Help designing a Turing Machine I am faced with the following question:


  Design a Turing Machine that recognizes the language $L = \{1^{2n+1}\mid n \text{ is a non-negative integer}\}$. Show the state diagram.


I started doing this using $Q \times \Gamma \rightarrow Q \times \Gamma \times \{L, R\}$, and setting up a 7 tuple but I cannot come up with the state diagram.
Hint: $L$ is regular. Draw a DFA accepting $L$, and modify it to a full-fledged Turing machine whose operation is essentially equivalent to that of the DFA.