Select a digital logic gate, choose 1 to 4 inputs, toggle input values and instantly see the output, Boolean expression and complete truth table.
๐ง Key Insight: A logic gate works with binary inputs: 0 and 1. NAND and NOR are called universal gates because complete digital circuits can be built using only one of them.
๐ Live Logic Gate Graphic
Logic Gate
Number of Inputs
Output Format
Input Values
Quick gates:ANDORNOTNANDXOR
๐ Boolean Formula Reference
Basic Gates
AND: Y = A ยท B OR: Y = A + B NOT: Y = Aฬ
Inverted Gates
NAND: Y = (A ยท B)ฬ NOR: Y = (A + B)ฬ XNOR: Y = (A โ B)ฬ
Exclusive Gate
XOR outputs 1 when inputs are different. For multiple inputs, XOR is 1 when the number of 1s is odd.
Universal Gates
NAND and NOR are universal gates. Any Boolean logic can be built using only NAND or only NOR gates.
๐ Common Logic Gate IC Reference
TTL 74xx
7408AND
7432OR
7404NOT
Universal / Special
7400NAND
7402NOR
7486XOR
Logic Levels
0LOW / False
1HIGH / True
OutputY
๐ Engineering Notes
Truth tables are the fastest way to learn gatesA truth table lists every possible input combination and the output for each case.
NAND and NOR are important in real circuitsThey are universal gates, which means complete digital logic can be built with just NAND gates or just NOR gates.
XOR is useful for comparisonXOR outputs 1 when inputs are different. It is commonly used in parity, adders and digital comparison circuits.
Good companion for binary toolsLogic gates connect naturally with binary numbers, Boolean algebra, K-map simplification and digital IC pinout references.
What is a Logic Gate Calculator?
A logic gate calculator helps you calculate the output of digital logic gates such as AND, OR, NOT, NAND, NOR, XOR and XNOR. This tool also generates the full truth table for 1-input, 2-input, 3-input and 4-input logic combinations.
Why use a Truth Table Generator?
A truth table generator is useful for students, makers and electronics engineers because it shows every possible input combination. It makes digital logic easier to understand before moving to Boolean algebra, microcontroller inputs or actual IC wiring.
Related digital electronics workflow
After checking basic logic gates, you can continue with binary number tools, Boolean expression simplification, K-map solver pages and IC pinout references. This page is also useful alongside Arduino, Raspberry Pi and sensor projects where digital HIGH/LOW logic must be understood clearly.
โ Frequently Asked Questions
The AND gate gives output 1 only when all selected inputs are 1.
OR gives 1 when at least one input is 1. XOR gives 1 when the inputs are different, or for multiple inputs, when the number of 1s is odd.
Because any Boolean logic function can be created using only NAND gates or only NOR gates.