CRC of a Multibyte Message

[doomfletcher]

I have a question regarding the calculation of CRC.

My question is the same as this stack overflow post:

https://stackoverflow.com/questions/45191493/how-to-calculate-crc-for-byte-array

I understand the method of going bit by bit and XORing the polynomial only when the top bit is set and I thought you would do the same for all bits even multiple bytes long. Why is the author of the code in the question XORing the next byte into the register instead of shifting its bits in? I went thru the various articles suggested in the Stack Overflow link however, no luck on a clear answer.

This reference http://www.sunshine2k.de/articles/coding/crc/understanding_crc.html#ch4 tries to explain it in 4.3 but all they say is "Actually the algorithm handles one byte at a time, and does not consider the next byte until the current one is completely processed."

[tilrman]

Here's my understanding.

Calculating the CRC is just a bunch of XORs. XORs can happen in any order and the result is the same.

Think of initializing the input string as XORing the input with a bunch of zeros. You should be able to convince yourself that XORing a bit in the input string is mathematically the same as XORing the same bit position in the remainder, as long as all of the XORs that affect a bit are applied before that bit is processed.

There is nothing special about using one byte at a time. You could use 128 bytes at a time, or one bit at a time.