$(20$ pts$)$ LUT design $($LUT $=$ LookUp Table$)$

Design a digital logic circuit with three $($binary$)$ inputs: $x,y$ and 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.

Set$-$up the appropriate truth table, simplify using K$-$maps. Implement, using LogiSim,

the simplified logic circuit with optimal number of logic gates.