# Lab 10

**Overview**: Turing machines

## Problems

- Draw the state diagram for a Turing machine that increments a binary
number. Assume that the input tape contains at least one non-blank
symbol. For example, if the binary representation of 4 is initially on the
tape
..b100b..

then the output should be the binary representation of 5,
..b101b..

or if the initial tape contains the binary representation of 11
..b1011b..

then the output should be the binary representation of 12,
..b1100b..

or if the initial tape contains the binary representation of 7
..b111b..

then the output tape should be the binary representation of 8,
..b1000b..

- Suppose we try to construct a Turing machine to solve a particular
problem, but we are not successful. Does this mean that no Turing machine
exists that can solve that problem? Explain and justify your answer.
- Does the fact that the Halting Problem is not computable mean that
we can never tell if a program we have written is going to halt? Explain.

### What to turn in:

- Nothing. You don't need to turn
in this one, but it's a good idea to look over the problems as
preparation for the exam.