$(15$ points$)$ Design a combinational logic circuit $($using logic gates only$)$ that accepts as input a $3-$bit number, and generates a $6-$bit output equal to the square of the $3-$bit input number. Show your truth table, Boolean expressions, and the resulting logic circuit. Make sure to minimize your logic. No need to implement it in Quartus Prime but it would be helpful if you need to verify your design.