$3.(32$ points, $2$ points for each addition scenario$)$ The $1\text{'}$s and $0\text{'}$s stored in a computer's memory can be interpreted by the computer as an instruction or a data item. The result of a computation can change based on the interpretation of the data. Perform each of the following $6-$bit additions assuming the values are

$($i$)$ unsigned $($i$.$e$.$ the values are $6-$bit binary numbers$),$

$($ii$)$ signed$-$magnitude,

$($iii$)1\text{'}$s complement, and

$($iv$)2\text{'}$s complement.

In each instance report if overflow occurs.

a$.\backslash (\backslash$begin$\{$array$\}\{$r$\}100111\backslash \backslash +\backslash$quad $111110\backslash \backslash \backslash$hline$\backslash$end$\{$array$\}\backslash )$

b$.010110$

c$.001100$

d$.111010$

$\backslash (+100001\backslash )$

$\backslash (+010101\backslash )$

$\backslash (+100101\backslash )$

Note: Be sure to show your work.