I started with (AB' + A'B)' and ended up with (A'B' + AB). Is this all the farther I can go? I feel like this is always going to be true, but I'm not sure how to prove it algebraically.
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$(fg)'=fg'+f'g, (fg)''=f''+2f'g+2fg'+g''$ etc. what are $x$ and $y$? what are you asking? – yoyo Apr 13 '11 at 01:25
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sorry, should have used A and B instead of x and y...A and B are booleans. – Marty Apr 13 '11 at 01:33
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1What do you mean by simpler? Fewer gates (AND/NOT/OR)? Smaller length when viewed as a string? – Aryabhata Apr 13 '11 at 01:37
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2In a sense, this is the farthest you can go. What you have reached is the equivalence operation, which is the negation of XOR. – bzc Apr 13 '11 at 02:31
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1@Brandon: You should probably write that as an answer. – Sophie Alpert Apr 13 '11 at 04:29
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As per request, I am making my comment into an answer.
In a sense, this is the farthest you can go. What you have reached is the equivalence operation, which is the negation of XOR. Equivalence, sometimes denoted XNOR, returns true if the inputs are either both true or both false. See the Wikipedia page for XNOR for more information.
bzc
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@Henry: NXOR would be more logical, but does not have an easy pronunciation like XNOR does. – bzc Apr 17 '11 at 18:48
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