Final answer:
To calculate the Cyclic Redundancy Check (CRC) code word for 1111001 with the polynomial 1101, append three zeroes, perform binary division, and then append the remainder to the original word. The transmitted CRC code word is 1111001010. At the receiver, division without a remainder confirms a valid transmission.
Step-by-step explanation:
To compute the Cyclic Redundancy Check (CRC) code word using the polynomial 1101 for the information word 1111001, we perform polynomial division in binary; we attach three zeroes to the information word (since the CRC polynomial is of degree 3), making it 1111001000, and then divide it by the CRC polynomial 1101.
The resulting quotient is the initial information word, and the remainder gives us the CRC bits that are appended to the original information word to form the CRC code word. The complete transmission consists of the original information word followed by this CRC remainder. Upon receiving, the receiver performs the same division process on the code word; if the remainder is zero, the word is considered valid. If it's nonzero, this indicates an error in transmission.
If we perform the division for 1111001000 by 1101, the remainder becomes 010, which is then appended to the original information word.
Therefore, the CRC code word is 1111001010.
At the receiver, the same division would confirm the validity of the message if no errors occurred during transmission.