Can someone help me simplify this boolean expression?

• Apr 16th 2013, 05:52 PM
elorabees
Can someone help me simplify this boolean expression?
Can someone please show me how to simplify this expression? I have no clue of how it's done so any help would be appreciated. Thank you!

x'y'+xz'+yz+x'yz'+xy'z
• Apr 16th 2013, 06:17 PM
chiro
Re: Can someone help me simplify this boolean expression?
Hey elorabees.

Hint: Try using De-morgans laws on a few of the terms.
• Apr 16th 2013, 06:21 PM
elorabees
Re: Can someone help me simplify this boolean expression?
Quote:

Originally Posted by chiro
Hey elorabees.

Hint: Try using De-morgans laws on a few of the terms.

Thanks for replying but I'm still lost.. I'm sorry, Discrete isn't one of my strongest courses.
• Apr 16th 2013, 06:41 PM
chiro
Re: Can someone help me simplify this boolean expression?
Demorgans theorems are as follows:

(a+b)' = a'b' and
(ab)' = a' + b'

Try using these to convert terms to common ones and simplify using the other laws (namely distributive).
• Apr 16th 2013, 07:00 PM
elorabees
Re: Can someone help me simplify this boolean expression?
Okay, but what can I do with xz'? I don't know what to do when we have a variable with a complement and a variable without a complement together?

I just reduced this part:
x'y'+xz'+yz=x'+y'+xz'+yz=(x'+x)(x'+z')+(y'+y)(y'+z )=(x'+z')+(y'+z)=x'z'+(y'+z) , Can we get y'z from that? and can you tell me if that is right?
• Apr 16th 2013, 07:48 PM
chiro
Re: Can someone help me simplify this boolean expression?
Just as a hint for these problems, you can double check your work by creating a truth table consisting of 0 and 1 for all variables to check whether two statements are equivalent. I recommend you do this to check your own answers.
• Apr 16th 2013, 07:51 PM
elorabees
Re: Can someone help me simplify this boolean expression?
Quote:

Originally Posted by chiro
Just as a hint for these problems, you can double check your work by creating a truth table consisting of 0 and 1 for all variables to check whether two statements are equivalent. I recommend you do this to check your own answers.

Oh, okay.. I will next time but I really appreciate all your help. I worked on it a bit more and I found the solution, it turns out to be 1. Really grateful for all the hints. I hope you have a great day ahead!