Free Logic Gate Calculator

Digital Logic Gate Calculator – Generate Truth Tables Instantly

A logic gate calculator serves as a handy truth table generator for anyone working with digital circuits. Whether you are a hobbyist or an electronics engineer, this free online tool lets you compute the output of any standard logic gate and automatically builds a complete truth table. By feeding in the input values (0 or 1), you instantly see how the gate behaves, saving time and reducing manual errors.

Logic gates are the fundamental building blocks of all digital systems – from microprocessors and memory chips to simple alarm circuits. They act as electronic switches that either pass or block a signal based on a set of logical conditions. Every gate accepts one or more binary inputs (on/high = 1, off/low = 0) and produces a single output determined by the type of logic operation performed.

Basic Logic Gates

Three elementary gates form the foundation of Boolean logic:

• AND Gate – Outputs 1 only when all inputs are 1.
  Boolean expression: $\text{Output} = A \cdot B$ (the multiplication sign represents AND in Boolean algebra).

• OR Gate – Outputs 1 when at least one input is 1.
  Boolean expression: $\text{Output} = A + B$ (the plus sign represents OR).

• NOT Gate (Inverter) – Outputs the complement of the input. For a single input A, the output is $\overline{A}$.
  If A = 1, output = 0; if A = 0, output = 1.

Derived (Combination) Gates

By combining the basic gates, we obtain four commonly used compound gates:

• NAND Gate (NOT‑AND) – Outputs 0 only when all inputs are 1; otherwise outputs 1.
  Expression: $\text{Output} = \overline{A \cdot B}$.

• NOR Gate (NOT‑OR) – Outputs 1 only when all inputs are 0; otherwise outputs 0.
  Expression: $\text{Output} = \overline{A + B}$.

• XOR Gate (Exclusive‑OR) – Outputs 1 when the two inputs differ.
  Expression: $\text{Output} = \overline{A} \cdot B + A \cdot \overline{B}$ (often written as $A \oplus B$).

• XNOR Gate (Exclusive‑NOR) – Outputs 1 when both inputs are equal (both 0 or both 1).
  Expression: $\text{Output} = A \cdot B + \overline{A} \cdot \overline{B}$ (or $\overline{A \oplus B}$).

Truth Tables for All Seven Gates

A truth table lists every possible input combination alongside the resulting output, making the gate’s behavior immediately clear. Below are the complete truth tables for each gate using two inputs (A and B) where applicable.

AND Gate

A	B	Output
0	0	0
0	1	0
1	0	0
1	1	1

OR Gate

A	B	Output
0	0	0
0	1	1
1	0	1
1	1	1

NOT Gate

A	Output
0	1
1	0

NAND Gate

A	B	Output
0	0	1
0	1	1
1	0	1
1	1	0

NOR Gate

A	B	Output
0	0	1
0	1	0
1	0	0
1	1	0

XOR Gate

A	B	Output
0	0	0
0	1	1
1	0	1
1	1	0

XNOR Gate

A	B	Output
0	0	1
0	1	0
1	0	0
1	1	1

How to Use the Free Logic Gate Truth Table Generator

This online tool makes generating truth tables as simple as a few clicks:

1. Select the gate type from the drop‑down menu (AND, OR, NOT, NAND, NOR, XOR, or XNOR).
2. The interface will display the corresponding gate symbol and input fields.
3. For two‑input gates, choose each input state using radio buttons (0 or 1).
4. The calculator instantly shows the output value based on the chosen gate and input combination.
5. Repeat step 3 for all possible input combinations to build the complete truth table for that gate.

No software installation is needed – the calculator works entirely in your browser, acting as a convenient truth table generator for both learning and quick prototyping.

Mastering logic gates is essential for understanding digital electronics. With this digital logic gate calculator, you can experiment with all seven gate types, verify Boolean expressions, and reinforce your knowledge of basic digital circuits.