GATE IT 2007 | Question: 79

Question

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?

• A. $\bar c \bar d+ a\bar d + ab\bar c + \bar a \bar cd$
• B. $\bar a\bar c + \bar c\bar d + a\bar d + ab\bar cd$
• C. $\bar a\bar c + a\bar d + ab\bar c + \bar cd$
• D. $\bar b\bar c \bar d + ac\bar d + \bar a \bar c + ab\bar c$

Comments

Watch Solution here!   

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fast way to do this would be find minterms of given expression. 
then check options 
for example A: c'd' = check in binary form wherever __00 -> there must be 4 unique strings ending with 00. 
ad' -> given in the question expression. 
abc' -> 110_ -> there must be 2 unique strings with prefix as 110. 
a'c'd -> 0_01 -> there must be 2 unique strings as 0101 and 0001 
all satisfies as min terms given in the question. 

now option C: 
a'c' -> given in the question - Correct
ad' -> also given in the question - correct
abc' -> checked in option A - correct
c'd -> 0001, 
            1001 -> not found so option C is incorrect as it has extra minterm 9, which is not in given minterm in question. 
            1101,  
            0101.

likewise check remaining options

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I done this question by using by case , consider A,B,C,D as 0,0,0,0 and check you will get option C fails

Answer 1

$ad'$  [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.

Comments

great work sir ..! thanks

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got it

Answer 2

by Case method credit , @GO Classes,@Deepak Poonia sir 

Comments

Solved in the same way, just while solving option D for A=1, did a whole lot of calculations 😓

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The given question uses the word "K-map", BUT it has nothing to do with K-map OR I can say that using K-map to solve this question is Not a good method.

Find the Minterm List of the given function, & Find the Minterm List of each option & compare.

Or use the by-case method.

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wrong by case method becoz  after taking common c' option c is also equal

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same here

Answer 3

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.

Answer 4

Correct answer is c

Answer 5

We Can Also Draw K-Map Of options and Match Them with K-map of Given Function By this method You get option C Kmap Does not match with the Kmap of Given Function