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How does the product of sum form work? I understand that you take the product of the sums of the negated inputs of all rows of the truth table whose output is false. Taking XOR for example:

A B Output
0 0 0
0 1 1
1 0 1
1 1 0

The product of sum form would be:

$(\bar A + \bar B)(A + B)$

However, I don't understand why this method yields the correct boolean equation?

I understand why the sum of product form works but the product of sum form seems quite unintuitive to me.

FarmerZee
  • 417

1 Answers1

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Considering your example, we have the logical expression:

Using similar logic to the sum of product form, we know that:

${(\bar A \bar B) + (AB)} = F$

Therefore:

$\overline{(\bar A \bar B) + (AB)} = T$

With continuous application of Demorgan's Theorem ($\overline{X+Y} = \bar X \bar Y$):

$\overline{(\bar A \bar B)} \overline{(AB)} = T$

$(\bar{\bar A } + \bar{\bar B}) (\bar A + \bar B) = T$

$(A + B) (\bar A + \bar B) = T$

As desired.

FarmerZee
  • 417