what is the largest $10-$bit binary number that can be represented with $($i$)$ unsigned numbers; $($ii$)$ two's complement numbers; $($ii$)$ sign$-$magnitude numbers?

b$)(9$ pommasitude them$-$map method, simplify the Boolean function F$($W$...)=2(3,8,11,12,13,15)$ together with the don't care conditions $(...)=(0,1,2,5,7,9,10,14)$ into minimal SOP expression. c$)(9$ points$)$ Using Boolean algebraic manipulations $($Do not use K$-$map!$),$ minimize the Boolean function F$($A$,$B$,$C$,$D$)$ given below into minimal SOP

expression. Note: Do not just write the result; show the steps of the simplification. There is no partial credit for the partially simplified version of the function. F$($A$,$B$,$C$,$D$)=[$C$+$AC$\text{'}($BD$+$BD$\text{'})]$D $+($BC$\text{'}+($B$+$C$)\text{'}+$D$\text{'})\text{'}$