Key points:Inputs: A$,$ B$,$ C $($each can be $0$ or $1)$Outputs: Y$0$Y$7($only one is active at a time$)$Minterms: Represent unique combinations of input states that activate specific outputsSteps to generate minterms:Convert indices to binary:$0=0002=0104=1006=1108=1,000($requires four bits for representation$)10=1,010$ Write minterm expressions:Use input variables $($A$,$B$,$C$)$ and their complements $($A$,$B$,$C$)$A $0$ in the binary representation corresponds to a complemented input in the mintermA $1$ in the binary representation corresponds to a non$-$complemented input in the mintermResulting minterm expressions:Y$0=$ABCY$2=$ABCY$4=$ABCY$6=$ABCY$8=$ABCD $($note the need for a fourth input, D$)$Y$10=$ABCDExplanation:Each minterm expression represents the specific input combination that activates the corresponding output.In a $3-$to$-8$ decoder, only one output is active at a time, determined by the binary input values.$($draw the decoder of this question