How do I calculate the binary form of a polynomial? The 4 bytes used in CDROM sectors is just a usual 32 bit CRC.  It uses the polynomial 
P(x) = (x^16 + x^15 + x^2 + 1).(x^16 + x^2 + x + 1) 

which expands to 
x^32 + x^31 + 2x^18 + 2x^17 + 3x^16 + x^15 + x^4 + x^3 + 2x^2 + x + 1

The CRC process reverses the bits of the input bytes and the final CRC value.  It is stored in big endian format in the sector.
So I have to pass a polynomial prime into crc32 algorithm.
How do I convert this polynomial expression into binary form. any explanation will be appreciated.

For a CRC32 algorithm with the polynomial
$$x^{32} + x^{31} + 2x^{18} + 2x^{17} + 3x^{16} + x^{15} + x^4 + x^3 + 2x^2 + x + 1$$
you first omit the $x^{32}$ term and reduce the remaining coefficients mod 2. This gives
$$x^{31} + x^{16} + x^{15} + x^4 + x^3 + x + 1$$
Now simply substitute $x=2\;$ and evaluate, this gives the 32 bit number for
the CRC polynomial:
$$10000000000000011000000000011011_2 = 8001801B_{16} = 2147581979_{10}
$$
But note that for an actual implementation there more design subtleties: Are
you using big-endian or little endian? There are different reflections modes,
initial values, final xoring etc.
