How to Convert P-O-S to S-O-P in Boolean Algebra?

[General_Sax]

Homework Statement

Obtain a sum of products expression for the following:

(A+B)(A+C')(A+D)(BC'D+E)

Homework Equations

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The Attempt at a Solution

Should I use DeMorgan's Law or can I simply expand the expression and then simplify?

If I use DeMorgan's Law, won't I be finding a P-O-S expression for the compliment?

ie, let f = (A+B)(A+C')(A+D)(BC'D+E)

If I use DeMorgan's Law, then won't I be stating f ' ?

f ' = A'B' + A'C + A'D' + (B' + C + D')E = A'B' + A'C + A'D' + B'E + CE + D'E

could I do this:

f = ( A'B' + A'C + A'D' + B'E + CE + D'E )'

Please and thank you.

 

[KataKoniK]

Thank you for your question. To obtain a sum of products expression for the given expression, you can either use DeMorgan's Law or expand and simplify the expression. Both methods will give you the same result.

If you choose to use DeMorgan's Law, you are correct that you will be finding the P-O-S expression for the compliment. However, this is not a problem because the compliment of a compliment is the original expression. So by finding the P-O-S expression for the compliment and then taking the compliment again, you will get the desired sum of products expression.

Alternatively, you can expand the expression and then simplify using Boolean algebra rules. This method may be more straightforward for some people, but it ultimately depends on personal preference.

In summary, you can use either method to obtain the desired sum of products expression. Both methods will give you the same result. I hope this helps. Good luck with your studies!