Digital electronics often makes use of DeMorgan theorem, which says that if we combine an inverter (NOT) with any gate, the gate performs the same function as the opposite type of gate.


Here we can see that NAND gate is equal to OR gate with inverted inputs, (A · B)' = A' + B'.
The NAND gate takes its name from NOT and AND.

NOR Gates

NOR gate outputs are the inverse of OR gate; NOR gets its name from NOT and OR, it is inverse of OR gate. The light will be on when both switches are open.

Using DeMorgan theorem, we can convert NOR gate to AND gate with inverted inputs where (A+B)' = A' · B'.

XOR Gates

XOR gate (exclusive OR) generates a logic HIGH output when either input is logic HIGH and the other is logic LOW, so only one input must be ON (not both inputs) to produce the output ON. The light will be ON if one switch is open while the other switch is closed.

XNOR Gates

XNOR gate (exclusive NOR) generates a logic HIGH output when either both inputs are logic HIGH or both inputs are logic LOW. It is the inverse of XOR gate. The light will be ON when both switches are open or both switches are closed.