$(2$ pts$)$ The decoder translates the binary value into a decimal value. The following

figure shows a block diagram of $3-$bit binary decoder. The $3-$to$-8$ decoder has three

inputs $A_2,A_1$ and $A_0,$ and eight outputs, i$.$e$.Y_7$ through $Y_0.$ Answer the following

questions. $($Note: You should show all the steps to receive full credits$)$

a$)$ If the inputs $A_2{A}_1{A}_0=111,$ what are the outputs $Y_7-Y_0?$

b$)$ If the inputs $A_2{A}_1{A}_0=010,$ what are the outputs $Y_7-Y_0?$