How to convert between Sum Of Products and Product of sums?

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I have a Boolean expression. we'll call it F.

for instance, F = ab' + ad + c'd + d'.

Assuming I did all the necessary steps too get F complement , i.e. F'.

I got: F' = b'd + ac'd'.

How do I get the Product of sums form of F?

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3 Answers

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$$F=(F')'=(b'd+ac'd\,')'=(b'd)'(ac'd\,')'=(b+d\,')(a'+c+d)\;.$$

(Note: I did not check your $F'$.)

Because of the way the De Morgan laws work, the complement of a product of sums is always a sum of products, and the complement of a sum of products is always a product of sums.

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F = ab' + ad + c'd + d'

F'= (ab' + ad + c'd + d')' = (ab')' . (ad)' . (c'd)' . (d')' ---> a'.b' =(a'+b') De Morgans law = (a'+b)(a'+b')(c+d')(d)

Hence Product of sums.

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If the boolean expression is AB+BC.Then the product of sum expression is (A+B)(B+C).To find this, the complement of sum product expression is the product of sum expression. (AB+BC)'=A'B'+B'C' By applying DEMORGANS LAW =(A'+B')(B'+C') Now, (A'+B')'(B'+C')'=(A+B)(B+C).

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