Computer Architecture: Answer the questions and show work please. Thank you.

$6-)$ In $5-$bit signed$/2\text{'}$s complement binary number system, perform the following operations between decimal

number equivalents?

a$.)13+7=?$

$($answer as a decimal equivalent!$)$

b$.)-14-4=?$

$($answer as a decimal equivalent!$)$

$7-)$ Find the number bases $($r$\text{'}$s$)$ in the following addition operations?

a$.)(341)r+(53)r=(434)r$

b$.)(543)r-(61)r=(452)r$

$8-)$ Suggest a short way $($without converting to another number base!$)$ for a conversion between base$-3$ and

base$-9$ number systems $($hint: note that $9=3^2).$ Perform the following conversions using your method

a$.)(126{)}_9=(?{)}_3$

b$.)(22102{)}_3=(?{)}_9$