$($Comparators $-20$ points$)$

a$)$ Consider A and B to be two $2$ bit vectors. You are asked to design a circuit where A & B are taken as

inputs and the ciruit gives an output f where $f=1$ if $AB$ and $f=0$ otherwise. Write a boolean

logic formula for f $.$

b$)$ Now consider a function $g$ such that $g=A-B$ where A and B are $2$ bit vectors. Write the truth tables

with $A$&$B$ as $2$ input bit vectors and g as the result of their subtraction using $1\text{'}$s complement method

and $2\text{'}$s complement method.

c$)$ Which one is a better method and why?