Logic Gate Calculator
Calculate outputs for AND, OR, NOT, NAND, NOR, XOR, and XNOR logic gates with truth tables
Logic Gate Calculator
Logic Gate Results
Logic Analysis
Logic Gate Examples
AND Gate Example
Application: Security system requiring two keys
Logic: Door opens only when both Key A AND Key B are present
Truth: A=1, B=1 → Output=1 (Door opens)
Truth: A=0, B=1 → Output=0 (Door remains closed)
OR Gate Example
Application: Room lighting with two switches
Logic: Light turns on when Switch A OR Switch B is pressed
Truth: A=1, B=0 → Output=1 (Light on)
Truth: A=0, B=0 → Output=0 (Light off)
XOR Gate Example
Application: Parity bit checker for error detection
Logic: Output is 1 when inputs are different
Truth: A=1, B=0 → Output=1 (Different inputs)
Truth: A=1, B=1 → Output=0 (Same inputs)
Logic Gate Types
Basic Gates
AND, OR, NOT
Fundamental building blocks
Universal Gates
NAND, NOR
Can implement any logic function
Comparison Gates
XOR, XNOR
For comparing and parity checking
Digital Logic Tips
0 represents False/Low/Off state
1 represents True/High/On state
NAND and NOR are universal gates
XOR is useful for binary addition
Truth tables show all possible combinations
Understanding Logic Gates
What are Logic Gates?
Logic gates are the fundamental building blocks of digital circuits. They perform basic logical operations on one or more binary inputs to produce a single binary output. Every digital device, from simple calculators to complex computers, relies on combinations of these basic gates.
Basic Operations
- •AND: Both inputs must be true
- •OR: At least one input must be true
- •NOT: Inverts the input
- •XOR: Inputs must be different
Boolean Algebra
Basic Operators
- · (dot) represents AND operation
- + (plus) represents OR operation
- ¯ (bar) represents NOT operation
- ⊕ (circled plus) represents XOR
De Morgan's Laws
- (A · B)̄ = Ā + B̄
- (A + B)̄ = Ā · B̄
Truth Tables Explained
A truth table is a complete representation of a logic gate's behavior. It lists all possible input combinations and their corresponding outputs. This systematic approach helps in understanding and designing digital circuits.
Why Truth Tables Matter:
- • Verify circuit behavior
- • Design complex logic systems
- • Debug digital circuits
- • Understand gate relationships
Reading Truth Tables:
- • Each row is one test case
- • Input columns show all combinations
- • Output column shows result
- • 0 = False/Low, 1 = True/High
Real-World Applications
Computer Processors
Millions of logic gates work together to perform calculations, decision making, and data processing in CPUs
Memory Systems
Logic gates enable data storage and retrieval in RAM, ROM, and cache memory systems
Control Systems
Automated systems use logic gates for decision making in industrial control, robotics, and IoT devices
Security Systems
Access control, alarm systems, and encryption rely on complex combinations of logic gates
Communication
Error detection, data encoding, and signal processing in telecommunication systems
Gaming Systems
Game logic, graphics processing, and user input handling in video game consoles and computers