Logic Gate Output Calculator

Work out logic gate output instantly with clear inputs, formula shown and shareable results.

About Logic Gate Output Calculator

Each logic gate implements one Boolean function of its inputs. NAND and NOR are universal: every other gate, and hence every digital circuit, can be built from copies of either one alone.

Formulas

NAND

NAND(A, B) = NOT(A AND B)

XOR

XOR(A, B) = 1 exactly when the inputs differ

Worked example

With the default values below, Logic Gate Output Calculator returns Two-input output of 0 (low). Change any input above and every figure here is recalculated in your browser.

Inputs used

Gateone of AND, OR, NAND, NOR, XOR, XNOR: NAND
Input Aaccepts 0–1: 1
Input Baccepts 0–1: 1
Input C (for three-input gates)accepts 0–1: 1

Results

Two-input output: 0 (low)
Three-input output: 0 (low)
Output as a bit: 0
Universality: Universal gate: any logic function can be built from it alone

Step by step

1Values used
2NAND
3XOR
4Two-input output= 0 (low)
5Three-input output= 0 (low)
6Output as a bit= 0
7Universality= Universal gate: any logic function can be built from it alone

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

NAND with both inputs high?

0. NAND outputs low only when every input is high.

Why are chips built mostly from NAND?

In CMOS a NAND needs fewer transistors than an AND, and its universality means one cell type can implement any function.