What is the difference between OR and XOR?

OR outputs 1 if at least one input is 1, including when both are 1. XOR (exclusive OR) outputs 1 only when the inputs differ, so it gives 0 when both inputs are 1. XOR is the basis of binary addition and parity checks.

Why are NAND and NOR called universal gates?

Any Boolean function can be built using only NAND gates or only NOR gates. Because of this, real silicon often uses one gate type throughout, simplifying fabrication. NAND is especially common in CMOS logic.

What does NOT do with two inputs?

NOT is a single-input gate, an inverter: it outputs the opposite of its one input. In this reference NOT is shown acting on input A only; B is ignored for the NOT row.

How does XNOR relate to equality?

XNOR outputs 1 when both inputs are equal (both 0 or both 1) and 0 when they differ. It is exactly an equality comparator for single bits, which is why it appears in comparators and error-detection circuits.

What are these gates used for?

Combinations of these gates build every digital circuit: adders, multiplexers, memory cells, and processors. Understanding the seven basic gates and their truth tables is the foundation of all digital electronics and CPU design.

Logic Gate Truth Table Reference

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Digital logic is built from a small set of gates that each implement a Boolean function of one or two inputs. This reference shows the truth tables for all seven basic gates and lets you toggle the inputs to see every output live.

How it works

Each gate maps input bits to an output bit:

AND — A · B, output 1 only when both inputs are 1.
OR — A + B, output 1 when at least one input is 1.
NOT — ¬A, the inverter; output is the opposite of A.
NAND — ¬(A · B), AND followed by an inverter.
NOR — ¬(A + B), OR followed by an inverter.
XOR — A ⊕ B, output 1 only when the inputs differ.
XNOR — ¬(A ⊕ B), output 1 only when the inputs are equal.

NAND and NOR are universal: any circuit can be built from one of them alone.

Tips and notes

XOR is the sum bit of a half-adder; AND is its carry bit.
XNOR is a single-bit equality check, used in comparators.
The full 4-row truth table below covers every (A, B) combination so you can cross-check a circuit by hand.