Exclusive or notation

[Bluebaron]

I am in need of just some notation help because I missed this lecture... And unfortunately I can't find the answer in my book.

We are making a truth table and I understand everything on the truth table except the notation for some parts of the exclusive or gate:

x^y is true when
x is true and y is not
or
y is true and x is not
x^y is fale when
x is true and why is true
or
x is not true & y is not true

Im purposely doing this in English for I may easily understand the explanation to this:

x^y^x

and x^y^y

I do not understand what this means and how to work with it.
If you could translate it into English for me, I think it would help me a lot in understanding it.

Thanks in advance!

[giblit]

x^y^x = (x^y)^z

So that would mean if there must be an odd amount of 1's to equal 1.

Another way to look at it would be say we have

8^11^5

that would mean
(8^11)^5

1000
1011
------
0011
0101
------
0110

or we could do this method (checking odd amount of 1s)

1000
1011
0101
------
0110

[Bluebaron]

Thanks! Seeing (x^y)^x helped a lot. I was able to figure it out with that...

If x and y are true:

(x^y) would end up being false, because its true, true.

but because x is true, and (x^y) is false, then the whole thing becomes true.

Your explanation with (8^11)^5 went over my head. I don't know how to decipher that. I just don't think we've covered that in class yet. Is

1000
1011 an 8? And then I unfortunately did not know what you meant by odd 1's to equal 1s either.

I do appreciate the help and it solved my problem. I would welcome an explanation to the rest of what you said, even though its not part of my assignment. I am doing this to understand more.

So if you have time, id love to hear it. If not, ill probably figure it out down the line.

Thanks again.

[giblit]

I unfortunately did not know what you meant by odd 1's to equal 1s either

1 1 = 2 1's even number of them so it is 0
1 0 = 1 1's odd number of them so it is 1
1 1 1 = 3 1's odd number of them so it is 1

1011 an 8?

1011 = 8 + 2 + 1 = 11 it's binary. That's normally what the bit-wise operators are meant for. Though if you are strictly speaking with booleans they are 1 or 0 which would be the first right most bit 0 or 1.

http://www.learncpp.com/cpp-tutorial/37-converting-between-binary-and-decimal/
http://www.learncpp.com/cpp-tutorial/38-bitwise-operators/