Cyclic Redundancy Check

In our daily ethernet communications the Cyclic Redundency Check is the first system that checks wether our data is received correctly. To calculate the CRC, which you append to the data, you need a so called generator/ key. When you repeatedly XOR the generator with the data the remainder is the CRC.

	Source
	data			=	1	0	1	0	1	0	1	0	1	0
	generator			=	1	0	1	1	1
	CRC			=	Generator – 1 bit = 4 bits long
	Calculate CRC
	data										CRC
	1	0	1	0	1	0	1	0	1	0	0	0	0	0
	1	0	1	1	1
	0	0	0	1	0	0	1	0
				1	0	1	1	1
				0	0	1	0	1	1	0
						1	0	1	1	1
						0	0	0	0	1	0	0	0	0
										1	0	1	1	1
										0	0	1	1	1
	Add the CRC extension to the data.
	data										CRC
	1	0	1	0	1	0	1	0	1	0	0	1	1	1
	Send to destination
	Received at destination
	data			=	1	0	1	0	1	0	1	0	1	0
	generator			=	1	0	1	1	1
	CRC			=	0	0	1	1	1
	Check if received data matches it's CRC
	data										CRC
	1	0	1	0	1	0	1	0	1	0	0	1	1	1
	1	0	1	1	1
	0	0	0	1	0	0	1	0
				1	0	1	1	1
				0	0	1	0	1	1	0
						1	0	1	1	1
						0	0	0	0	1	0	1	1	1
										1	0	1	1	1
										0	0	0	0	0
	The remainder is 0, so the CRC is valid.