A new code called the $x-$code is defined as follows:

For any even number $x_e$ between $0000$ and $1111,$ the $x-$code is $(\frac{x_e}{2}).$

The code is not defined for all odd numbers.

Desing a digital circuit that implements binary$-$to$-$x$-$code conversion. Show all the steps. Final circuit only will result in zero marks. Implement the circuit using a multiplexer with the lowest number of inputs possible.