Q$1$: Convert the decimal number $(123\mathrm{.}456{)}_{10}$ into the following indicated bases:

$($a$)$ Binary number $($b$)$ Octal number $($c$)$ Hexadecimal number

Q$2$: Convert the decimal number $879$ to binary in two ways:

$($a$)$ convert directly to binary;

$($b$)$ convert first to hexadecimal and then from hexadecimal to binary.

Q$3$: Let $x=9316$ and $Y=4918.$ Find $x-Y$ and $Y-x$ by using $9\text{'}$s and $10\text{'}$s complement methods.

Q$4$: Let $x=1010101$ and $Y=0101001$ be two binary numbers. Calculate $x-Y$ and $Y-x$ by using

$1\text{'}$s & $2\text{'}$s complement method.

Q$5$: Simplify the following Boolean expressions to a minimum number of literals:

$($i$),xy+x{y}^{\text{'}}$

$($ii$)$ ABC$+A^{\text{'}}B+AB{C}^{\text{'}}$

$($iii$)xyz+x^{\text{'}}y+xy{z}^{\text{'}}$

$($iv$)xy+x(wz+w{z}^{\text{'}})$