Make a Turing machine for computing the function f(x) = 2x .

General Strategy: You can think of 2x as " 2 added to itself x times". We can use the string representing the input x as a counter. Each time you add in two 1's, remove a 1 from the counter. (Of course you have to adjust for the input/output conventions given in the course; namely, that you input the number n by putting n + 1 consecutive 1's on the tape. The output is n if the number of 1's on the tape - not necessarily consecutive - is n.)