Give the transition function for a Turing Machine that begins with the symbol # followed by a numberN in binary on its tape and finishes its computation with the value of N $+1$ on its tape and halt in anaccepting state. Let the start state be q$0$ and qa be the accept state. For example your Turing machinewill begin in the configuration, q$0$$$1111$ and end in the configuration qa$10000.$ As another exampleyour Turing machine will begin in the configuration, q$0$$$10101$ and end in the configuration qa$10110.($a$)$ Give the state diagram of your Turing machine and explain the purpose of each state. $($b$)$ Trace your Turing machine on the input $$111$ giving each configuration in the computation.