# Three Way Light Switch using Two Binary Switches

Somebody presented me with an interesting problem that I can't seem to figure out. Is it possible to build a three-way switch circuit for a light bulb (akin to common household light fixtures) using only two SPST switches (on/off switches that cannot carry current in the off state)? If so, how would one go about doing it? No components other than a single voltage source, the switches, wiring, and the light bulb itself are allowed (so no transistors, resistors, capacitors, etc.) Note that creating a short circuit to turn off the light is a viable option.

• two XOR gates or 1P2T ...or do you mean using 1P1T ( these are all binary but different) – Tony Stewart Sunnyskyguy EE75 Nov 27 '16 at 15:32
• No, the kind of switch I'm referring to will block all current in the off state. I also don't think it's as simple as two xor gates since no transistors are allowed. Thank you for the suggestion though. – user2950265 Nov 27 '16 at 15:35
• ok then it is not a binary switch per se, but a SPST or 1P1T switch . Binary switches are normally low impedance at 2 voltages. not as you describe which is binary position but normally open NO or normally closed, NC or toggle type – Tony Stewart Sunnyskyguy EE75 Nov 27 '16 at 15:38
• Ah, ok. Forgive me since I'm a beginner with terminology. Thank you for the clarification. – user2950265 Nov 27 '16 at 15:41
• It needs to be XOR not OR or SPST – Tony Stewart Sunnyskyguy EE75 Nov 27 '16 at 15:44

I think it should be very obvious that you cannot produce a "3-way" switching setup within the confines you have specified. If there were a way to do it then I can assure you that it would be used for the switching of lights in general practice.

There are ways to achieve the switching using the two simple switches (particularly if they are momentary type) by adding a multi-pole relay to do the actual switch toggling.

• Thanks for your input. Normally I would agree, but short-circuiting to turn off the light is an option, which would explain why such a circuit wouldn't be used in practice. Do you have a more concrete proof of your assertion? – user2950265 Nov 27 '16 at 17:18
• @user2950265, we have 4 circuit elements with 2 terminals each. There are a finite number of ways to connect them. How about you draw up all possible netlists and evaluate if they work? Your question, you do the work. ;-) – mkeith Nov 27 '16 at 17:32

A three-way switch is a misnomer in logic. It only means 3 wire connection for a SPDT switch.

F=A XOR B is the requirement.

SPDT switch can open or connect any intermediate input or output to any input or output. You cannot implement XOR with 2 switches it takes 4 in which 2 are switched simultaneously.

simulate this circuit – Schematic created using CircuitLab

This question is illogical... ie bad logic.