How do you compute the XOR Remainder used in CRC?

I'm trying to remember how the math is worked out to compute the remainder of an XOR algorithm in Cyclical Redundancy Checks to verify the remainder bits of a network message.

I shouldn't have tossed that text book.

This is easily done in code, but how is it worked out by hand?

I know it looks something like a standard division algorithm, but I can't remember where to go from there to get the remainder.

1010 | 101101000

Note: I did google it, but wasn't able to find a place where they mapped the steps in figuring the remainder.


  • It is long division by binary 11. There is an example on Wikipedia.