P$4/$ Design a combinational circuit that converts a four$-$bit Gray code $($ Table $1\mathrm{.}6)$ to a four$-$bit binary number.

$($a$)$ Implement the circuit with exclusive$-$OR gates.

$($b$)$ Using a case statement, write and verify a HDL model of the circuit.

Gray Code Decimal Equivalent

$00000$

$00011$

$00112$

$00103$

$01104$

$01115$

$01016$

$01007$

$11008$

$11019$

$111110$

$111011$

$101012$

$101113$

$100114$

$100015$