This paper puts forward the background of the CRC arithmetic by which it means how important the arithmetic can be in the field of the communication, tells us the principles of CRC arithmetic, introduces a kind of common ways about how to make the code and how to decode of the CRC arithmetic, uses a lot of words to introduce how the CRC codes be made through one kind of the CRC arithmetic which is called CRC-16, gives the main idea of programming and a part of the program. At last, the CRC arithmetic is used on the control chip which is called DSP successfully.