$($a$)$ Several integer numbers need to be represented, using $12$ bits for each. Some of them

are negative and therefore a question arises of their exact representation.

One option is to commit the most significant bit $($MSB$)$ to representing sign

$(1$ negative, $0$ positive$),$ and then use the rest of the bits to encode the absolute value

$($sign $+$ magnitude representation$).$ Another is to use the $2$s complement representation.

Find binary encoding of the following numbers: $2022$dec, $-2020$dec, $0$dec and $-5$dec, in

sign$+$magnitude and in $2$s complement representation. $(8$ marks$)$

$($b$)$ Find the range of integers that can be encoded in each of these two representations