What does a caret (^) do in a SQL query?

Question

What is the caret (^) doing in the following SQL Server query?

SELECT 1^2,  1^3;

which gives the results:

3   2

I came across this before I found the SQUARE() function.

Answer 1

The caret (^) translates to the XOR operator, which is a "bitwise exclusive or". In plain english it means "either, but not both". Here's what it does:

decimal 1 = binary 001                     decimal 1 = binary 001
XOR                                        XOR
decimal 2 = binary 010                     decimal 3 = binary 011
=                                          =
decimal 3 = binary 011                     decimal 2 = binary 010

More info on the MSDN page for bitwise operations.

Answer 2

   3^2
   =
   000011  (3)
   xor
   000010  (2)
   =  
   000001  (1)
   =
   1