It is quite common to have a single lightbulb in the home that has two switches to control it. It works so that whichever way the light is (on/off) you can change the state of either switch and it will change the state of the bulb.
For this you could use something like an XNOR gate circuit. (Is this how it is done in practice?).
Is it possible to do the same thing with three switches? So that if any of the three switches changes state it will toggle the state of the light?
Just to be clear, a 3-way switch (i.e., one light bulb controlled by two switches) is wired up like this:
simulate this circuit – Schematic created using CircuitLab
For a 4-way switch (three switches controlling the light-bulb) you start with the same two switches as shown above, but you add a DPDT switch in the middle. That DPDT switch is set to route electricity straight through in one position, but cross connect the upper and lower wires in the other position.
Your analysis is correct. In practice it is done with mechanical switches rather than logic gates, but (((Functionally))) it is an exclusive-nor circuit. If both switches are up (ones) or both switches are down (zeros), the light is on (one).
Any well-stocked hardware store will have switches built for three-location control of one light. I have not seen anything beyond that.
Yes, that kind of device exist. It is named 4-way switch. You can put how many you need between two 3-way switches. It is can be bought in any hardware store and quite expensive. It just cross switching two lines.
No, there are no XNOR gates in light switches. Schematic-wise, the two SPDT switches are wired so that they only connect the lamp to mains voltage when both switches are in same direction. So if switch 1 is connecting voltage to wire A, the switch 2 has to select wire A to lamp. If one of the switches are turned to other position, the circuit is broken, until the state of either switch is changed.
Yes, it is possible with three switches, or even more, but the middle switches need to be DPDT switches.
