Decimal to Octal Converter

Convert decimal (base-10) numbers to octal (base-8) representation. Essential for Unix permissions and legacy systems.

Input (Decimal)
Enter a decimal number
Output (Octal)
Octal representation

What is Decimal to Octal Conversion?

Decimal to octal conversion transforms base-10 numbers into base-8 numbers. Octal is a numeral system that uses digits 0-7.

Why Use Octal?

Octal was widely used in early computing systems and still has applications today:

Common Use Cases:

  • Unix/Linux file permissions (chmod)
  • Digital electronics and embedded systems
  • Compact representation of binary data
  • Legacy computing systems

How Does It Work?

Decimal to octal conversion involves repeatedly dividing the decimal number by 8 and recording the remainders in reverse order.

Examples:

  • Decimal 64 becomes Octal 100
  • Decimal 255 becomes Octal 377
  • Decimal 8 becomes Octal 10

Understanding Octal

Each position in an octal number represents a power of 8:

  • Position 0 (rightmost): 8^0 = 1
  • Position 1: 8^1 = 8
  • Position 2: 8^2 = 64
  • Position 3: 8^3 = 512

Unix File Permissions

In Unix/Linux, file permissions are often represented in octal:

  • 755 means rwxr-xr-x (owner: read/write/execute, group: read/execute, others: read/execute)
  • 644 means rw-r--r-- (owner: read/write, group: read, others: read)