**Due: Tuesday, September 25th by 11:59 PM**

## Your Task

Using JFLAP, create Turing Machines to perform the tasks described below.

### First Task

Create a Turing Machine that increments a binary number.

The initial tape will be a sequence of ones and zeroes specifying a binary (base 2) number. The final contents of the tape should be a sequence of ones and zeros specifying a binary number that is one greater than the original number.

For example, if the initial sequence is

10010111

Then the final sequence (once the Turing Machine has halted) should be

10011000

Another example, if the initial sequence is

111

then the final sequence should be

1000

#### Hints

The Turing Machine should start by moving to the end of the input string, then start moving to the left.

If the Turning Machine sees a 0 on its scan to the left, it can change it to a 1 and halt. If it sees a 1, it should change the 1 to a zero and continue to the left (essentially carrying the result of adding 1 to 1 one place to the left.)

Don't forget that the result can overflow past the left side of the string (as in the second example above.)

### Second Task

Create a Turning Machine which *decrements* (subtracts one from) the binary
number on the input tape.

The process will be similar to incrementing.

For example, if the initial string is

1001

then the final string should be

1000

Another example: if the initial string is

1000

then the final string should be

0111

(If you would like to trim unnecesssary 0's from the left side of the string, you can, but it's not required.)

## Submitting

Submit a zip file with both JFLAP (.jff) files containing your Turing Machines to Marmoset
as **assign3**:

https://cs.ycp.edu/marmoset/