Given a bit string of length n, the shift-left-cyclic operation places the first bit at the end, leavin the rest of the bits unchanged. For example, SLC(100110) = 001101.

(i) Build a Mealy machine with input and output alphabet {0 1 $} such that for any bit string x when we input the n+1 bits x$, we get as ouput the n+1 bit string $ SLC(x).

(ii) Explain why this cannot be done without a $.

Please provide step-by-step explanations. Thanks!