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

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. Thanks!

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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