Can Demorgan's Theorem Help Solve This Boolean Function Problem?

[asd1249jf]

Homework Statement

F = xy+x'y'+y'z

Implement the boolean function using only And nad Inverter Gates.

Homework Equations

Demorgan's Theorem

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.

 

[asd1249jf]

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]

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