Give a detailed description (i.e. state machine diagram) of a deterministic Turing machine which, when started with a binary string on it's tape, ends with a string on the tape that contains all of the 1s in w but none of the 0s. That is, the Turing machine removes all of the 0s and compresses the remaining 1s into a single string. For example: when started with 01101 on it's tape, the machine should end with 111 on its tape.

(note: if it helps, the output can appear on a different location of the tape from where the input originally appeared)