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
?
boolean-algebra
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
?
Best Answer
$$F=(F')'=(b'd+ac'd\,')'=(b'd)'(ac'd\,')'=(b+d\,')(a'+c+d)\;.$$
(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.