Given a bit string of length n, the shift-left-cyclic operation places the first bit at the end, leaving 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 output the n + 1 bit string $ SLC(x).
(ii) Explain why this cannot be done without a $.