XOR – The Interesting Gate

Note: The interesting features in XOR and XNOR are somehow the same but with small difference, I’ll speak in details here about XOR and will provide another article for XNOR later.

Among other logic gates, XOR and XNOR are  interesting gates having some unique features.

Multi-input XOR

All 2-input logic gates have the same meaning when they have more than 2 inputs. For example an AND gate is a gate that outputs 1 when all its inputs are 1, an OR gate outputs 1 when any of the inputs is 1, a NAND gate outputs 0 when all its inputs are 1, a NOR gate outputs 1 when all its inputs are 0.

A 2-input XOR gate outputs 1 when there’s exactly a single 1 at the inputs which means it’s exclusively there and that’s from where the name XOR (Exclusive OR) comes. We can alternatively say that it outputs 1 when the 2 inputs are different.

A multi-input XOR gate however doesn’t necessarily have the same meaning as the 2-input XOR above. There’re two different interpretations for a multi-input XOR and let’s check that on a 3-input XOR as an example: