Hex To Octal Converter
Enter the hexadecimal value to convert to octal or Octal to Hexadecimal.
Hexadecimal:
Hexadecimal (Base-16) is widely used in programming and computer science.
Octal:
Octal (Base-8) is used in Unix permissions and some legacy computing applications.
How to Convert Hexadecimal to Octal — Formula:
Hex → Decimal (Σ dᵢ×16ⁱ) → Octal (repeated division by 8).
Example: Hex FF → Decimal 255 → Octal 377.
Technical Details:
No direct digit mapping exists between hex and octal (4 bits vs 3 bits). The conversion requires an intermediate decimal or binary step. Hex FF = Binary 11111111 = Octal 377.
Hex To Octal Converter:
Convert hexadecimal to octal. The conversion goes through decimal as an intermediate step.
Binary ↔ Hex ↔ Octal: Grouping Relationship
Binary → Hex (group by 4 bits):
Binary → Octal (group by 3 bits):
Frequently Asked Questions
How do I convert Hexadecimal to Octal?
Hex → Decimal (Σ dᵢ×16ⁱ) → Octal (repeated division by 8).
What is the Hexadecimal number system?
Hexadecimal (Base-16) is widely used in programming and computer science.
What is the Octal number system?
Octal (Base-8) is used in Unix permissions and some legacy computing applications.
Where is Hexadecimal to Octal conversion used?
No direct digit mapping exists between hex and octal (4 bits vs 3 bits). The conversion requires an intermediate decimal or binary step. Hex FF = Binary 11111111 = Octal 377.
Can I convert large hexadecimal numbers?
Yes. This converter handles numbers of any practical size. For very large numbers, the conversion is performed using arbitrary-precision arithmetic to ensure accuracy.
How to Convert Hexadecimal to Octal (Base-16 to Base-8)
Converting hex to octal requires an intermediate step since 16 and 8 are not direct powers of each other. The most efficient method is to convert hex to binary first (each hex digit = 4 bits), then regroup the binary bits into 3-bit clusters for octal. This two-step process is faster than converting through decimal for large numbers.
- Convert each hex digit to its 4-bit binary equivalent.
- Concatenate all binary groups into one binary string.
- Regroup the binary string into sets of 3 bits from the right.
- Pad the leftmost group with leading zeros if needed.
- Convert each 3-bit group to its octal digit (0-7).
Hex to Octal: Common Values
Frequently encountered hex values and their octal equivalents:
| Input | Output |
|---|---|
| 0x7 | 7 |
| 0xF | 17 |
| 0x10 | 20 |
| 0x1F | 37 |
| 0x20 | 40 |
| 0x41 | 101 |
| 0x7F | 177 |
| 0xFF | 377 |
| 0x1FF | 777 |
| 0x100 | 400 |
| 0x1ED | 755 |
| 0xFFFF | 177777 |
Solved Examples: Hex to Octal
Question 1: Convert hex 0x1ED to octal (to find the file permission).
Solution:
Hex to binary: 1=0001, E=1110, D=1101 → 000111101101
Regroup in 3s from right: 000 111 101 101
Convert to octal: 0, 7, 5, 5 → 755
Answer: 0x1ED = 755₈ — this confirms that chmod 755 equals 0x1ED in hex (493 decimal).
Question 2: Convert hex 0xCAFE to octal.
Solution:
C=1100, A=1010, F=1111, E=1110 → 1100101011111110
Regroup: 001 100 101 011 111 110
Convert: 1, 4, 5, 3, 7, 6 → 145376
Answer: 0xCAFE = 145376₈. Verify: both equal 51,966 in decimal.
Question 3: A C string uses octal escape \101 for letter A. Verify by converting hex 0x41.
Solution:
Hex 41: 4=0100, 1=0001 → 01000001
Regroup: 001 000 001
Convert: 1, 0, 1 → 101
Answer: 0x41 = 101₈ — confirming that \101 in C strings is indeed the letter A (ASCII 65).
Practice: Hex to Octal
Try solving these on your own to test your understanding:
- Convert 0x2A to octal. (Answer: 52)
- Convert 0xFF to octal. (Answer: 377)
- Convert 0x1A4 to octal. (Answer: 644)
- Convert 0x3E8 to octal. (Answer: 1750)
- Convert 0xDEAD to octal. (Answer: 157255)
- Convert 0x8 to octal. (Answer: 10)
Octal Escapes in Strings
C, C++, and many other languages support octal escape sequences in strings: \012 is a newline (10₁₀ = 12₈), \101 is letter A (65₁₀ = 101₈), \040 is a space (32₁₀ = 40₈). When debugging string contents shown in hex dumps, converting hex to octal helps you recognize these escape values. For example, hex 0x0A (newline) = octal 012, hex 0x09 (tab) = octal 011.
When to Use Hex vs. Octal Representation
Hex is preferred for byte-oriented data (memory dumps, colors, network packets) because bytes split evenly into two hex digits. Octal is preferred for permission bits and systems where word sizes are multiples of 3 bits. Modern computing overwhelmingly uses hex, but octal persists in Unix permissions, C string escapes, and some assembly languages for historical architectures.
Key Takeaways
- Convert hex → binary (4 bits per digit) → octal (3 bits per digit).
- No direct digit-to-digit mapping exists since 16 and 8 share factor 2 but not cleanly.
- ASCII characters in octal: A=101, space=040, newline=012.
- File permissions: 0x1ED = 755₈ = rwxr-xr-x.
- Octal escapes in C strings (\nnn) require this conversion when debugging hex dumps.
- Values 0-7 are the same in both hex and octal.