Chapter 6 CRC size and transmission correctness detectability
The previous chapter CRC size is 4 bits and the message in A register is 8 bit (1 byte). It’s obviously that A size may be any multiple of byte. But what is the correctness detectability when CRC size is 4 bits? The CRC is kind of “division remainder”when A message is a “dividend” and 11001 is a “factor“. For the real division 3784:25 for example the remainder is 3, and this same remainder=3 is for many dividends 3759, 3734, 3709,…,28. Analogously for 4 bits CRC and given “factor” there are many (16?) these same CRC-s. The transmission error will cause the original message A change and the CRC change probably. Why is the word “probably” used? It’s obviously. Because it’s possible that the new calculated CRC is the same! (as dividends 3759, 3734, 3709,…,28) The receiver will treat this new but false message as a true!
The bigger is the CRC the bigger is correctness detectability. 1 byte gives 256 these same CRC, and 4 bytes gives 4 294 967 296! This same CRC with different message is less possible than lotto! So we treat the message in the receiver with the same CRC as CRC transmitter as almost sure. Unfortunately, almost sure and not simply sure.
Transmission correctness detectability depends on the CRC size but depends on the CRC value yet! Why? I respond as simply as possible.
I am not a mathematician and I don’t know.
Mathematicians invented for example that CRC=100000100110000010001100110110111 is very good and is commonly used in data transmission as CRC32 .