Design and test Turing machines to solve the following
problems. Submit a your transition tables or a scan of 
your state-and-transition diagrams with short comments 
saying the purpose of each part, with your .tm files 
and an indication of what the expected input format is.

Apart from start and stop, I recommend that you use different
state names in each of your machine designs. That way it
becomes very easy to join a number of smaller machines
together to perform a larger task. Just like the sensible
use of functions in normal programming.

Whenever I say number, assume I mean positive integer in
binary.

A. Subtract one from a number (don't worry about zero).

B. Find out whether a number is equal to zero or not.
   How to reveal the answer: maybe have two stop states
   called stop-yes and stop-no.
   
C. Reverse a number, so #1110011110# becomes #0111100111#
   
D. Add two numbers together the easy but boringly slow
   way - repeatedly increment one number and decrement
   the other until it is reduced to zero.
   
E. Add two numbers together the good and sensible way,
   do it digit by digit as you would normally perform
   binary addition, creating the sum as a new third number.
   When finished, restore the two original numbers to
   their original state.
   e.g. #101#110# becomes #101#110#1011# (5+6=11)