了解XOR逻辑运算符

Question

I don't understand this

2.0.0p247 :616 > 5 ^ 2
 => 7 
2.0.0p247 :617 > 5 ^ 1
 => 4 

What 7 and 4 means in those scenarios?

I try reading here http://en.wikipedia.org/wiki/Exclusive_disjunction but cannot figure out by looking into the diagrams what is the subtract here. Sorry if this is simple math question.

Answer 1

It has to do with the binary representation of the values.

5 = 0101
2 = 0010
1 = 0001

Now the XOR works like this:

0 ^ 0 = 0
0 ^ 1 = 1
1 ^ 0 = 1
1 ^ 1 = 0

so to compute 5 ^ 2, let's apply the ^ operation to each column :

0101   (this is 5)
0010   (this is 2)
----
0111   ==> which is the binary representation of 7

How did this work? In the leftmost column, we computed 0^0=0 . In the second column, 1^0=1 . In the third column 0^1=1 , and so on.

and 5 ^ 1

0101   (this is 5)
0001   (this is 1)
----
0100   ==> which is the binary represenation of 4