Binary Converter - Convert Binary, Decimal, Hex & Octal
Free binary converter to instantly convert between binary, decimal, hexadecimal, and octal number systems with accurate results
Binary Converter
Conversion Results
Quick Reference
What is a Binary Converter?
A Binary Converter is a free tool that converts numbers between different number systems including binary (base-2), decimal (base-10), hexadecimal (base-16), and octal (base-8). It's essential for computer science, programming, and digital electronics.
This converter works for:
- Programming - Convert between number systems for code development
- Computer Science - Understand data representation and storage
- Digital Electronics - Work with binary logic and circuits
- Network Engineering - Calculate IP addresses and subnet masks
To understand percentage calculations in programming and data analysis, check out our Percentage Calculator to perform various percentage operations with instant results.
For converting fractions to percentages in data representation, explore our Fraction to Percent Calculator to simplify your mathematical conversions.
To work with decimal to percentage conversions in statistical analysis, use our Decimal to Percent Converter for accurate results.
For temperature conversions in scientific computing, try our Temperature Converter to convert between Celsius, Fahrenheit, and Kelvin.
To generate random numbers for testing and simulations, check our Random Number Generator for customizable random number generation.
How Binary Conversion Works
Binary conversion uses mathematical formulas to convert between number systems:
Example: 1011₂ = (1×8) + (0×4) + (1×2) + (1×1) = 11₁₀
Example: 11₁₀ ÷ 2 = 5 R1, 5 ÷ 2 = 2 R1, 2 ÷ 2 = 1 R0, 1 ÷ 2 = 0 R1 → 1011₂
Key Number System Concepts
Binary (Base-2)
Uses only 0 and 1. Each position represents a power of 2. Fundamental to all digital computing.
Decimal (Base-10)
Uses digits 0-9. The standard number system we use daily. Each position represents a power of 10.
Hexadecimal (Base-16)
Uses 0-9 and A-F. Compact representation of binary. Each hex digit = 4 binary bits.
Octal (Base-8)
Uses digits 0-7. Common in Unix permissions. Each octal digit = 3 binary bits.
How to Use This Converter
Enter Value
Type a number in any input field (binary, decimal, hex, or octal)
Auto-Convert
All other number systems update automatically in real-time
View Results
See equivalent values in all four number systems instantly
Reset Anytime
Click Reset to clear all fields and start fresh
Benefits of Using This Converter
- • Real-time Conversion: Instant conversion as you type with no delays or button clicks required.
- • Multiple Systems: Convert between all four major number systems in one place.
- • Accurate Results: Precise mathematical conversions with proper validation and error handling.
- • Educational Tool: Learn number system relationships and understand how computers represent data.
- • Free & Fast: No registration, no downloads, works instantly in your browser.
Common Use Cases
1. Programming & Development
Convert color codes (hex to RGB), work with bitwise operations, debug binary data, and understand memory addresses.
2. Network Engineering
Calculate IP addresses, subnet masks, and network ranges using binary and decimal conversions.
3. Digital Electronics
Design logic circuits, understand binary arithmetic, and work with digital signals and data encoding.
4. Computer Science Education
Learn number systems, practice conversions, understand data representation, and prepare for exams.
Frequently Asked Questions (FAQ)
Q: What is a binary converter?
A: A binary converter is a tool that converts numbers between different number systems including binary (base-2), decimal (base-10), hexadecimal (base-16), and octal (base-8). It's essential for computer science, programming, and digital electronics.
Q: How do you convert binary to decimal?
A: To convert binary to decimal, multiply each binary digit by 2 raised to its position power (starting from 0 on the right) and sum the results. For example, binary 1011 = (1×2³) + (0×2²) + (1×2¹) + (1×2⁰) = 8 + 0 + 2 + 1 = 11 in decimal.
Q: How do you convert decimal to binary?
A: To convert decimal to binary, repeatedly divide the number by 2 and record the remainders. Read the remainders from bottom to top to get the binary representation. For example, 11 ÷ 2 = 5 remainder 1, 5 ÷ 2 = 2 remainder 1, 2 ÷ 2 = 1 remainder 0, 1 ÷ 2 = 0 remainder 1, giving binary 1011.
Q: What is hexadecimal and how does it relate to binary?
A: Hexadecimal (base-16) uses digits 0-9 and letters A-F to represent values 0-15. Each hexadecimal digit represents exactly 4 binary digits (bits), making it a compact way to represent binary data. For example, binary 1111 equals hexadecimal F, and binary 10101100 equals hexadecimal AC.
Q: What are common uses of binary conversion?
A: Binary conversion is used in computer programming, digital electronics, network addressing (IP addresses), color codes in web design, data encoding, cryptography, and understanding how computers store and process information at the fundamental level.
Q: What is octal and when is it used?
A: Octal (base-8) uses digits 0-7 and each octal digit represents exactly 3 binary digits. It's commonly used in Unix/Linux file permissions, some programming contexts, and as a more compact representation of binary data than decimal but simpler than hexadecimal.