$1.$ PROBLEM DESCRIPTION:

A room has five doors with a light switch next to each door numbered from $1$ to $5,$ and one light

in the center of the room. Design a circuit that allows any light switch to change the state of the light

$($that is$,$ if the light is currently off, any switch can turn it on$,$ and vice$-$versa$)$ and display the

corresponding switch number used.

Each of the five inputs can be ON or OFF $($a $1$ or a $0),$ so you can represent all possible

combinations of inputs in a truth table. The first row $($all $0$s$)$ represents a state where the light is

OFF and number $0$ is displayed. From there, if any input equal to a $1($ON$),$ the light toggles ON

and the corresponding switch used will be displayed. When the output is ON$,$ any of the input equal

to a $1($ON$)$ will set the light OFF again and the switch number will be displayed, and then any of

the input equal to a $1($ON$)$ will turn the light back ON and the switch number will be displayed,

etc.

You need to set a rule for the system on what to be done if more than one switches equal to a

$1($ON$)$ at the same time to avoid any error that may occur $($The system will always toggle the

light unless all switches are OFF$).$