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Consider the cyclic redundancy check $\text{(CRC)}$ based error detecting scheme having the generator polynomial $X^3+X+1$. Suppose the message $m_4m_3m_2m_1m_0=11000$ is to be transmitted. Check bits $c_2c_1c_0$ are appended at the end of the message by the transmitter using the above $\text{CRC}$ scheme. The transmitted bit string is denoted by $m_4m_3m_2m_1m_0c_2c_1c_0$. The value of the checkbit sequence $c_2c_1c_0$ is

1. $101$
2. $110$
3. $100$
4. $111$

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Correct Option: C

The given polynomial $x^3+x+1$ is written as 1011, which consists of 4 bits so, append 3 bits of 0s to the message.

$M= 11000000$
$$\begin{array}{l} 1011\overline{\smash{)}11000000}\\ \phantom{1011\smash{)}}\underline{1011}\\ \phantom{{x-31}}1110\\ \phantom{{1011\smash{)}1}}\underline{1011}\\ \phantom{1011\smash{)11}}{1010}\\ \phantom{1011\smash{)}11}\underline{1011}\\ \phantom{1011\smash{)}11111}{100}\\ \end{array}$$ There the check bits sequence is: 100.

Option A Option C should be the correct answer

by
1

No 100 should be answer. check applied ai solution...
ans is 100
Edited, thanks.