Chapter $2,$ problem $2$: $(5+5pts)$ Show truth tables for each of the following.

b$)$ The system has four inputs and three outputs. The first two inputs, a and $b,$ represent a $2-$bit

binary number $($range of $0$ to $3).$ A second binary number $($same range$)$ is represented by the

other two inputs, $c$ and $d.$ The output $f$ is to be $1$ if and only if the two numbers differ by exactly

$2.$ Output $g$ is to be $1$ if and only if the numbers are equal. Output $h$ is to be $1$ if and only of the

second number is larger than the first.

f$)$ The system has four inputs. The first two, a and $b,$ represent a number in the range $0$ to $2(3$ is

not used$).$ The other two, $c$ and $d,$ represent a second number in the same range. The output, $y,$ is

to be $1$ if and only if the two numbers do not differ by more than $1.$