PoS-SoP convertion of function bellow (NOT using K-map)

Question

Function F as: $$ F=\overline{C} \space \space \overline{D} +A\overline{D} + A\overline{B}$$ is a SoP (sum of products) which is given by grouping K-map's 1's.

I tried to complement the function \$F\$ to get PoS (product of sums), like: $$ \overline{F}= (C+ D) \cdot (\overline{A}+D) \cdot (\overline{A}+B) $$ but I checked the K-map's 0's to see if it's a correct PoS, but it is not even a PoS because it contains max terms that the correct PoS shouldn't have.

Does any one know where I'm wrong?

Answer 1

$$ F=\overline{C} \space \overline{D} +A\overline{D} + A\overline{B}$$

DeMorgan's

$$ \overline F=\overline{\overline{C} \space \overline{D} +A\overline{D} + A\overline{B}}$$

$$ \overline F= (C + D) (\overline A + D) (\overline A + B)$$

First two terms: $$ \overline F= (C\overline A + D\overline A + CD + DD) (\overline A + B)$$

Simplify: $$ \overline F= (C\overline A + D) (\overline A + B)$$

Finish multiplying out last term, reduce and take DeMorgan's.

That should get you to your answer.

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