$(18$ pts$.)$ A circuit has four inputs ABCD and four outputs XYZW $.$ ABCD represents a binary$-$coded decimal digit. XY represents the quotient and $ZW$ represents the remainder when ABCD is divided by $3($ XY and ZW represent $2-$bit binary numbers$).$ Assume the invalid inputs will not occur, which outputs can be considered as don't cares.

$4$