Octal to Decimal Converter | Convert Octal to Decimal Numbers
Free online octal to decimal converter. Convert octal numbers to decimal with step-by-step explanations and instant results. Includes conversion tables and examples.
Octal to Decimal Converter
Understanding Octal Place Values
8³ | 8² | 8¹ | 8⁰ |
---|---|---|---|
512 | 64 | 8 | 1 |
Powers of 8
8⁰ = 1
8¹ = 8
8² = 64
8³ = 512
Detailed Examples
Octal: 377
Decimal: 255
(3 × 8²) + (7 × 8¹) + (7 × 8⁰) = 192 + 56 + 7 = 255
Octal: 123
Decimal: 83
(1 × 8²) + (2 × 8¹) + (3 × 8⁰) = 64 + 16 + 3 = 83
Octal: 10
Decimal: 8
(1 × 8¹) + (0 × 8⁰) = 8 + 0 = 8
Octal: 777
Decimal: 511
(7 × 8²) + (7 × 8¹) + (7 × 8⁰) = 448 + 56 + 7 = 511
Common Octal Values
Octal: 10
Decimal: 8
Octal: 20
Decimal: 16
Octal: 40
Decimal: 32
Octal: 100
Decimal: 64
Octal: 200
Decimal: 128
Octal: 400
Decimal: 256
How Octal to Decimal Conversion Works
Step-by-Step Process
- Identify the position value of each digit (powers of 8)
- Multiply each digit by its position value
- Sum all products to get the decimal result
Converting "47"₈
4 in position 1: 4 × 8 = 32
7 in position 0: 7 × 1 = 7
Sum: 32 + 7 = 39₁₀
Important Tips
- Valid octal digits: 0-7 only
- Each position is 8 times the previous
- Right-most position value is 1
Practice Problems
Convert: 77₈
Answer: 63₁₀
Convert: 123₈
Answer: 83₁₀
Convert: 200₈
Answer: 128₁₀
Real-World Applications
Unix File Permissions
chmod 777 - Full permissions (read, write, execute)
chmod 644 - Standard file permissions
chmod 755 - Executable file permissions
Other Uses
- Legacy computing systems
- Assembly language programming
- Data representation
Related Conversions
About this Calculator
Free online octal to decimal converter. Convert octal numbers to decimal with step-by-step explanations and instant results. Includes conversion tables and examples.
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