How do you compute the XOR Remainder used in CRC?

xor crc polynomial-math
Jeremiah picture Jeremiah · Dec 5, 2008 · Viewed 12.3k times · Source

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.

Answer

Anant Rao picture Anant Rao · May 12, 2011 
1010 | 101101000
       1010
       0001 this result is 1011 XOR 1010 = 0001
          1010
          1010
          0000  thus no remainder.

Thus 101101000 is perfect and no error has occurred in transmission/reception

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