Find the codeword for the dataword 1001 if the CRC error detection technique is usedwith the divisor 101 1.

To find the codeword for the dataword 1001 using the CRC error detection technique with the divisor 1011, follow these steps:

1. Write the dataword and the divisor in binary form:

   • Dataword: 1001
   • Divisor: 1011

2. Append zeros to the dataword to match the length of the divisor:

   • Dataword (after appending zeros): 1001000

3. Perform the division using binary long division:

   • Start with the leftmost bit of the dataword (1) and divide it by the divisor (1011).
   • The result of the division is 1, which is written above the dividend.
   • Multiply the divisor by 1 and subtract it from the dividend:
     • Dividend: 1001000
     • Divisor: 1011
     • Subtract: 1011
     • Remainder: 111

4. Continue the division process:

   • Bring down the next bit of the dataword (0) and append it to the remainder:
     • Remainder: 1110
   • Divide the new remainder (1110) by the divisor (1011):
     • The result of the division is 1, which is written above the dividend.
     • Multiply the divisor by 1 and subtract it from the dividend:
       • Dividend: 1110
       • Divisor: 1011
       • Subtract: 1011
       • Remainder: 011

5. Repeat the division process:

   • Bring down the next bit of the dataword (0) and append it to the remainder:
     • Remainder: 0110
   • Divide the new remainder (0110) by the divisor (1011):
     • The result of the division is 0, which is written above the dividend.
     • Multiply the divisor by 0 and subtract it from the dividend:
       • Dividend: 0110
       • Divisor: 1011
       • Subtract: 0000
       • Remainder: 0110

6. Perform the final division:

   • Bring down the last bit of the dataword (0) and append it to the remainder:
     • Remainder: 01100
   • Divide the new remainder (01100) by the divisor (1011):
     • The result of the division is 0, which is written above the dividend.
     • Multiply the divisor by 0 and subtract it from the dividend:
       • Dividend: 01100
       • Divisor: 1011
       • Subtract: 00000
       • Remainder: 01100

7. The remainder obtained after the final division is the CRC (Cyclic Redundancy Check) code:

   • CRC code: 01100

8. Append the CRC code to the original dataword to get the codeword:

   • Codeword: 100101100

Therefore, the codeword for the dataword 1001 using the CRC error detection technique with the divisor 1011 is 100101100.