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# Explain the Cyclic Redundancy Checks (CRCs)

The Cyclic Redundancy Checks (CRC) is the most powerful method for Error-Detection and Correction. It is given as a kbit message and the transmitter creates an (n – k) bit sequence called frame check sequence. The out coming frame, including n bits, is precisely divisible by some fixed number. Modulo 2 Arithmetic is used in this binary addition with no carries, just like the XOR operation.

Redundancy means **duplicacy.** The redundancy bits used by CRC are changed by splitting the data unit by a fixed divisor. The remainder is CRC.

**Qualities of CRC**

It should have accurately one less bit than the divisor.

Joining it to the end of the data unit should create the resulting bit sequence precisely divisible by the divisor.

**CRC generator and checker**

## Process

A string of n 0s is added to the data unit. The number n is one smaller than the number of bits in the fixed divisor.

The new data unit is divided by a divisor utilizing a procedure known as binary division; the remainder appearing from the division is CRC.

The CRC of n bits interpreted in phase 2 restores the added 0s at the end of the data unit.

**Example**

Message D = 1010001101 (10 bits)

Predetermined P = 110101 (6 bits)

FCS R = to be calculated 5 bits

Hence, n = 15 K = 10 and (n – k) = 5

The message is generated through 2^{5}:accommodating 1010001101000

The product is divided by P.

The remainder is inserted to 2^{5}D to provide T = 101000110101110 that is sent.

Suppose that there are no errors, and the receiver gets T perfect. The received frame is divided by P.

Because of no remainder, there are no errors.

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