I want to write a Turing machine which checks for unary powers of 2 but without the use 0s, only accepting as input a series of 1s and dashes. I do not know of a sequence of states which would allow me to demonstrate this. I worked out 1 of the 2 I started with, which is make a palindrome checker but as for this I'm clueless, any help would be appreciated, even just a description how to begin to develop such algorithm.
Basically it works like this: you insert a sequence of 1s such as 1111 and the algorithm checks whether the number is divisible by 2, by checking the length of the input - hope I'm being more descriptive here, sorry if I'm not.