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Network and Data Communications20825 marksNumerical: CRC error detectionCRC transmitted frame encoding

A bit stream 11011001 is transmitted using a standard CRC method. The generator polynomial is x3 + x - 1. Show the actual bit string transmitted and show the error checking on the receiver side.

A bit stream 11011001 is transmitted using a standard CRC method. The generator polynomial is $x^3 + x - 1$. Show the actual bit string transmitted and show the error checking on the receiver side. [5]

  • Message bit stream (M): 11011001 (8 bits) - Generator polynomial: $x^3 + x - 1$ - In modulo-2 (GF(2)) arithmetic, $-1 \equiv +1$, so $x^3 + x - 1 = x^3 + x + 1$ - Generator (G): 1011 (4 bits, degree $r = 3$) --- $$M' = 11011001 ,\, 000 = 11011001000$$ Step trace (leading-bit alignment, XOR wh...
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