A hypothetical logic circuit sometimes known as a half$-$subtractor can be created by combining exactly three logic gates. Similar to the need for carrying bits when adding, subtraction sometimes requires borrowing bits. The following truth table shows the logic of a half$-$subtractor circuit to subtract a single$-$digit binary number $B$ from a single$-$digit binary number $A$ :

$\backslash$table$[[$A$,$B$,$Borrow needed,Difference$],[0,0,0,0],[0,1,1,1],[1,0,0,1],[1,1,0,0]]$

a$.$ Complete the logic diagram for a half$-$subtractor by identifying three different logic gates for each of the three boxes below $,$ and $Z)$:

b$.$ In reality, the designers of processor chips don't actually use 'subtractor' circuits; instead they only use adders. Suggest how you might ise an adder to subtract one number from another.