$($b$)$ In addition to BCD and Excess$-3,$ the $2-$out$-$of$-5$ code is another code used to represent decimal digits. The table below lists the $2-$out$-$of$-5$ representations for the decimal digits $0-9.$ Use $4-$to$-16$ decoder and OR gates to implement a combinational system that accepts a $4-$bit binary number and yields the corresponding $5-$bit $2-$out$-$of$-5$ code.

$\backslash$table$[[$A $2-$out$-$of$-5$ code,$],[$Decimal digit,$2-$out$-$of$-5$ code$],[0,11000],[1,00011],[2,00101],[3,00110],[4,01001],[5,01010],[6,01100],[7,10001],[8,10010],[9,10100]]$