$4)$ Carry out addition and subtraction $($first number subtracted by the second number$)$ of the following pairs of numbers in $2\text{'}$s complement representation: a$)10100$ and $11100$ ; b$)0101011$ and $1010010$; Clearly underline your sums$/$differences$.$ Convert the two operands and results to decimal format and check if the sums and differences are correct.

$5)$ Carry out sign extension to derive $8-$bit $2$s complement representations of the numbers in pair b$)$ of question $4).$ Repeat the addition and subtraction and check if the results are correct.