🔁 Binary ⇄ Decimal Converter Tool
Convert binary to decimal and decimal to binary instantly with our free online converter. Also view octal and hexadecimal results. Fast, simple, and mobile-friendly.
📐 Looking to convert dimensions for web or print? Try our free tool: Inches to Pixels Calculator
🔢 What is Binary? Definition with Examples
The binary number system is a base-2 numeral system that uses only two digits: 0 and 1. It is the core language of all computers and digital systems. Every operation and piece of data inside a computer—whether it’s text, image, audio, or code—is ultimately represented in binary format.
💡 How Binary Works (Examples)
Example 1: Binary to Decimal
Binary: 1010
Calculation:= 1×2³ + 0×2² + 1×2¹ + 0×2⁰ = 8 + 0 + 2 + 0 = 10 (decimal)
Example 2: Decimal to Binary
Decimal: 13
Division steps:13 ÷ 2 = 6 remainder 1
6 ÷ 2 = 3 remainder 0
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1
Binary = 1101
🧠 Why is Binary Important?
- Used in all computers: CPUs and microcontrollers understand binary.
- Digital electronics: Logic gates, circuits, and memory rely on binary operations.
- Reliable signal system: Easy to differentiate two voltage levels — ON (1) and OFF (0).
- Networking: IP addresses and subnet masks are binary-based.
🌐 Where is Binary Used?
Binary is used in everything from computer processors and memory, to digital images, mobile phones, and the internet.
📘 Learn more in-depth about the Binary Number System on GeeksforGeeks.
🔟 What is Decimal? Explanation with Examples
The decimal number system, also known as the base-10 system, is the standard system for denoting integer and non-integer numbers. It uses ten digits: 0 through 9. Each digit’s position represents a power of 10, making it a positional number system.
💡 How Decimal Works (Examples)
Example 1: Understanding 345= 3×10² + 4×10¹ + 5×10⁰
= 300 + 40 + 5 = 345
Example 2: Decimal to Binary
Let’s convert 8 to binary:8 ÷ 2 = 4 remainder 0
4 ÷ 2 = 2 remainder 0
2 ÷ 2 = 1 remainder 0
1 ÷ 2 = 0 remainder 1
Binary = 1000
📌 Why Do We Use Decimal?
- Human-friendly: It’s intuitive and has been used for centuries.
- Everyday use: It is used in math, finance, science, and daily life.
- Foundational: Basis for fractions, percentages, currency, and measurements.
📚 Decimal in Computing
Although computers process binary, decimal is used in programming interfaces, user displays, and floating-point math. Decimal values are often converted to binary internally and back to decimal for the user.
🔗 Want to go deeper? Visit the Decimal Number System guide on TutorialsPoint.
🧮 What is Octal Number System?
The octal number system is a base-8 numeral system that uses eight digits: 0 to 7. Each position in an octal number represents a power of 8. It is mostly used in computing as a shorthand representation of binary numbers, especially in Unix-based systems.
💡 Example: Octal to Decimal
Octal: 57
Calculation: 5×8¹ + 7×8⁰ = 40 + 7 = 47 (decimal)
💡 Example: Decimal to Octal
Decimal: 65
Division steps:
65 ÷ 8 = 8 remainder 1
8 ÷ 8 = 1 remainder 0
1 ÷ 8 = 0 remainder 1
Octal = 101
📌 Where Octal is Used?
- File permissions in Linux/Unix (e.g.,
chmod 755) - Shorthand for representing binary (3 bits per digit)
- Older programming languages and assembly code
🔗 Learn more about Octal Number System on GeeksforGeeks.
🔡 What is Hexadecimal Number System?
The hexadecimal number system is a base-16 system that uses digits from 0 to 9 and letters A to F to represent values 0–15. It is commonly used in programming, web development (colors), and memory addressing.
💡 Example: Hexadecimal to Decimal
Hex: 2F
Calculation: 2×16¹ + F×16⁰ = 32 + 15 = 47 (decimal)
💡 Example: Decimal to Hexadecimal
Decimal: 255
Division steps:
255 ÷ 16 = 15 remainder 15 (F)
15 ÷ 16 = 0 remainder 15 (F)
Hexadecimal = FF
📌 Where Hexadecimal is Used?
- Web colors: #FF5733, #000000
- Memory addresses: 0xA3B2
- Machine-level programming: Compact representation of binary (4 bits per digit)
🔗 Learn more about Hexadecimal Number System on TutorialsPoint.
