Basically, it goes like this.

Say I have a file with the following in it:

ABCD

to compute an 8-bit checksum, we add the numeric values of the characters (shown in hexadecimal):

0x41 + 0x42 + 0x43 + 0x44 = 0x010A (or 266 indecimal). Since we want an 8-bit only checksum, we just lop off the upper 8 bits and that leaves us with 0x0A. So an 8-bit checksum for ABCD is 0x0A (or 10 in decimal).

The problem is that there are as many ways of computing a checksum as you can imagine. You can do 8, 16, 24, 32, etc., bits of checksum. You can truncate the upper bits or you can fold them back in. It just depends. A bit of detective work on your data file and some calculations will probably yield its secrets.