$6-$ A priority encoder has $2^N$ inputs. It produces an $N-$bit binary out$-$ put indicating

the most significant bit of the input that is TRUE, or $0$ if none of the inputs are

TRUE. It also produces an output NONE that is TRUE if none of the input bits are

TRUE. Design an eight$-$input priority encoder with inputs $A_{7\text{:}0}$ and outputs $Y_{2\text{:}0}$

and NONE. For example, if the input is $00100000,$ the output $Y$ should be $101$

and NONE should be $0.$ Give a simplified Boolean equation for each output, and

sketch a schematic.