Which is true about the given $2-$bit carry$-$lookahead adder? Hint: g $=$ ab$,$ p $=$ a $+$ b$,$ and the expression for each digit's carry$-$out is co $=$ ab $+($a $+$ b$)$ci $=$ g $+$ p$$ci$.$

A$.$

c$0=0,$ when a$0=1,$ b$0=1,$ and cin $=0$

B$.$

c$0=1,$ when a$0=1,$ b$0=1,$ and cin $=1$

C$.$

c$1=1,$ when cin $=1,$ g$0=1,$ p$0=1,$ g$1=0,$ and p$1=0$

D$.$

c$1=0,$ when cin $=0,$ g$0=1,$ p$0=1,$ g$1=1,$ and p$1=1$