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?

  • \$\begingroup\$ Multiply it out, reduce and invert a second time. You've done DeMorgan's once. You have to do it twice to go from PoS to SOP. \$\endgroup\$ – StainlessSteelRat Nov 16 '18 at 17:31
  • \$\begingroup\$ @StainlessSteelRat does it work? I did and it didn't work \$\endgroup\$ – parvin Nov 16 '18 at 17:32
  • \$\begingroup\$ It works. I did it. Answer was the same as K-map. \$\endgroup\$ – StainlessSteelRat Nov 16 '18 at 17:32
  • \$\begingroup\$ @StainlessSteelRat the answer is (C'+A')*(D'+A)*(B'+D') and when I draw the K-map it has wrong max terms. \$\endgroup\$ – parvin Nov 16 '18 at 17:34
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    \$\begingroup\$ Correction: I get \$ f= (\overline B + \overline{D}) (A + \overline C) (A + \overline D ) \$ \$\endgroup\$ – StainlessSteelRat Nov 16 '18 at 18:17

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


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

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

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.

wide demo pic

  • \$\begingroup\$ +1 for 3k+ rep. Yay... you earn new privileges! \$\endgroup\$ – KingDuken Nov 16 '18 at 18:32
  • \$\begingroup\$ Thanks. For the couple times a month I lurk I here. Rapidly down votes a couple of questions. \$\endgroup\$ – StainlessSteelRat Nov 16 '18 at 19:16

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