HW$3)$ Design a combinational circuit with three inputs, $x,y$ and $z,$ and three outputs, $A,B,C.$ When the binary input is $0,1,2,$ or $3,$ the binary output is one greater than the input. When the binary input is $4,5,6,$ or $7,$ the binary output is two less than the input.

HW$4)$ A majority circuit is a combinational circuit whose output is equal to $1$ if the input variables have more l$\text{'}$s than $0\text{'}$s$.$ The output is $0$ otherwise. Design a $3-$input majority circuit by finding the circuit's truth table, Boolean equation, and a logic diagram.