$($a$)$ Consider the following binary number :

$01011110$

What decimal value do these $1$s and $0$s represent if we interpret these bits to represent:

$($i$)$ an unsigned $8-$bit binary integer?

$($ii$)$ an $8-$bit two$$s complement integer?

$($iii$)$ an integer number represented in $8-$bit sign$-$magnitude notation?

$($b$)$ Perform the operation:

$(-15)$

$+(+1)$

$=-14$

using $5-$bit twos complement arithmetic. Indicate whether overflow has occurred.

$($c$)$ Perform the operation:

$(-15)$

$+(+1)$

$=-14$

using $5-$bit sign magnitude arithmetic. Indicate whether overflow has occurred.

$($d$)$ Perform the operation:

$-16$

x $(-1)$

$=+16$

using $5-$bit two$$s complement multiplication following the $$pencil$-$paper$$ method using

sign extension.

$($e$)$ Perform the operation:

$(+4)$

$-(+6)$

$=-2$

in $5-$bit two$$s complement arithmetic $,$Please answer according to discrete mathamatics