Simplifying with DeMorgan's Law

Thread Starter


Joined Nov 6, 2011

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


Joined Nov 25, 2009
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.


Joined Nov 25, 2009
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.