Consider the following expression: ad' + (ac)' + bc'd. Which of the following…
2007
Consider the following expression: ad' + (ac)' + bc'd. Which of the following expressions does not correspond to the Karnaugh Map obtained for the above expression?
- A.
c'd' + ad' + abc' + (ac)'
- B.
(ac)' + c'd' + ad' + abc'd
- C.
a'c' + ad' + abc' + c'd
- D.
b'c'd' + acd' + (ac)' + abc'
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Correct answer: C
Original expression: F = ad' + (ac)' + bc'd. Using De Morgan's law, (ac)' = a' + c', so F = ad' + a' + c' + bc'd. The term bc'd is absorbed by c', and a' + ad' = a' + d'. Hence F = a' + c' + d'. Options A, B and D simplify to this same expression. Option C = a'c' + ad' + abc' + c'd is not equivalent; for a = 0, b = 0, c = 1, d = 0, the original expression is 1 while option C is 0. Therefore option C is the expression that does not correspond to the K-map.