Introduction

Cyclic Redundancy Check (CRC) is a popular error-detecting code primarily used in digital networks and storage devices to detect accidental changes or corruption of raw data. The objective of CRC is to identify alterations, either intentional or unintentional, in the original data. This article provides a step-by-step guide to understanding the calculation of CRC.

The Process of CRC Calculation

1. Polynomial Selection

The first step in calculating the CRC is to choose a generator polynomial. The generator polynomial is a key determinant of the overall efficiency and performance of the CRC algorithm. Commonly used polynomials include 0x04C11DB7, 0x82608EDB, and 0x8EDB883.

2. Bit Padding

Next, you need to append a number of zero bits (to the input data block) equal to the length of the generator polynomial minus one. This step helps ensure that the remainder isn’t affected by discrepancies in size between different input data blocks.

3. Division

Now it’s time to perform bitwise division using XOR (Exclusive OR) operations between the input data (padded with zeros) and the generator polynomial. Note that you can only XOR bits that are aligned from left to right, ignoring leading zeros.

Example:

Data: 11010011101100

Polynomial: 1011

Padded Data: 11010011101100 000

4. Calculation and Remainder

Perform XOR operations until a single division iteration cannot be executed anymore due to fewer bits remaining than the degree of the generator polynomial. The remaining bits (after the division is exhausted) constitute your CRC checksum or remainder.

5. Appending Remainder

Finally, append the calculated CRC remainder to the original unpadded input data bits as a
checksum.

Now that you have an understanding of how to compute a CRC, let’s take a look at its benefits.

Benefits of CRC

– Error Detection: CRC is a highly effective method for detecting errors in data transmissions or storage.

– Quick Computation: CRC can be computed quickly with minimum processing and memory requirements using Lookup Tables (LUTs) and shifting registers.

– Compatibility: CRC is compatible with most communication protocols and data storage systems, making it the ideal choice for error detection.

– Adaptability: With different generator polynomials available, the robustness of this algorithm can be easily adjusted to suit specific applications or requirements.

Conclusion

Cyclic Redundancy Check is a widely used error-detecting algorithm that utilizes simple mathematical operations to calculate remainders and verify data integrity. It offers a quick, adaptive, and compatible approach to error detection. Familiarizing yourself with the CRC calculation process can help you understand how different systems utilize this technique to maintain data transmission quality and accuracy.