Q$5(6$ points$)$ A combinational circuit has four inputs and three outputs. The first two inputs, a and $b,$ represent a $2-$bit binary number in the range $0$ to $3.$ The other two inputs, $c$ and $d,$ represent a second $2-$bit binary number in the same range. The first output $f$ should be $1$ if and only if the two numbers differ by exactly $2.$ The second output $g$ should be $1$ if and only if the two numbers are equal. The third output $h$ should be $1$ if and only if the second number is larger than the first. Draw the truth table for this combinational circuit.