# Simplifying with DeMorgan's Law

#### victoria277

Joined Nov 6, 2011
4
Hi,

I am having some problems simplifying the following equation I got as far as

F = (ac' + abd' + acd)' (original equation)
F' = (ac')'(abd')'(acd)'
F' = (a'+c'')(a'+ b'+ d'')(a' + c' + d')
F' = (a' + c)(a' + b' + d)( a' + c' + d') (used Involution / double complement law to deal with the compliments for C and D)
F' = (a' + a'b' + a'd + a'c + b'c + cd)(a'+ c' + d')

From here I am stuck and can't simplify more than that, I am making further research at the moment but I appreciate any help at this stage

#### Georacer

Joined Nov 25, 2009
5,182
How do you need to simplify this? Reduce the terms? Do it with as many gates as possible? Do it with as little 2-input gates as possible? There are many approaches for this.

Your first form seems quite simplified, with the a being only the common term.

#### victoria277

Joined Nov 6, 2011
4
I need to reduce it to sum of products form, that's why the first form will not do

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#### Georacer

Joined Nov 25, 2009
5,182
Okay, this is a lead. Do you need a sum of any products or the minimum Sum of Products, as given by a Karnaugh map?

Another detail. If F=(a+b)' then F is equal to F=a'b', and not F'=a'b'.
That said, all the lines of your solution depict the F function, not the F'.

If I were you I 'd go another step and multiply the last two parentheses and then sort out any simplifications. That's if I wanted any sum of products.

If I wanted the minimum sum of products, I wouldn't go the DeMorgan's way. As I 've said before in similar threads, I don't know of a way to use DeMorgan's laws to obtain the minimal SoP. That would be like entering a maze and taking the right turns to reach the exit. It just isn't obvious. I 'd suggest Karnaugh mapping for that purpose.