Question

Q1.1. A bit stream 1011011 is transmitted using standard CRC. The generator polynomial is x3+x2+1. Show the actual bit stream transmitted also check error occurred at receiver end.

Answer 1

Step-by-step explanation:

Given:A bit stream 1011011 is transmitted using standard CRC. The generator polynomial is x³+x²+1.

To find: Show the actual bit stream transmitted also check error occurred at receiver end.

Solution:

The generator polynomial is x³+x²+1 is and it's bits can be written as 1101.

Generator polynomial consist of 4 bits,thus a string of 000 is append to the bit stream to be transmitted.

Resulting bit stream is 1011011000.

Divide 1011011000 by 1101 to generate CRC bit

$\begin{gathered}1101)1011011000(110101 \\ 1101 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ - - - - - \\ 1100 \\ 1101 \\ - - - - - \\ 1110 \\ 1101 \\ - - - - - \\ 1100 \\ 1101 \\ - - - - - \\ 0001 \\ \end{gathered}$

Quotient of division is 110101 and Remainder is 001.

Append these bits with message to be transmitted.

Thus,

The bits to be transmitted 1011011001.

At receiver end 1011011001 is divided by again 1101(Generator polynomial)

$</p><p>\begin{gathered}1101)1011011001(110101 \\ 1101 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \: - - - - - - \\ 1100 \\ 1101 \\ - - - - \\ 1110 \\ 1101 \\ - - - - \\ 1101 \\ 1101 \\ - - - - \\ 000 \\ \end{gathered}$

Thus,

Remainder is 000.

Thus,

No error present in the received message.

Final answer:

1) Actual bitstream transmitted 1011011001.

2) No error occurred in the received message.

Note*: In division XOR operation is performed in place of subtraction.

Hope it helps you.

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