Design a Turing machine that takes as input a number N and adds 1 to it in binary. To be precise, the tape initially contains a $ symbol followed by N in binary. The tape head is initially scanning the $ in state qo. After computation, your TM should halt (at state q) with N+1, in binary form, on its tape, scanning the leftmost bit of N+1. You may destroy/overwrite the $ in creating N+1, if necessary. For instance: If the input is $10011, then the output should be $10100, and If the input is $11111, then the output should be 100000. Provide the solution in the form of a formal description.