$(20$ pts$)$ LUT design $($LUT $=$ LookUp Table$)$ Design a digital logic circuit with three $($binary$)$ inputs: x$,$ y and z$,(07$ in decimal$)$ and the three $($binary$)$ outputs, A$,$ B$,$ and C$.$ When the binary input is $0,1,2,$ or $3,$ the binary output is $2$ greater than the input. When the binary input is $4,5,6,$ or $7,$ the binary output is $2$ less than the input. decimal x y z A B C $00001001201030114100510161107111$ Set$$up the appropriate truth table, simplify using K$$maps$.$ Implement, using LogiSim, the simplified logic circuit with optimal number of logic gates