I am parsing binary files and have to implement a CRC algorithm to ensure the file is not corrupted. Problem is that I can't seem to get the binary math working when using larger numbers.

The example I'm trying to get working:

BigInteger G = new BigInteger("11001", 2);
BigInteger M = new BigInteger("1110010000", 2);
BigInteger R = M.remainder(G);

I am expecting:
R = "0101"

But I am getting:
R = "1100"

I am assuming the remainder of 0101 is correct since it is given to me in this book I am using as a reference for the CRC algorithm (it's not based in Java), but I can't seem to get it working. I can get small binary calculations to work that I have solved by hand, but not the larger ones. I'll admit that I haven't worked the larger ones by hand yet, that is my next step, but I wanted to see if someone could point out a glaring flaw I have in my code.

Can anyone confirm or deny that my methodology is correct?

Thanks