Octal To Hex Converter
Enter the octal value to convert to hexadecimal or Hexadecimal to Octal.
Octal:
Octal (Base-8) numbers use digits 0-7.
Hexadecimal:
Hexadecimal (Base-16) uses digits 0-9 and letters A-F for compact binary representation.
How to Convert Octal to Hexadecimal — Formula:
Octal → Decimal (Σ dᵢ×8ⁱ) → Hex (repeated division by 16).
Example: Octal 377 → Decimal 255 → Hex FF.
Technical Details:
Alternative method: Octal → Binary (expand each digit to 3 bits) → Hex (group into 4 bits). 377 → 011111111 → 0FF.
Octal To Hex Converter:
Convert octal numbers to hexadecimal format.
Binary ↔ Hex ↔ Octal: Grouping Relationship
Binary → Hex (group by 4 bits):
Binary → Octal (group by 3 bits):
Frequently Asked Questions
How do I convert Octal to Hexadecimal?
Octal → Decimal (Σ dᵢ×8ⁱ) → Hex (repeated division by 16).
What is the Octal number system?
Octal (Base-8) numbers use digits 0-7.
What is the Hexadecimal number system?
Hexadecimal (Base-16) uses digits 0-9 and letters A-F for compact binary representation.
Where is Octal to Hexadecimal conversion used?
Alternative method: Octal → Binary (expand each digit to 3 bits) → Hex (group into 4 bits). 377 → 011111111 → 0FF.
Can I convert large octal 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 Octal to Hexadecimal (Base-8 to Base-16)
Octal-to-hex conversion is best done via binary as an intermediate step: expand each octal digit to 3 bits, then regroup the bits into 4-bit nibbles for hex. This is the standard approach because there is no simple direct digit mapping between base-8 and base-16.
- Convert each octal digit to its 3-bit binary representation.
- Concatenate all binary groups into one string.
- Regroup the binary string into sets of 4 bits from the right.
- Pad the leftmost group with zeros to complete 4 bits if needed.
- Convert each 4-bit group to its hex digit (0-9, A-F).
Octal to Hex: Reference Values
Key octal values and their hex equivalents for systems programming:
| Input | Output |
|---|---|
| 7 | 0x7 |
| 10 | 0x8 |
| 17 | 0xF |
| 20 | 0x10 |
| 101 | 0x41 |
| 141 | 0x61 |
| 377 | 0xFF |
| 644 | 0x1A4 |
| 755 | 0x1ED |
| 777 | 0x1FF |
| 1000 | 0x200 |
| 177777 | 0xFFFF |
Solved Examples: Octal to Hex
Question 1: Convert octal 755 to hex (to use in a programmatic permission check).
Solution:
Octal to binary: 7=111, 5=101, 5=101 → 111101101
Regroup in 4s from right: 0001 1110 1101
Convert to hex: 1, E, D → 0x1ED
Answer: 755₈ = 0x1ED. In C: if ((mode & 0x1ED) == 0x1ED) checks for full 755 permissions.
Question 2: Convert octal 177777 to hex.
Solution:
Octal to binary: 1=001, 7=111, 7=111, 7=111, 7=111, 7=111
Binary: 001111111111111111 (16 bits after removing leading zero)
Regroup: 1111 1111 1111 1111
Convert: F, F, F, F → 0xFFFF
Answer: 177777₈ = 0xFFFF = 65535₁₀ — max unsigned 16-bit integer.
Question 3: Convert the ASCII octal value 101 to hex to look up in a hex dump.
Solution:
1=001, 0=000, 1=001 → 001000001
Regroup: 0100 0001
Convert: 4, 1 → 0x41
Answer: 101₈ = 0x41 — the ASCII code for uppercase A, confirming \101 = 'A' in C.
Practice: Octal to Hex
Try solving these on your own to test your understanding:
- Convert octal 52 to hex. (Answer: 0x2A)
- Convert octal 377 to hex. (Answer: 0xFF)
- Convert octal 644 to hex. (Answer: 0x1A4)
- Convert octal 1750 to hex. (Answer: 0x3E8)
- Convert octal 7777 to hex. (Answer: 0xFFF)
- Convert octal 40 to hex. (Answer: 0x20)
The Binary Bridge: Why It Works
Both octal (3 bits per digit) and hex (4 bits per digit) are powers of 2. Binary serves as the universal bridge because any power-of-2 base can be directly converted to/from binary without arithmetic. The Least Common Multiple of 3 and 4 is 12, meaning a 12-bit binary string maps perfectly to both 4 octal digits and 3 hex digits. For numbers that are not multiples of 12 bits, padding with leading zeros completes the conversion cleanly.
Practical Use: Permission Checks in Code
System calls like stat() return file permissions as an integer. To check permissions programmatically in C: mode_t mode = st.st_mode & 07777; extracts the permission bits using an octal mask. The same value in hex is 0x0FFF. When reading kernel source code, you will see both notations: octal in permission-related code (for readability) and hex in bitmask operations (for byte alignment). Being able to convert between them quickly is essential for systems programmers.
Key Takeaways
- Convert octal → binary (3 bits/digit) → hex (4 bits/digit).
- Binary is the bridge between these two power-of-2 bases.
- chmod 755₈ = 0x1ED, 644₈ = 0x1A4, 777₈ = 0x1FF.
- 377₈ = 0xFF (one byte), 177777₈ = 0xFFFF (two bytes).
- Kernel code mixes octal (permissions) and hex (bitmasks) freely.
- The LCM of 3 and 4 is 12, so 12-bit values align in both systems.