This turing machine duplicates a string of 1's.  

Specifically, if q is the initial state and f is the final state, then
the machine operates as...

                q00w |-*- f0w0w  (replace the last 0 with 0w)

where w is a string of 1's.  

Method:  Mark the rightmost 1 with an x, go left and replace the leftmost
       0 with 01.  Repeat until all 1's in the rightmost w are x's.  Then
       replace all x's with 1's, go to left end of tape and halt.

States:   {0,1,2,3,4,5,6,7,8,9,a}  
Final state: {a}
Alphabet: {0,1}
-------------------------------------------------------

(0000r      state 0:  to start off find w
(0111r      state 1:  once in w, get to the right end
(1111r
(1  2l      state 2:  found the right end.  Mark the last 1 with an x
(21x3l      state 3:  duplicate the 1 that was just marked...  move left
(3113l                   entering in turn states 4, and 5 to do so
(3004l      state 4:  have gone past the rightmost dividing 0.
(4114l                  going past 1's that have already been duplicated.
(4015l      state 5:  just replaced the leftmost 0 with 1, now
(5 06r                  add a leftmost 0.  

---------- now repeat....
(6116r      state 6:  move to the right to repeat
(6007r      state 7:  moved onto the rightmost w.  Test it...

(7111r           ....There are 1's left to duplicate
(1xx2l                  found the right end.  Mark the last 1 with an x
                        by looping back up to the (21x3l) quintuple above
                 ....There are no more 1's left, so
(7x18r      state 8:  All the 1's were already marked.  Change x's back to 1's
(8x18r
(8  9l      state 9:  Move to left end and halt
(9119l
(9009l
(9  ar      state a:  Final state