Binary Converter

Convert between Binary, Decimal, Hexadecimal, and Octal number systems with detailed explanations

🔢 Converter
📊 Breakdown
💡 Examples
📚 Info
📝 History
🔢 Binary Base 2
🔟 Decimal Base 10
🔡 Hexadecimal Base 16
🔠 Octal Base 8
10
Decimal Example
1111
Binary Example
A
Hex Example
12
Octal Example
📊 Step-by-Step Conversion Breakdown

Enter a number in any field to see the breakdown

The conversion process will be explained step by step.

💡 Common Examples

Decimal Binary Hex Octal
0 0 0 0
1 1 1 1
8 1000 8 10
15 1111 F 17
16 10000 10 20
255 11111111 FF 377
1024 10000000000 400 2000

🎯 Programming Examples

Colors in Web Development:

  • FF0000 - Red
  • 00FF00 - Green
  • 0000FF - Blue
  • FFFFFF - White
  • 000000 - Black

File Permissions (Octal):

  • 755 - rwxr-xr-x
  • 644 - rw-r--r--
  • 777 - rwxrwxrwx

🔬 Technical Examples

Computer Memory:

  • 1024 - 1 KB
  • 1048576 - 1 MB
  • 65536 - 64 KB

Network & IP:

  • 192 - First octet of 192.168.x.x
  • 255 - Subnet mask component
  • C0A8 - 192.168 in hex

📚 Number Systems Overview

Binary (Base 2): Uses only digits 0 and 1. Each position represents a power of 2.

Decimal (Base 10): Uses digits 0-9. Our everyday number system.

Hexadecimal (Base 16): Uses digits 0-9 and letters A-F. Common in programming.

Octal (Base 8): Uses digits 0-7. Used in file permissions and some programming contexts.

🔧 Conversion Methods

To Decimal:

  • Binary: Multiply each digit by 2^position and sum
  • Hex: Multiply each digit by 16^position and sum
  • Octal: Multiply each digit by 8^position and sum

From Decimal:

  • Divide by base repeatedly, collect remainders
  • Read remainders in reverse order

💻 Programming Applications

  • Binary: Computer logic, bitwise operations
  • Hexadecimal: Memory addresses, color codes, debugging
  • Octal: File permissions, some assembly languages
  • Decimal: User interfaces, calculations

🎨 Real-World Uses

  • Web Design: Hex colors (#FF0000 for red)
  • System Admin: Octal file permissions (755, 644)
  • Programming: Memory addresses, bit manipulation
  • Networking: IP addresses, MAC addresses
  • Graphics: RGB values, pixel data
📝 Conversion History