The figure below shows a logic circuit realized with logic blocks studied in class.

a$)$ What does input X do$?$ What is the difference in output if X $=0$ vs if X $=1?$

b$)$ Modify the logic circuit below to implement an adder$/$subtractor logic circuit that computes

A $+$ B or A $$ B depending on the value of X $($you can hand$-$draw your design$).$