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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?

Billie
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3 Answers3

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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.

Brian M. Scott
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  • Thank you, but that is exactly what I've got (on my paper...) and it doesn't work .. are you sure it's right? – Billie Feb 03 '13 at 08:25
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    @user1798362: I’m sure that it would be right if your $F'$ were right. The problem is that your $F'$ is wrong: I get $a'b'cd+ab'c'd'$ for $F'$. – Brian M. Scott Feb 03 '13 at 20:30
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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.

Masiha
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    Hello, welcome to Math.SE. Thank you for your answer! It is, however, rather difficult to read. For some basic information about writing maths at this site see e.g. here, here, here and here. – Lord_Farin Oct 24 '13 at 07:00
  • I've been asking it a 1 year ago .. as you can guess it's not relevant anymore – Billie Oct 24 '13 at 10:24
  • Hi from 7 years in the future to let you know that it's still relevant! Always worth taking the time to improve an answer since the Q&A format is just as much about helping future visitors as it is the OP. Nonetheless, this answerer has unregistered but the sentiment stands... – ggorlen Sep 30 '20 at 03:04
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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).

KhasSravya
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