Hexadecimal to Octal Converter
Quick Conversions
A → 12
F → 17
10 → 20
FF → 377
100 → 400
1A3 → 643
Conversion Methods
Converting hexadecimal numbers to octal requires either converting through decimal or using binary as an intermediate step. Both methods produce accurate results.
Method 1: Hex → Decimal → Octal
- Convert each hexadecimal digit to decimal by multiplying by powers of 16
- Starting from the rightmost digit, multiply by 160, then 161, 162, etc.
- Add all products together to get the decimal equivalent
- Divide the decimal number by 8 repeatedly
- Record the remainder at each step
- Write remainders in reverse order to get the octal result
Example: Convert A516 to Octal
Step 1: Convert to Decimal
A5₁₆ = (A × 16¹) + (5 × 16⁰)
= (10 × 16) + (5 × 1)
= 160 + 5 = 165₁₀
Step 2: Convert Decimal to Octal
165 ÷ 8 = 20 remainder 5
20 ÷ 8 = 2 remainder 4
2 ÷ 8 = 0 remainder 2
Read remainders upward: 245₈
Result: A5₁₆ = 245₈
Method 2: Hex → Binary → Octal
- Convert each hexadecimal digit to its 4-bit binary equivalent
- Combine all binary digits into one sequence
- Group binary digits into sets of 3, starting from the right
- Add leading zeros if the leftmost group has fewer than 3 digits
- Convert each 3-bit group to its octal equivalent
Example: Convert 2C16 to Octal
Step 1: Convert each hex digit to binary
2₁₆ = 0010₂
C₁₆ = 1100₂
Combined: 00101100₂
Step 2: Group into 3-bit sets from right
00 101 100
Step 3: Convert each group to octal
000₂ = 0₈, 101₂ = 5₈, 100₂ = 4₈
Result: 2C₁₆ = 054₈
Conversion Reference Table
| Hexadecimal | Octal | Decimal | Binary |
|---|---|---|---|
| 0 | 0 | 0 | 0000 |
| 1 | 1 | 1 | 0001 |
| 2 | 2 | 2 | 0010 |
| 3 | 3 | 3 | 0011 |
| 4 | 4 | 4 | 0100 |
| 5 | 5 | 5 | 0101 |
| 6 | 6 | 6 | 0110 |
| 7 | 7 | 7 | 0111 |
| 8 | 10 | 8 | 1000 |
| 9 | 11 | 9 | 1001 |
| A | 12 | 10 | 1010 |
| B | 13 | 11 | 1011 |
| C | 14 | 12 | 1100 |
| D | 15 | 13 | 1101 |
| E | 16 | 14 | 1110 |
| F | 17 | 15 | 1111 |
| 10 | 20 | 16 | 00010000 |
| 1F | 37 | 31 | 00011111 |
| 20 | 40 | 32 | 00100000 |
| FF | 377 | 255 | 11111111 |
| 100 | 400 | 256 | 100000000 |
Common Conversions
Single Digit
A16 = 128
F16 = 178
E16 = 168
Two Digits
1A16 = 328
FF16 = 3778
A016 = 2408
Three Digits
10016 = 4008
1FF16 = 7778
ABC16 = 52748
Number System Overview
Hexadecimal System
Hexadecimal is a base-16 number system using digits 0-9 and letters A-F. Each position represents a power of 16, making it compact for representing large binary values. Widely used in computing, programming, and color codes.
Octal System
Octal is a base-8 number system using only digits 0-7. Each position represents a power of 8. Historically used in computing for representing groups of three binary bits, though less common today than hexadecimal.
Worked Examples
Example 1: Convert C116 to Octal
C1₁₆ = (C × 16¹) + (1 × 16⁰)
= (12 × 16) + (1 × 1)
= 192 + 1 = 193₁₀
193 ÷ 8 = 24 remainder 1
24 ÷ 8 = 3 remainder 0
3 ÷ 8 = 0 remainder 3
Answer: C1₁₆ = 301₈
Example 2: Convert 1BC16 to Octal (Binary Method)
1₁₆ = 0001₂, B₁₆ = 1011₂, C₁₆ = 1100₂
Combined: 000110111100₂
Group into 3 bits: 000 110 111 100
000₂ = 0₈, 110₂ = 6₈, 111₂ = 7₈, 100₂ = 4₈
Answer: 1BC₁₆ = 674₈
Example 3: Convert 3D16 to Octal
3D₁₆ = (3 × 16¹) + (D × 16⁰)
= (3 × 16) + (13 × 1)
= 48 + 13 = 61₁₀
61 ÷ 8 = 7 remainder 5
7 ÷ 8 = 0 remainder 7
Answer: 3D₁₆ = 75₈
Frequently Asked Questions
What is the difference between hexadecimal and octal?
Hexadecimal is a base-16 system using digits 0-9 and letters A-F, while octal is a base-8 system using only digits 0-7. Hexadecimal is more compact and commonly used in modern computing, whereas octal was historically popular for representing binary data in groups of three bits.
Can I convert hexadecimal directly to octal?
While there’s no direct formula, you can convert by using binary as an intermediate step. Convert each hex digit to 4 binary bits, then group the resulting binary number into 3-bit segments and convert each to octal. Alternatively, convert hex to decimal first, then decimal to octal.
Why are letters used in hexadecimal?
Hexadecimal needs 16 unique symbols to represent values 0-15. Since we only have 10 numeric digits (0-9), letters A through F represent values 10 through 15 respectively. This allows the system to represent base-16 efficiently.
When would I use octal instead of hexadecimal?
Octal is primarily used in legacy computing systems and Unix file permissions. It’s useful when working with systems that naturally divide into groups of three bits. However, hexadecimal has largely replaced octal in modern computing due to better alignment with byte boundaries.
What is the largest single-digit hex value in octal?
The largest single hexadecimal digit is F (representing 15 in decimal), which equals 17 in octal. Single hex digits 0-7 remain the same in octal, while 8-F become two-digit octal numbers (10-17).
How do I verify my conversion is correct?
Convert both your hexadecimal input and octal output to decimal separately. If both decimal values match, your conversion is correct. You can also convert both to binary and verify they produce the same binary sequence.
Are uppercase and lowercase letters treated differently in hex?
No, hexadecimal letters are case-insensitive. Both ‘A’ and ‘a’ represent the value 10, ‘F’ and ‘f’ both represent 15. Most converters accept either case and treat them identically.
Which conversion method is faster?
The binary method (hex → binary → octal) is generally faster for manual calculations because it involves pattern matching rather than arithmetic. The decimal method requires multiplication and division but may be more intuitive for those familiar with decimal conversions.