Decimal to Octal Converter - Convert Base 10 to Base 8 Numbers
Result:
10₁₀ = 12₈
How Decimal to Octal Conversion Works
Input Decimal
Enter base 10 number
Divide by 8
Repeatedly divide by 8
Collect Remainders
Note each remainder
Step-by-Step Calculation
Converting 10₁₀ to Octal:
Result: Reading remainders from bottom to top: 12₈
Decimal to Octal Conversion Table
| Decimal | Octal | Decimal | Octal | Decimal | Octal |
|---|---|---|---|---|---|
| 0 | 0 | 15 | 17 | 30 | 36 |
| 1 | 1 | 16 | 20 | 31 | 37 |
| 2 | 2 | 17 | 21 | 32 | 40 |
| 3 | 3 | 18 | 22 | 33 | 41 |
| 4 | 4 | 19 | 23 | 34 | 42 |
| 5 | 5 | 20 | 24 | 35 | 43 |
| 6 | 6 | 21 | 25 | 36 | 44 |
| 7 | 7 | 22 | 26 | 37 | 45 |
| 8 | 10 | 23 | 27 | 38 | 46 |
| 9 | 11 | 24 | 30 | 39 | 47 |
| 10 | 12 | 25 | 31 | 40 | 50 |
| 11 | 13 | 26 | 32 | 41 | 51 |
| 12 | 14 | 27 | 33 | 42 | 52 |
| 13 | 15 | 28 | 34 | 43 | 53 |
| 14 | 16 | 29 | 35 | 44 | 54 |
Number System Progression Chart
Decimal: 8
Decimal: 16
Decimal: 32
Decimal: 64
Decimal: 128
Decimal: 256
Practice Problems
Problem 1:
Convert 25₁₀ to octal
Solution: 25 ÷ 8 = 3 remainder 1, 3 ÷ 8 = 0 remainder 3 → 31₈
Problem 2:
Convert 64₁₀ to octal
Solution: 64 ÷ 8 = 8 remainder 0, 8 ÷ 8 = 1 remainder 0, 1 ÷ 8 = 0 remainder 1 → 100₈
Problem 3:
Convert 100₁₀ to octal
Solution: 100 → 144₈ (using division method)
Problem 4:
Convert 255₁₀ to octal
Solution: 255 → 377₈ (largest 8-bit number)
Problem 5:
Convert 512₁₀ to octal
Solution: 512 → 1000₈ (power of 8)
Daily Uses of Octal Numbers
Unix file permissions use octal notation for access control
Digital electronics circuits often use octal for grouping bits
Computer programming languages support octal literals for constants
Network addressing sometimes uses octal for subnet calculations
Assembly language programming uses octal for memory addresses
Export Options
What is Decimal to Octal Conversion?
Decimal to octal conversion means changing numbers from base 10 (decimal) to base 8 (octal). Decimal numbers use digits 0-9, while octal numbers only use digits 0-7.
This conversion is useful in computer programming, digital electronics, and file permissions in Unix systems. Our decimal to octal converter makes this process simple and fast.
Key Points:
- Decimal uses base 10 (digits 0-9)
- Octal uses base 8 (digits 0-7)
- Each octal digit represents 3 binary digits
- Widely used in computer systems
How to Convert Decimal to Octal
Converting decimal to octal is easy with the division method. Follow these simple steps:
Step-by-Step Method:
- Divide the decimal number by 8
- Write down the remainder
- Divide the quotient by 8 again
- Repeat until quotient becomes 0
- Read remainders from bottom to top
Example: Convert 25 to Octal
Common Decimal to Octal Examples
8 = 1×8¹ + 0×8⁰
16 = 2×8¹ + 0×8⁰
64 = 1×8² + 0×8¹ + 0×8⁰
100 = 1×8² + 4×8¹ + 4×8⁰
255 = 3×8² + 7×8¹ + 7×8⁰
512 = 1×8³ + 0×8² + 0×8¹ + 0×8⁰
Decimal to Octal Calculation Table
This table shows how decimal numbers convert to octal format:
| Decimal | Division Steps | Octal Result |
|---|---|---|
| 10 | 10÷8=1 r2, 1÷8=0 r1 | 12₈ |
| 20 | 20÷8=2 r4, 2÷8=0 r2 | 24₈ |
| 50 | 50÷8=6 r2, 6÷8=0 r6 | 62₈ |
| 75 | 75÷8=9 r3, 9÷8=1 r1, 1÷8=0 r1 | 113₈ |
| 128 | 128÷8=16 r0, 16÷8=2 r0, 2÷8=0 r2 | 200₈ |
Frequently Asked Questions
What is the difference between decimal and octal?
Decimal uses base 10 with digits 0-9, while octal uses base 8 with digits 0-7. Decimal is what we use in everyday counting, while octal is used in computer systems.
Why do we need octal numbers?
Octal numbers are useful in computer programming, especially for file permissions in Unix systems. They also help represent binary numbers in a shorter form since each octal digit equals 3 binary digits.
How do you convert large decimal numbers to octal?
Use the same division method: keep dividing by 8 and collect remainders. For very large numbers, you can use our online converter to get instant results.
Can decimal fractions be converted to octal?
Yes, but our converter focuses on whole numbers. For decimal fractions, you multiply the fractional part by 8 repeatedly and collect the integer parts.
Is octal still used today?
Yes, octal is still used in Unix file permissions, some programming languages, and digital electronics. It's less common than hexadecimal but still important.
What's the largest octal digit?
The largest octal digit is 7. Octal only uses digits 0, 1, 2, 3, 4, 5, 6, and 7. When you need 8, it becomes 10 in octal (1×8¹ + 0×8⁰).
Tips for Decimal to Octal Conversion
Quick Recognition
Powers of 8 are easy to spot: 8=10₈, 64=100₈, 512=1000₈. These follow a pattern like powers of 10 in decimal.
Check Your Work
Convert back to decimal to verify: multiply each octal digit by its place value (powers of 8) and add them up.
Binary Connection
Each octal digit represents exactly 3 binary digits. This makes octal useful for shortening binary numbers.
Practice Regularly
Start with small numbers and work your way up. Practice with numbers like 8, 16, 32, 64 to see patterns.
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