Boolean expression with only OR,NOT gates

I have the expression: x'y+xy'+y'z . I want to express this with only OR, NOT gates, but the issue is I have no idea how to remove the AND functions. I was thinking of using demorgans law, but I am unsure how and if it can be used on only part of the expression. Is there a way to simplify it and remove the ANDS?

• Hint: Can you make an AND gate out of an OR gate and three NOT gates? Commented Feb 15, 2018 at 0:31
• x'y+xy'+y'z === (x'y)+(xy')+(y'z). Now you can use De Morgan's laws inside each parathesis until all the ANDs are gone. Commented Feb 15, 2018 at 0:47
• Oh I see. So (x'y) would be (x+y') correct? @Dampmaskin Commented Feb 15, 2018 at 0:50
• The whole paranthesis also gets inverted. If De Morgan's laws are not clear to you, you should study them more closely. Commented Feb 15, 2018 at 0:55

Q: $\overline{x}y+x\overline{y}+\overline{y}z$, Turn this into NOT and OR gates only.

Just apply De Morgan's law on each of them individually.

Here's a refreshener:

$\overline{AB}=\overline{A}+\overline{B}$

$\overline{A+B}=\bar{A}\bar{B}$

$\overline{\overline{A}}=A$

$\overline{\overline{\overline{x}y}}+\overline{\overline{x\overline{y}}}+\overline{\overline{\overline{y}z}}$

Then De Morgan them to the maximum.

Here's the continuation in hidden format, I do encourage you to apply De Morgan's law on your own.

$\overline{\overline{\overline{x}}+\overline{y}}+\overline{\overline{x}+\overline{\overline{y}}}+\overline{\overline{\overline{y}}+\overline{z}}$

And after you've applied De Morgan's Law, then you might want to remove unnecessary gates. Use these two yellow boxes as a way to control that you've calculated correctly.

$\overline{x+\overline{y}}+\overline{\overline{x}+y}+\overline{y+\overline{z}}$

This is how it looks like in a schematic.

• Thank you, that makes much more sense. Now since the parenthesis have a complement, how would I go about making an AND gate? Wouldn't I need to have the complement somehow removed? Commented Feb 15, 2018 at 2:30
• "how would I go about making an AND gate?", from what? And wasn't the OR + NOT gates the goal? - I am not following you. Commented Feb 15, 2018 at 2:32
• sorry, misworded. I meant the or gate. How would I deal with the complement on the parenthesis since I need just the or gate Commented Feb 15, 2018 at 2:34
• Are you talking about inverting the OR gate? $\overline{x+y}=$ NOT(OR(x,y)). - Just add a NOT gate at the output of the OR gate. Commented Feb 15, 2018 at 2:42
• @Kytex Added schematic for clarity. Commented Feb 15, 2018 at 2:51