The following binary numbers are all represented using $4-$bit signed $2\text{'}$s complement. All addition and subtraction should also be conducted in $2\text{'}$s complement form. $\backslash (\backslash$mathrm$\{$A$\}=1101$ ; $\backslash$mathrm$\{$B$\}=0110\backslash )$

$($a$)$ What is the range of numbers that a $4-$bit signed $2\text{'}$s complement system can correctly represent?

$($b$)$ What is A$\text{'}$s value in decimal?

$($c$)$ What is B$\text{'}$s value in decimal?

$($d$)$ Perform addition $\backslash (\backslash$mathrm$\{$C$\}=\backslash$mathrm$\{$A$\}+\backslash$mathrm$\{$B$\}\backslash ).$ What is C in $4-$bit signed $2\text{'}$s complement form? Is there overflow? Is the calculation correct?

$($e$)$ Perform subtraction $\backslash (\backslash$mathrm$\{$D$\}=\backslash$mathrm$\{$A$\}\backslash )-$B$.$ What is D in $4-$bit signed $2\text{'}$s complement form? Is there overflow? Translate A$,$ B$,$ D into their decimal values. Is the calculation correct?