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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. $\bar b\bar c \bar d + ac\bar d + \bar a \bar c + ab\bar c$
in Digital Logic by Boss (16.3k points) | 1.3k views
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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.

2 Answers

+24 votes
Best 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.

So, answer is C.

by Veteran (56.6k points)
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great work sir ..! thanks
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got it
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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.

the answer is c.
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