A priority encoder has $2$N inputs. It produces an N$-$bit binary output. This output indicates the bit

number for a far$-$left bit when it is TRUE $(1)$ in the binary input. $($Bit numbers start from zero. Bit

$0$ is the right$-$most bit.$)$ It produces $0$ if none of the N bits are TRUE. It also produces an output

NONE that is TRUE if none of the inputs are TRUE. Design a priority encoder with $4$ inputs A$3$:$0$

and outputs Y$1$:$0$ and NONE. For example, if the input is $0100,$ the output Y should be $10($decimal

$2)$ because bit $2$ is the far$-$left bit that is $1.$ Also, NONE should be $0.$ Write a truth table using the

don$$t care symbol $($X$).$ In addition, give a Boolean equation for each output. You do not need to

simplify the Boolean equations.