A circuit has four inputs D$,$ C$,$ B$,$ A encoded in $8421$ natural binary

form. The inputs in

the range $00002=0$ to $10112=11$ represent the months of the year

from January $(0)$ to

December $(11).$ Inputs in the range $1100$ to $1111($i$.$e$.,12$ to $15)$

cannot occur or don$$t

care. The output of the circuit is a logical one if the month

represented by the input has

$31$ days. Otherwise the output is false.