$[10p]1.($a$)$ Find the $8\text{'}$s complement of $(2360{)}_8.$

$($b$)$ Convert $(2360{)}_8$ to binary. $($Preserve all bits after conversion!$)$

$\frac{2360}{2}$

$($c$)$ Find the $2\text{'}$s complement of the result in $($b$).$

$($d$)$ Convert the answer in $($c$)$ to octal and compare with the answer in $($a$),$

$[15$p$]2.($i$)$ Express the following Boolean function with a minimum number of literals:

$a^{\text{'}}bc+ab{c}^{\text{'}}+abc+a^{\text{'}}b{c}^{\text{'}}$

$,a^{\text{'}}{b}^{\text{'}}{c}^{\text{'}}+b+a{b}^{\text{'}}{c}^{\text{'}}$

$($ii$)$ Find $F^{\text{'}}$ while $F=(a+b^{\text{'}})(a+c^{\text{'}})(c+a^{\text{'}})$

$[25$p$]3.$ Determine the minterms of the following Boolean functions given below:

$a^{\text{'}}{b}^{\text{'}}{c}^{\text{'}}+ab+b^{\text{'}}c$