Logic Gate
Generate truth tables for AND, OR, NAND, NOR, XOR, and XNOR logic gates. Free online boolean algebra calculator for digital logic students and engineers.
About This Calculator
The Logic Gate Calculator generates truth tables for the six fundamental two-input logic gates: AND, OR, NAND, NOR, XOR, and XNOR. Select a gate from the dropdown and instantly see the output for all four possible input combinations of A and B. This tool is ideal for students learning digital logic design, computer science undergraduates studying boolean algebra, and electronics hobbyists prototyping circuits.
Logic gates are the building blocks of digital electronics. Each gate implements a boolean function that takes one or more binary inputs and produces a single binary output. This calculator evaluates all four combinations: (0,0), (0,1), (1,0), (1,1) using standard boolean logic definitions. The truth table clearly shows the relationship between inputs and output for each gate type, making it easy to understand and verify circuit behavior.
AND outputs true only when both inputs are true. OR outputs true when at least one input is true. NAND (NOT AND) inverts the AND output -- it is known as a universal gate because any other gate can be constructed using only NAND gates. NOR (NOT OR) inverts the OR output and is also a universal gate. XOR (exclusive OR) outputs true when inputs differ, making it useful for parity checking and binary addition circuits. XNOR (exclusive NOR) outputs true when inputs match, serving as an equality comparator.
Truth tables are fundamental to understanding how digital systems work. Engineers use them to design and verify logic circuits, programmers use them to reason about boolean expressions, and students use them to build a foundation for computer architecture. Each row in the table represents a distinct input state, and the output column shows how the gate processes that combination. For two-input gates, the four-row format provides a complete functional description.
Frequently Asked Questions
How does the logic gate calculator work?
Select a logic gate (AND, OR, NAND, NOR, XOR, XNOR) from the dropdown and click Generate Truth Table. The calculator evaluates the gate for all four combinations of inputs A and B (0,0), (0,1), (1,0), (1,1) and displays the output in a truth table.
What logic gates are supported?
The calculator supports all six fundamental logic gates: AND, OR, NAND (NOT AND), NOR (NOT OR), XOR (exclusive OR), and XNOR (exclusive NOR). Each gate is evaluated for all possible two-input combinations.
What is the difference between XOR and XNOR?
XOR (exclusive OR) outputs true when the inputs are different (one true, one false). XNOR (exclusive NOR) outputs true when the inputs are the same (both true or both false). XNOR is the complement (inverse) of XOR.
Is this logic gate calculator free?
Yes, it is completely free to use with no registration or hidden charges. Results can be shared via a unique URL that saves your selected gate.
Can I share my logic gate truth table?
Yes, the URL automatically saves your selected gate so you can bookmark or share the exact truth table.
Why are NAND and NOR called universal gates?
NAND and NOR are called universal gates because any other logic gate (AND, OR, NOT, XOR, XNOR) can be constructed using only NAND gates or only NOR gates. This property makes them fundamental building blocks in digital circuit design.
What is the truth table for an AND gate?
The AND gate truth table has four rows: when A=0 and B=0, output is 0; when A=0 and B=1, output is 0; when A=1 and B=0, output is 0; when A=1 and B=1, output is 1. The AND gate outputs 1 only when both inputs are 1.
How are logic gates used in computer processors?
Logic gates are the fundamental building blocks of computer processors. Millions of gates are combined to form arithmetic logic units (ALUs), multiplexers, decoders, and memory cells. For example, XOR gates are used in binary adders, AND gates in enable signals, and flip-flops constructed from NAND or NOR gates form registers and cache memory.