Q$1.$ Given $A=1M\mathrm{.}52$ and $B=2N\mathrm{.}24(,A=19\mathrm{.}52,B=210\mathrm{.}24$

$($a$)$ Use binary to convert between octal and hexadecimal: convert hexadecimal numbers $($A$)16$ and $($B$)16$ into

their corresponding octal numbers.

$($b$)$ Convert decimal numbers $($A$)10$ and $($B$)10$ into their corresponding binary numbers with at least $5$ bits in

their integer parts and $4$ bits in their fractional parts.

$($c$)$ By using the results obtained in part $($b$),$ calculate A$-$B using binary arithmetic with $2\text{'}$s complement,

show your answer in decimal number.

$($d$)$ By using the results obtained in part $($b$),$ multiply A$\text{'}$s fractional part with B$\text{'}$s fractional part using binary

arithmetic, show your answer in decimal number.

Show appropriate steps in your conversions and calculations.