Question 4.4: Determine the BCS for the following data and CRC generating ......
Determine the BCS for the following data and CRC generating polynomials:
Data G(x) = x^7 + x^5 + x^4 + x^2 + x^1 + x^0
= 10110111
CRC P(x) = x^5 + x^4 + x^1 + x^0
= 110011
Step-by-Step
First, G(x) is multiplied by the number of bits in the CRC code, which is 5:
x^5(x^7 + x^5 + x^4 + x^2 + x^1 + x^0) = x^{12} + x^{10} + x^9 + x^7 + x^6 + x^5 = 1011011100000
Then the result is divided by P(x):
\begin{aligned}\begin{matrix} \\ 1&1&0&0&1&1& \end{matrix} & \begin{array}{lllllllllllll}&&&&&&1&1&0&1&0&1&1&1\\\hline|&1 & 0 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0\end{array} \\ & \begin{array}{lllllll}\quad\,\,1 & 1 & 0 & 0 & 1 & 1 \\\hline &1 & 1 & 1 & 1 & 0 & 1\end{array} \\ & \quad\begin{array}{lllllll}\quad\,\,\,\,\,1 & 1 & 0 & 0 & 1 & 1\\\hline &1 & 1 & 1 & 0 & 1 & 0\end{array} \\ & \quad\quad\quad\begin{array}{lllllll}\quad\,\,1 & 1 & 0 & 0 & 1 & 1 \\ \hline &1 & 0 & 0 & 1 & 0 & 0\end{array} \\ &\quad\quad\quad\quad\quad \begin{array}{lllllll}\,\,\,\,\,1 & 1 & 0 & 0 & 1 & 1\\ \hline & 1 & 0 & 1 & 1 & 1 & 0\end{array} \\ &\quad\quad\quad\quad\quad\quad \begin{array}{lllllll}\quad\,\,1 & 1 & 0 & 0 & 1 & 1 \\ \hline &1 & 1 & 1 & 0 & 1 & 0\end{array} \\ & \quad\quad\quad\quad\quad\quad\quad\quad~\begin{array}{llllll}\,\,\,\,1 & 1 & 0 & 0 & 1 & 1 \\ \hline &0 & 1 & 0 & 0 & 1&=C R C\end{array} \end{aligned}
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