Design a combinational circuit with four inputs, $w,x,y,$ and $z,$ and four outputs, $A,B,C,$ and D$.$ When the binary input is $0,1,3,7,9,$ or $11,$ the binary output is three greater than the input. Otherwhile, the ouput is one less than the input.

Design a $3-$bit counter that follows a specific sequency using two $JK$ flip$-$flops and one $D$ flip$-$flop. The counter should follow this sequen: $000010011101111011.$