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Consider the following expression

$a\bar d + \bar a \bar c + b\bar cd$

Which of the following expressions does not correspond to the Karnaugh Map obtained for the given expression?

1. $\bar c \bar d+ a\bar d + ab\bar c + \bar a \bar cd$
2. $\bar a\bar c + \bar c\bar d + a\bar d + ab\bar cd$
3. $\bar a\bar c + a\bar d + ab\bar c + \bar cd$
4. $\bar b\bar c \bar d + ac\bar d + \bar a \bar c + ab\bar c$
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NOTE: In October 2016 GO Book(page no. 765) it is given  ad' + (ac)' + bc'd , middle term is wrong there.

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The question contains a term $b\bar cd$. Observing the options it can be seen that in C) the term $\bar cd$ is present. Since $\bar cd$ isn't completely covered in the original expression, this option is the answer.

$ad'$  [fill minterm in K-map in front for $a$ and $d'$ ] Similarly, fill all minterms  for $ad'+a'c' +bc'd$, resulting K-map will be: Option (a) $c'd'+ ad' + abc' + a'c'd$ is equivalent to given expression

Option (b) $a'c' + c'd' + ad' + abc'd$ is equivalent to given expression.

Option (c) $a'c' + ad' + abc' + c'd$ is not equivalent to given expression.

Option (d) $b'c'd' + acd' + a'c' + abc'$ is equivalent to given expression.

by Veteran (57.1k points)
edited
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great work sir ..! thanks
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got it
+1 vote
Draw kmap for original function then try to derive each element from options which are not in original function. The trick is to start with 2 literals elements(example- c'd') bcoz this has to cover 4 minterms in kmap which are easy to see if it is present or not.

by Active (4.5k points)