# What is CRC? Explain its working with an example.

CRC is based on
binary division. In this a sequence of redundant bits, called CRC remainder is
appended to the end of a data unit so that the resulting data unit becomes
exactly divisible by a second predetermined binary number. At its destination,
the incoming data unit is divided by the same number. If at this step there is
no reminder, the data unit is assumed to be intact and therefore accepted. A
remainder indicates that the data unit has been changed in transit and
therefore must be rejected.

Here, the remainder is the CRC. It must have
exactly one less bit than the divisor, and appending it to the end of the data
string must make the resulting bit sequence exactly divisible by the divisor.

Fig: How CRC Works |

First, a string
of n-1 0s is appended to the data unit. The number of 0s is one less than the
number of bits in the divisor which is n bits. Then the newly elongated data
unit is divided by the divisor using a process called binary division. The
remainder is CRC. The CRC is replaces the appended 0s at the end of the data
unit.

The data unit arrives at the receiver first,
followed by the CRC. The receiver treats whole string as the data unit and
divides it by the same divisor that was used to find the CRC remainder. If the
remainder is 0 then the data unit is error free. Otherwise it having some error
and it must be discarded.

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