A CRC is the remainder of a division done in Z/2Z[X].
The data is representes as msb of first byte is the coefficient
of the highest order x term, x^l for l bits, and the lsb of the
last byte is the constant.

Hence CRC(x^y)=CRC(x)^CRC(y).

Cksum does a crc of a file. However the linearity will not
be apparent using cksum. By convention, 0xffffffff is prepended 
and the length is appended to the file. This is a non-linear
modification to the file.

crc32.c is from FreeBSD cksum command
crc-32.c is from airsnort.

cksum
-----
cksum of 0 bytes is ffff ffff
cksum of 8 bytes of aa is accd 7ed2
cksum of 8 bytes of 55 is 610a aad6
cksum of 8 bytes of ff is 1430 c643

by modifing csc-32.c we can get to the heart of the
algorithm alone and demonstrate the linearity.

[burt@sherman crc]$ ./crc-m
0x21 0x8db061f6
0xffffffde 0xc9d66183
0xff 0x44660075
exor i1, i2, i3 = 0x00000000