Please answer all parts, but if not, please focus on part c. Thanks!

1. (40 points) Consider a CRC code with a generator polynomial of g(x) = x + x2 +1. a. (10 points) Show the shift-register circuit that implements this CRC code. b. (10 points) Show step by step (using the longhand division) how to find the codeword that corresponds to five information bits of 00001. c. Suppose the codeword length is 10. Answer the following questions, with proper justifications. 1. (10 points) Give one example error vector of an undetectable error burst of length 7. ii. (10 points) Give one example error vector of an undetectable 7-bit error. 1. (40 points) Consider a CRC code with a generator polynomial of g(x) = x + x2 +1. a. (10 points) Show the shift-register circuit that implements this CRC code. b. (10 points) Show step by step (using the longhand division) how to find the codeword that corresponds to five information bits of 00001. c. Suppose the codeword length is 10. Answer the following questions, with proper justifications. 1. (10 points) Give one example error vector of an undetectable error burst of length 7. ii. (10 points) Give one example error vector of an undetectable 7-bit error