How does CRC work?

Chapter 2. The transmisions with the simple CRC examples

Chapter 2.1 Introduction
We asked in the chapter 1.3 “Why does the register RR in London know that the received number 38547 is different from the number  32547 send by the transmitter in Warsaw?”.  In other words.  “Why does the register RR in London know that that there are transmision errors. The redundand information principle will be used. This redundand information, added to the information in Warsaw is just called CRC.

Chapter 2.2 CRC as replicated appropriate information
In other words. “Halo, halo repeat it again.  Method is used in phone calls for example.

Fig. 2-1 ANIMATION

Redundand Information is a repeated Appropriate Information here. 
Transmitter and Receiver know the transmision algorithm–>repeat the Appropriate Information.
There are 2 phases:
Phase 1
Transmision AIR–>RR. The registers RIR and CR are updated concurrently and they fill a CRC role!
Phase 2
Transmision faultlessness verification. The green and input CR bytes are compared. It means that all the CR and RIR bytes are compared.  The result CR=00000 tells that transmision is ok.
The animation will convince you.

Chapter 2.3 CRC as a division rest  (another word – remainder)
The previous method is more didactical than used in practice. The main weakness is the big size of the redundand information. Please notice that the appropriate information has thousands bytes practically, not 5 as in the Fig. 2-1!  The redundand information, which size is the same as appropriate information, reduces transmission speed! The problem solving is the redundand information reduction. 

Fig. 2-2   ANIMATION
CRC as a division remainder
The appropriate information 32547 is a dividend. The number 325 is a factor in the FR registers. Please notice that the receiver and transmitter know the factor. More generally – the receiver and transmitter know RDR registers calculation algorithm.
The RDR registers fill a CRC role!

5 transmissions phases
1. Initial state
2. The division rest-remainder calculation in the transmitter as 32547/325=47
3
. Transmission of the 32547 from the transmitter to the receiver
4. The division rest calculation in the receiver as 32547/325=47
5
. Transmission faultlessnes testing as receiver and transmitter RDR registers comparison.   Are they the same?–>transmission is ok. Exactly- Transmisison is very probably ok! Why? The received nunber with this same remainder=47 (32500 for example) is treated as faultless!

Let’s study it more generally
1. Transmitter attaches “small something” (47 here) to the “big something” (32547 here) and sends it to the receiver.
2. Receiver receives “big something” (32547 here)  with “small something” (47 here)
3Receiver calculates his own “small something” regardless of  received “small something” (47 here)
4. Receiver compares “his small something” with received “small something”:
Are they equal?
yes–>transmission is correct
no–>transmission isn’t correct
The other name of the attached “small something” is a CRC!

The real CRC method difference is:
1. The information is send by bits formed in bytes.
2. There are thousands of bytes instead of as in a/m eaxample (32547)
3. The different remainder calculating method. The real method is more simpler  than a decimal remainder calculation.
4. The remainder calculation is performed during every byte (or bit) sending. Not as a separate phase!
5. The real “remainder” isn’t a remander even! It’s similar only!

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