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

edited | 1.7k views

$2$ quads are getting formed:

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

by Junior (611 points)
edited
+2
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
by Boss (31.4k points)
+1
hi, why we are not taking m0,m4,m12,m8 means with dont care
0
Yeah how to know when to take don't cares or not to take them?
0
use don't care only when you can form a bigger group with the help of don't cares.
by Loyal (8.6k points)

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 Active (3.6k points)