$($a$)$

$($b$)$

Construct a Turing machine with one tape, that accepts the following languages:

a$)\{02$n$1$n : n $0\}.$

b$)\{$w : w contains twice as many $0$s as $1$s$\}.$

Assume that, at the start of the computation, the tape head is on the leftmost symbol

of the input string.