Question

create and submit your own example, using the CRC-8 polynomial (x⁸+ x⁷ + x⁶ + x⁴ + x² +1) to show that an error does or does not occur.

Answer 1

CRC= cyclic redundancy check

Consider the input :101101 (data to be send)

As we are using CRC 8 add (n-1) zeroes to the input data

That is 7 zeroes are added to the data to obtain the CRC value

The CRC value is obtained by dividing the new obtained input with the given CRC polynomial

The CRC polynomial given here is: x⁸+ x⁷ + x⁶ + x⁴ + x² +1

Which can be converted to binary format as: 111010101 = CRC polynomial

Now the division done is like the polynomial division , but here when the results are added NO CARRY BIT IS CONSIDERED, the carry is discarded, its like XOR operation.

New input data after adding 7 zeroes is: 1011010000000

Now divide this with the CRC polynomial

As shown below:

So the a remainder is obtained and the 7 bits after discarding the leftmost ZEROES are taken as the remainder value.

Now the sender sends this value concatenated with the original input data:

That is the sender in this case send the value : 1011011010011

So this value will be received by the receiver

Now receiver checks whether the data obtained is correct

For that sender performs the same division operation as discussed above using the obtained input and the CRC polynomial

· If remainder of that division is 0, then there is no error in the obtained data

· Else if its non zero remainder, then the data obtained is corrupted or its having some error.

The calculation at the receiver side is shown below (case for error free data obtained):