Boolean expression with only OR,NOT gates

Question

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?

Answer 1

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

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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\$

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First add some not gates.

\$\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}}\$

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This is how it looks like in a schematic.