A certain BCD$-$to$-$decimal decoder has four input lines and $10$ output lines. If four input lines are capable of $16$ possible combinations and only $10$ output combinations are required, why have four inputs?

With four input lines, the decoder can provide for those rare occasions when input codes greater than $10012$ may require decoding.

With three input lines the maximum number of output combinations would be limited to eight.

With three input lines the maximum number of output combinations would be equal to nine, including zero, and this would be sufficient, but decoders are not manufactured with only three inputs.

Both A and $C$