Decimal to Octal Converter | Convert Decimal to Octal Numbers

Free online decimal to octal converter. Convert decimal numbers to octal with step-by-step explanations. Includes conversion tables and examples.

Decimal to Octal Converter

Sponsors

AIVideo.to logo

AIVideo.to

Turn any topic in to short Videos with AI in 1 minute.

Spiff.store logo

Spiff.store

Discover and explore the best AI tools and resources.

WorldClass.domains logo

WorldClass.domains

Create your profile page to showcase all your projects.

AnimePFP logo

AnimePFP

Discover anime profile pictures for your social media accounts.

Powers of 8 Reference

80
= 1
81
= 8
82
= 64
83
= 512
84
= 4,096
85
= 32,768

Step-by-Step Examples

255₁₀ = 377₈

Maximum 8-bit value

255 ÷ 8 = 31 remainder 7
31 ÷ 8 = 3 remainder 7
3 ÷ 8 = 0 remainder 3
Reading from bottom up: 377

64₁₀ = 100₈

Power of 8 (8²)

64 ÷ 8 = 8 remainder 0
8 ÷ 8 = 1 remainder 0
1 ÷ 8 = 0 remainder 1
Reading from bottom up: 100

511₁₀ = 777₈

Maximum 9-bit value

511 ÷ 8 = 63 remainder 7
63 ÷ 8 = 7 remainder 7
7 ÷ 8 = 0 remainder 7
Reading from bottom up: 777

How Decimal to Octal Conversion Works

Division Method

  1. Divide the decimal number by 8
  2. Note down the remainder (0-7)
  3. Divide the quotient by 8
  4. Repeat until quotient becomes 0
  5. Read the remainders from bottom to top

Key Points

  • Valid octal digits are 0-7 only
  • Each octal digit represents 3 binary digits
  • Octal is common in Unix systems
  • Powers of 8 are important reference points

Common Values

8₁₀ = 10₈

64₁₀ = 100₈

255₁₀ = 377₈

511₁₀ = 777₈

Unix File Permissions

Octal Permission String Usage
777 rwxrwxrwx Full permissions for all
755 rwxr-xr-x Standard executable
644 rw-r--r-- Standard file
600 rw------- Private file

Practice Problems

Convert: 42₁₀

Answer: 52₈

Convert: 100₁₀

Answer: 144₈

Convert: 255₁₀

Answer: 377₈

Real-World Applications

Unix/Linux Systems

Octal numbers are used extensively in Unix-like systems for:

  • File permissions
  • Access control
  • System configuration

Legacy Systems

Octal notation is still used in:

  • Embedded systems
  • Assembly programming
  • Hardware interfaces

Related Conversions

Decimal to Binary
Decimal to Hex
Octal to Decimal
Binary to Octal

About this Calculator

Free online decimal to octal converter. Convert decimal numbers to octal with step-by-step explanations. Includes conversion tables and examples.

Related Searches

decimal to octaldec to octdecimal octal converterconvert decimal to octalbase-10 to base-8decimal to oct calculator