The given binary data is [ D = 1101101010 ] and the generator polynomial is [ G(x)=x^4+x+1. ] The generator polynomial has the binary representation [ G = 10011 ] because the coefficients of (x^4+x+1), from (x^4) to (x^0), are (1,0,0,1,1). Since the highest power of the generator polynomial is 4, four zeros are appended to the original data before performing the CRC division. [ 1101101010 ; \longrightarrow ; 11011010100000 ] Thus, the dividend for the modulo-2 division is [ 11011010100000 ] and the divisor is [ 10011. ] CRC division uses modulo-2 arithmetic, in which subtraction is performed using the XOR operation. The basic XOR rules are [ 0\oplus0=0,\quad 0\oplus1=1,\quad 1\oplus0=1,\quad 1\oplus1=0. ] The binary division proceeds as follows. First, take the first five bits of the dividend: [ 11011 ] Since the first bit is 1, XOR with the generator: [ \begin{array}{r} 11011\ 10011\ \hline 01000 \end{array} ] The leading zero is ignored, and the next bit of the dividend is brought down. This gives [ 10000. ] Again, the first bit is 1, so XOR with (10011): [ \begin{array}{r} 10000\ 10011\ \hline 00011 \end{array} ] The result begins with 0, so no XOR with the generator is performed at this position. The next bit is brought down. The effective intermediate value becomes [ 00111. ] Since the first bit is 0, the generator is not XORed at this stage. The next bit is brought down, giving [ 01110. ]