The COPY algorithm reads a tape of characters and copies it at the end of the tape. The

algorithm can be described in the following manner:

$($C$1)$ move to the end of the tape, write # in the first empty field $($this separates the

original and the copied part of the tape$)$;

$($C$2)$ move to the tape start;

$($C$3)$ move one to the right and read the symbol;

$($C$4)$ if the symbol is $0$ : write $ and move to tape end, write $0,$ return to $ and write $0$ ;

$($C$5)$ if the symbol is $1$ : write $ and move to tape end, write $1,$ return to $ and write $1$ ;

$($C$6)$ repeat $($C$3)-($C$5)$ until # is read.

$($a$)$ Explain the importance of writing $ at each step before copying.

$1$mark$(s)$

$($b$)$ Design a Turing Machine to execute the above algorithm.