A priority encoder is an encoder circuit with priority. If $2$ or more inputs are equal to $1,$ the input with the highest priority will take precedence. The truth table of a $4-$input priority encoder is shown below. An output $V$ is added which is set tol when one or more inputs are equal to $1$ ; othervise $V$ is $0.$ The tivo outputs $x$ and $y$ are not inspected when $V$ equals $0$ and hence they are specified as don't care outputs. Note that wheras $x^{\text{'}}s$ in output columns represent don't care outputs, the $x^{\text{'}}s$ in the input'columns are useful for representing a truth table in compact form.

For example, input X$100$ represents the $2$ input combinations: $0100$ and $1100.$ Derive the simplified SOP expressions for $x,y$ and $V,$ and draw the logic diagram.

$\backslash$table$[[$Inputs$,$Outputs$],[D_0,D_1,D_2,D_1,x,y,$