Explain how CRC is used in detecting errors for the following polynomial, g(x)=x^4+x+1.

Question

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

PLEASE SOLVE WITH WORKING

Answer 1

Here CRC polynomial is X⁴+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 x⁴ so after counting from rhs ...2,1,0 like this we made the 4th one 1 ..again for X(means X¹)  we made the second from rhs 1 and we have already 1 here so X⁰ 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 11010110110000

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

Answer 2

g(x)=x⁴+x+1

here degree of polynomial  = 4 , So x⁴ will be used to augument the dataword

dataword = 1101011011

dataword polynomial = x⁹+x⁸+x⁶+x⁴+x³ +x+1

 augumented dataword polynomial = (x⁹+x⁸+x⁶+x⁴+x³ +x+1).x⁴

 augumented dataword polynomial =x¹³+x¹²+x¹⁰+x⁸+x⁷ +x⁵+x⁴