Probably the most complicated explanation I have seen, especially if you are trying program with a mod2 function.
As already said, 0+0=0,0+1=1,1+0=1,1+1=0 i.e you only get a zero if both bit positions are the same.
This is what the xrl (XOR) instruction does in 8051. Better to look at your example of this and work simply by looking at each bit position individiually.
1 1 0 1 xrl
0 0 1 1
----------------------------------------------------------------------------------------------------- Result is 1110
=1 as they are different, =1 as they are different,=1 as they are different,=0 as they are the same
mov A,#0x0D; //1101
xrl A,#0x03; //0011
A will then be 0x0E ; // 1110