POS expression is (B+D)(B'+D').