consider a logical circuit that accepts $4-$bit binary numbers representing decimal numbers $0$ to $15.$ the circuit checks the $4$ bit binary equivalent of the decimal number. if the number is odd and it is a prime number the function outputs a $1.$ based on the above: $($i$)$ draw the function table for the above$-$mentioned logical circuit. $($ii$)$ map the function table to a $4$ variable k$-$map. $($iii$)$ simplify the expression obtained by the k$-$map. $($iv$)$ sketch the logic circuit using logic gates.