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Consider the information sequence 1101011011.Find the codeword corresponding to this sequence

PLEASE SOLVE WITH WORKING

PLEASE SOLVE WITH WORKING

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Best answer

Here CRC polynomial is X^{4}+X+1

so we can transform it to a string of binary word i.e 10010

[convert a polynomial functio to a binary word by making the places 1 which are valid for x and other places 0 starting from right hand side as place 0]

look here we have x^{4} so after counting from rhs ...2,1,0 like this we made the 4th one 1 ..again for X(means X^{1}) we made the second from rhs 1 and we have already 1 here so X^{0} means LSB is 1..

now polynomial is **10010** (5 bit)

so we have to append (5-1)=4 0's after the data word [add n-1 0's if poly is n bit]

now the modified dataword is 1101011011**0000**

**now apply simple divide and then xor...as mentioned in book**

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here degree of polynomial = 4 , So x^{4} will be used to augument the dataword

dataword = 1101011011

dataword polynomial = x^{9}+x^{8}+x^{6}+x^{4}+x^{3 }+x+1

augumented dataword polynomial = (x^{9}+x^{8}+x^{6}+x^{4}+x^{3 }+x+1).x^{4}

augumented dataword polynomial =x^{13}+x^{12}+x^{10}+x^{8}+x^{7 }+x^{5}+x^{4}

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