Question

Let G(x) = x5

+ x4

+ x + 1 be the polynomial generator(pattern) and Message(M) = 

11100011. Find the CRC for this message and the codeword.

Answer 1

Given polynomial is

$G(x) = x^5 +x^4+x+1$

Message from the destination node$(T)=11100011$

The Divisor polynomial bit $=1\times x^5 +1\times x^4+0\times x^3+0\times x^2+1\times x+1\times1$

$=110011$

Bits to be appended to the message = (Divisor polynomial bits -1)$=6-1= 5$

Now, append 5 zero to the message bit, hence$=1110001100000$

$1110001100000/110011$ Remainder =1000

Hence, CRC = 1110

Hence, we have to append 1110 to the frame.

So, the receiver will receive 111000111110