Binary Calculator
Free binary calculator with step-by-step conversion. Convert between binary (base 2), decimal (base 10), hexadecimal (base 16), and octal (base 8) number systems instantly.
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Convert Numbers Between Any Base
Our binary calculator makes number base conversion easy. Whether you're a programmer, student, or working with digital electronics, instantly convert between binary, decimal, hexadecimal, and octal with detailed step-by-step explanations.
What is the Binary Number System?
Binary is a base-2 number system that uses only two digits: 0 and 1. It's the foundation of all digital computing because electronic circuits can easily represent two states (on/off). Decimal uses 10 digits (0-9), hexadecimal uses 16 (0-9, A-F), and octal uses 8 (0-7).
Base Conversion Formula
Decimal = dₙ × bⁿ + dₙ₋₁ × bⁿ⁻¹ + ... + d₁ × b¹ + d₀ × b⁰Why Use a Binary Calculator?
Programming & Development
Work with memory addresses, bit flags, and low-level data representations.
Computer Science Education
Learn how computers store and process numbers at the fundamental level.
Digital Electronics
Design circuits, work with microcontrollers, and debug hardware.
How to Use the Binary Calculator
Common Use Cases
Color Codes
Convert hex color codes (#FF0000) to decimal RGB values.
IP Addresses
Understand subnet masks and network calculations.
Assembly Language
Work with opcodes and memory addresses.
Permissions
Convert Unix file permissions (chmod 755) between formats.
Frequently Asked Questions
Computers use binary because electronic circuits have two stable states: on (1) and off (0). This makes binary the most reliable way to store and process data. All higher-level numbers are built from these basic binary states.