# Proving XOR

Discussion in 'Homework Help' started by thisonedude, Jul 13, 2014.

1. ### thisonedude Thread Starter Member

Apr 20, 2014
52
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Can someone help me prove the following?

(A XOR B)' = A' XOR B

Apr 5, 2008
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3. ### MrCarlos Active Member

Jan 2, 2010
400
136
Hello thisonedude

I think it would be a lot of words trying to prove that (A XOR B)' = A' XOR B.

Maybe if you look at the attached images you can find it.
In these cases it would be faster to search in Google.com for answers.

Among the many answers I found is that you look at the following link:
http://pubs.sciepub.com/jcsa/1/1/3/
I hope you serve

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4. ### NorthGuy Active Member

Jun 28, 2014
611
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(a xor b)' = (a xor b) xor 1 = a xor b xor 1 = a xor 1 xor b = (a xor 1) xor b = a' xor b.

Edit: It was all in capitals. Forum software has changed it.

thisonedude likes this.
5. ### kubeek AAC Fanatic!

Sep 20, 2005
4,875
863
You ca prove it either by making a table, or using boolean algebra.

6. ### amilton542 Active Member

Nov 13, 2010
496
64
$

(a'b + ab)' = [(a'b)'][(ab')]

(a'' + b')(a' + b'') = (aa') + (ab) + (a'b') + (bb') = a' xor b

$

7. ### MrChips Moderator

Oct 2, 2009
14,521
4,282
A XOR B is an inequality function.
Hence (A XOR B)' - is equality function

Hence (A XOR B) ' = (A' XOR B) = (A XOR B')

This is not a proof but rationalized logic.