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)
and then,
                q0w0w |-*- f0ww0w

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:   {0,1,2,3,4,5,7,8,9}   (there is no state 6)
Final state: {9}
Alphabet: {0,1}
-------------------------------------------------------

(0000r      state 0:  to start off, find the right end
(0110r  
(0xx0r             some 1's may have already been marked

(0  2l      state 2:  found the right end.  Mark the last 1 with an x
(2xx2l             move past already marked locations.
!(21x3l
(2007r      state 7:  No more 1's to duplicate, change x's back to 1's
(21x3l      state 3:  duplicate the 1 that was just marked...  move left
                         to find the leftmost 0
(3113l                 
(3003l
(3xx3l
(3  4r      state 4:  found the front of the string.  Add a 1.
(4015l      state 5:  add a terminating 0
(5 00r      state 6:  now go to the right end of string and repeat

(7x17r
(7  8l      state 8: move to left end and halt.
(8008l
(8118l
(8  9r      state 8: final state