Pick your Logic Gate Type, set the Number of Inputs, and this Logic Gate Truth Table Calculator builds the complete truth table for you — with every possible input combination laid out clearly. Toggle Show Binary Numbers or Show Boolean Expression to also display the Boolean Expression and Total Input Combinations alongside your gate's logic.
Logic Gate
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Boolean Expression
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Total Input Combinations
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A logic gate is a digital circuit that performs a logical operation on one or more binary inputs to produce a single binary output. Logic gates are the fundamental building blocks of digital circuits and computers.
The basic logic gates are AND, OR, and NOT gates. These three gates can be combined to create any logical function. Additionally, NAND and NOR gates are called universal gates because they can be used to construct any other logic gate.
Both NAND and NOR gates are called universal gates because any Boolean function can be implemented using only NAND gates or only NOR gates. This makes them extremely versatile in digital circuit design.
The NOT gate is called the logical inverter gate because it inverts the input signal. If the input is 1 (True), the output is 0 (False), and vice versa.
To create an AND gate from a NAND gate, connect the output of the NAND gate to the input of a NOT gate (inverter). Since NAND produces the complement of AND, inverting it gives you the AND function.
There are seven basic types of digital logic gates: AND, OR, NOT, NAND, NOR, XOR, and XNOR. Each gate performs a specific logical operation and has its own unique truth table and symbol.
XOR (Exclusive OR) outputs 1 when inputs are different, and 0 when inputs are the same. XNOR (Exclusive NOR) is the complement of XOR, outputting 1 when inputs are the same and 0 when inputs are different.
A truth table shows all possible input combinations and their corresponding outputs. Read from left to right: input columns show all possible combinations of 0s and 1s, and the output column shows the gate's response to each combination.