Consider the Cyclic Redundancy Check (CRC) coding algorithm with 4-bit generator G = 1110. Assume the data to be sent U = 11110110.

What are the CRC bits R? Please show the entire computation steps to get full points.

What is ? Perform another CRC computation as the above using the data instead of U2^t. What is the reminder value now? Please show the entire computation steps to get full points.

Give an example error with the minimum number of flipped bits where the CRC cannot detect that there is an error for the above computed . You can represent the error as a binary string X of the same length as the payload concatenating CRC bits, , where a bit in X is 0 represents the corresponding bit in is not flipped, and a bit is 1 represents the corresponding bit in is flipped. Taking the XOR of X and will generate the received payload and CRC bits at the receiver (after the bit error happens). For a simpler example, assume = 10010 011 where the last 3 bits are CRC, then a bit error string X = 00110 001 (with 3 flipped bits; 3 = the number of 1s in X) will result in the receiver side receiving = 10100 010.