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[Solved]: Rewriting gates such as XOR into three basic gates?

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Problem Detail: 

How would I rewrite an XOR gate into the three basic logic gates (AND, OR, NOT). To be more specific, I have to write it in such a way with 2 NOT gates, 2 OR gates, and 1 AND gate. I also have to do it with 1 OR gate, 2 AND gates, and 1 NOT gate.

I'm not looking for just the answer, I'm looking for a way to come up with the answer.


Asked By : 4everPixelated

Answered By : Pål GD

Hint: $a \oplus b = \neg \big( (a \land b) \lor (\neg a \land \neg b)\big)$ (you can't have both true and you can't have both false). Using De Morgan's, you should be able to break up the negation and the main $\lor$.

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