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In the Karnaugh map shown below, $X$ denotes a don’t care term. What is the minimal form of the function represented by the Karnaugh map?

1. $\bar{b}.\bar{d} + \bar{a}.\bar{d}$

2. $\bar{a}.\bar{b} + \bar{b}.\bar{d} + \bar{a}.b.\bar{d}$

3. $\bar{b}.\bar{d} + \bar{a}.b.\bar{d}$

4. $\bar{a}.\bar{b} + \bar{b}.\bar{d} + \bar{a}.\bar{d}$

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$2$ quads are getting formed:

Value for first one is $a'd'$ and value for 2$^{\text{nd}}$ one is $b'd'.$

### 1 comment

Also, only 2 essential PI are formed and they cover all the minterms.The size of each EPI is of $2^2$ so final minimum expression must have exactly 2 terms and in each term you'll have only $4-2=2$ variables.Only (A) satisfies.
m0 ,m1,m8 ,m9 form one quad a'd'

So f=a'd'+b'd'

Ans is a

hi, why we are not taking m0,m4,m12,m8 means with dont care
Yeah how to know when to take don't cares or not to take them?
use don't care only when you can form a bigger group with the help of don't cares.

X denotes a don’t care term ,means we can take them whenever necessary.Here, if we take 1 don't care,it is sufficient (m10)

m0 ,m1,m8 ,m9 -> a'd'

m0,m2,m8,m10 -> b'd'

So, Option A is correct

by
Answer – A ( Easiest Question in 2008).

If you know How to apply K-Map