Subtraction $101$ The binary subtraction operation takes two $n-$bit binary strings as its input and returns their $n-$bit difference.

$($a$)$ Describe a boolean circuit for this operation for an arbitrary $n$ that uses $O(n)$ size.

$($b$)$ Show that this operation is in the class $A{C}^0.($That is$,$ for each bit of the output, there is an $A{C}^0$ circuit to compute that bit.$)$