Q$1.$ Given two decimal numbers $\backslash (\backslash$mathrm$\{$A$\}=\backslash$mathrm$\{$M$\}\mathrm{.}43\backslash )$ and $\backslash (\backslash$mathrm$\{$B$\}=\backslash$mathrm$\{$N$\}\mathrm{.}87\backslash ),$

$($a$)$ Convert A and B into its corresponding binary numbers with at least $7$ bits in their integer parts and $6$ bits in their fractional parts.

$($b$)$ Calculate $\backslash (\backslash$mathrm$\{$A$\}+(-\backslash$mathrm$\{$B$\})\backslash )$ using binary arithmetic, show your answer in hexadecimal number.

$($c$)$ Calculate $\backslash (\backslash$mathrm$\{$A$\}\backslash$times $\backslash$mathrm$\{$B$\}\backslash )$ using binary arithmetic, show your answer in decimal number.

$($d$)$ Calculate $\backslash (\backslash$mathbf$\{$M$\}\backslash$times $16\backslash$div $\backslash$mathbf$\{$N$\}\backslash )$ using binary arithmetic, show your quotient and remainder in octal numbers.

Show appropriate steps in your conversions and calculations.