GO Classes DPP | GATE CS | Digital Logic | K-map Don’t Cares

Answer 1

Given $\mathrm{F}(\mathrm{A},\mathrm{B},\mathrm{C},\mathrm{D})=\Sigma _m(1,3,7,11,15)+\mathrm{d}(0,2,5)$.

Here, $1$s are placed at $m_1,m_3,m_7,m_{11},m_{15}$.

Don’t care cells are placed at $m_0,m_2,m_5$.

In K-map simplification, don’t care cells can be used as $1$ if they help in making larger groups.

First, group $m_3,m_7,m_{11},m_{15}$.

These four cells form a group in the column $\mathrm{C}\mathrm{D}=11$.

In this group, $\mathrm{A}$ and $\mathrm{B}$ change, but $\mathrm{C}=1$ and $\mathrm{D}=1$ remain constant.

So, this group gives $\mathrm{C}\mathrm{D}$.

Now $m_1$ is still not covered.

Use the don’t care cell $m_5$ and group $m_1,m_3,m_5,m_7$.

In this group, $\mathrm{B}$ and $\mathrm{C}$ change, but $\mathrm{A}=0$ and $\mathrm{D}=1$ remain constant.

So, this group gives $\mathrm{A}'\mathrm{D}$.

Therefore, the minimal SOP form is $\mathrm{F}=\mathrm{A}'\mathrm{D}+\mathrm{C}\mathrm{D}$.

Final Answer: A

Answer 2

Option A