(30) a crc is constructed to generate a 4-bit fcs for a 9-bit message. the generator polynomial is x4 +x3 +1. a) draw the shift-register circuit that would perform this task. b) encode the data bit sequence 111011001 using the generator polynomial and give the codeword t(x). c) now assume that the 7th bit (counting from the left side) in the codeword is in error and show that the detection algorithm detects the error.