$($Extra Credit$)$ Prove that given an $n-$bit binary number $x=[x_{n-1},$dots,$x_0]$ in $2\text{'}$s

complement,

then $\stackrel{}{x}+1=[\frac{?}{\text{b}\text{a}\text{r}}(x_{n-1}),$dots$\frac{,}{b}ar(x_0)]+1=-x$