1. Construct a Turing Machine that transforms a unary string into its binary representation. Initially the input tape contains the number n in unary notation (alphabet:1). When the machine stops, the input has been erased, and the binary representation of n (alphabet {0, 1) is on the tape. To simplify matters, assume that the tape is unbounded in both directions, and that the final binary representation is written to the left of the original input. If the initial tape configuration contains the number 13: then when the machine stops the tape looks as follows: 1101x Use the standard algorithm: the remainder of successive divisions by 2 produces the digits from least significant to most significant. The tape alphabet includes a separator X, feel free to add more characters if it helps. Try to minimize the number of states you use. It might be helpful to draw the machine as a graph, where each edge is labelled with the triple: input symbol output symbol, direction]