Demorgan's Theorem Problem

[l46kok]

1. The problem statement, all variables and given/known data
F = xy+x'y'+y'z

Implement the boolean function using only And nad Inverter Gates.

2. Relevant equations
Demorgan's Theorem


3. The attempt at a solution

X' means inversion btw.

So I thought how you do this is to invert the variables, and change the type of gate.

Therefore, I had

(xy)(xy)(yz')

But if I actually use real numbers to check.. this conversion is wrong.

Am I looking at the demorgan's theorem wrong? Please give me any suggestions

[Crosson]

Do you use xy to mean (x)(y) ?

If so you forgot to apply ((x)(y))' = x' + y'

If that doesn't make any sense it is because I made a bad guess at your notational conventions.

[l46kok]

Do you use xy to mean (x)(y) ?

If so you forgot to apply ((x)(y))' = x' + y'

If that doesn't make any sense it is because I made a bad guess at your notational conventions.

I'm sorry, let me clarify a little bit.

xy = x and y
x+y = x or y
(xy)(xy) = x and y anded with x and y

[doodle]

I think you're looking at the theorem wrongly alright. Care to explain how F = xy+x'y'+y'z became F = (xy)(xy)(yz')?

[berkeman]

[b]

So I thought how you do this is to invert the variables, and change the type of gate.

Therefore, I had

(xy)(xy)(yz')

But if I actually use real numbers to check.. this conversion is wrong.

Am I looking at the demorgan's theorem wrong? Please give me any suggestions

Does this link help? (we've used it in a couple recent threads similar to yours):

http://www.vias.org/feee/karnaugh_09.html