The binary numbers (divident and divisor) are not treated as normal integer values, but as binary polyonimals where the actual bits are used as coefficients. However, reality is a bit more complicated. The remainder of this division is the checksum value.
The actual input data is interpreted as one long binary bit stream (divident) which is divided by another fixed binary number (divisor).
Refer also to for a short or to for a very detailed CRC introduction.ĬRC is based on division. A checksum, calculated by CRC, is attached to the data to help the receiver to detect such errors.
Afterwards, the achieved knowledge is expanded to CRC-16 and CRC-32 calculation, followed by some CRC theory and maybe a FAQ section.ĬRC ( Cyclic Redundancy Check) is a checksum algorithm to detect inconsistency of data, e.g. Here an exemplary CRC-8 polynomial is used. Here the emphasis lies on the target to really get the point of the code compared to the manual calculation. Based on those observations, implementations of CRC calculation are presented step by step, from naive ones till more efficient algorithms. Subsequently, some examples are calculated by hand to get familiar with the process of CRC calculation. At first, the general idea and functionality of CRC is discussed. Please note that this article is not indented to be a full comprehensive CRC guide explaining all details - it should be used as an additional, practical oriented note to all general explanations on the web. And this in exactly the same order I concerned myself with CRC. Therefore I decided to write this article, trying to cover all topics I had difficulties with. This article is the result of the fact that I found finally time to deal with CRC.Īfter reading Wikipedia and some other articles, I had the feeling to not really understand completely in depth. 8.6 When using an initial value other than zero in the shift register, the result is incorrect.Īrticle updated March 2019 (for details, click here to see the changelog). 8.5 Why does multiplication with x n append n zeros?. 8.4 Why is addition is the same as subtraction in CRC arithmetic?. 
Additional remarks (points worth to know)
7.3.1 Reversed CRC lookup table and calculation of reciprocal CRC. 7.2 Representation of generator polyonomials. 4.4 Improved CRC-8 byte-by-byte algorithm (lookup table based). 4.3 General CRC-8 bitwise implementation. 
4.2 Modified CRC-8 bitwise implementation for one byte input data.4.1 Simple CRC-8 shift register implementation for one byte input data.
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