What is an XOR sum?

Question

I am not sure of the precise definition of this term.

I know that a bitwise XOR operation is going bit by bit and taking the XOR of corresponding bits position wise. Is

Answer 1

In a bit wise XOR operation:

a   b   a^b
-----------
0   0    0
0   1    1
1   0    1
1   1    0 

XOR sum refers to successive XOR operations on integers.
Suppose you have numbers from 1 to N and you have to find their XOR sum then for N = 6, XOR sum will be 1^2^3^4^5^6 = 7.

1 = 001,  2 = 010,   3 = 011,   4 = 100,   5 = 101,   6 = 110  

 1^2          = 1^2  = 001^010 = 011 = 3  
(1^2)^3       = 3^3  = 011^011 = 000 = 0
(1^2^3)^4     = 0^4  = 000^100 = 100 = 4
(1^2^3^4)^5   = 4^5  = 100^101 = 001 = 1
(1^2^3^4^5)^6 = 1^6  = 001^110 = 111 = 7 --> XOR sum

Hope this will help.