HEX HeroConvert Octal to Hex
Enter your octal numbers below—one per line—and get instant hexadecimal conversions. Whether you're working with Unix file permissions (like chmod 755), legacy system configurations, or converting between number bases for programming assignments, this tool simplifies octal-to-hex conversions.
How to convert Octal to Hexadecimal - a step by step tutorial
Use binary as a bridge between base-8 and base-16. Learn the 3-bit to 4-bit grouping technique for converting Unix permissions and legacy system values.
How It Works
Converting octal to hex requires going through binary as an intermediate step. Each octal digit = 3 bits, each hex digit = 4 bits.
Convert Each Octal Digit to 3-Bit Binary
Replace each octal digit (0-7) with its 3-bit binary equivalent.
755 → 111 101 101
Regroup into 4-Bit Nibbles
Group the binary result into sets of 4 bits from right to left. Pad with zeros if needed.
0001 1110 1101
Convert Each Nibble to Hex
Replace each 4-bit group with its hexadecimal digit (0-F).
0001=1, 1110=E, 1101=D
Combine Result
Write the hex digits together. Add 0x prefix for clarity.
755₈ = 0x1ED₁₆
Unix File Permissions: Octal to Hex
Unix chmod uses octal for file permissions. Converting to hex helps understand the underlying bit patterns for advanced permission analysis.
Understanding chmod Octal Notation
Each octal digit represents permissions for owner, group, and others. Bits: 4=read, 2=write, 1=execute.
Common chmod Values in Hex
| Octal | Hexadecimal | Meaning |
|---|---|---|
| 755 | 0x1ED | rwxr-xr-x (standard executable) |
| 644 | 0x1A4 | rw-r--r-- (standard file) |
| 777 | 0x1FF | rwxrwxrwx (full access - insecure) |
| 700 | 0x1C0 | rwx------ (owner only) |
| 600 | 0x180 | rw------- (private file) |
| 444 | 0x124 | r--r--r-- (read-only for all) |
Why Convert Octal to Hex
Linux Permission Analysis
Security audits examine file permissions at the bit level. Converting chmod 755 (octal) to 0x1ED (hex) then to binary (111101101) reveals exact read/write/execute flags. Essential for rootkit detection and security hardening.
Archive File Formats
Tar archives store file permissions in octal. Hex conversion aids in parsing tar headers programmatically. Legacy Unix backup systems (cpio, dump) use octal extensively; hex provides a bridge to modern tools.
Legacy System Migration
PDP-11 and VAX systems used octal for memory addresses and machine code. Converting to hex helps port old assembly code to modern architectures. Historical computing hobbyists working with vintage systems need octal-to-hex for documentation.
Device Driver Development
Some embedded Linux drivers use octal for register configurations. Converting to hex aligns with modern development tools and debuggers that display memory in hexadecimal. Kernel module parameters occasionally require octal-to-hex translation.
Historical Documentation
Classic Unix books (K&R C, Lions' Commentary) use octal notation. Converting examples to hex helps modern programmers understand historical code. Early C escape sequences (\\033 for ESC) were octal; hex equivalents (\\x1B) are clearer today.
Tape & Disk Formats
Magnetic tape formats (9-track, QIC) used octal for block addressing. Hex conversion aids data recovery from legacy media. Filesystem inodes on old Unix systems displayed in octal; hex provides compatibility with modern forensic tools.
Octal to Hex Quick Reference
Single-digit octal conversions and common multi-digit patterns for Unix administration.
Single Digit (0-7)
Common Patterns
Octal to Hex: Unix & Legacy Systems FAQs
Why does Unix use octal for file permissions?
Historical reasons: early Unix (1970s) ran on PDP-11 computers that used octal. Each permission bit triplet (rwx = 3 bits) maps perfectly to one octal digit (0-7). This made chmod intuitive: 755 = rwxr-xr-x is easier to remember than binary 111101101 or hex 0x1ED.
How to convert chmod 755 to hexadecimal?
Convert each octal digit to 3-bit binary: 7=111, 5=101, 5=101 → 111101101. Regroup as 4-bit nibbles: 0001 1110 1101. Convert to hex: 1=0x1, 14=0xE, 13=0xD → 0x1ED. So chmod 755 = 0x1ED in hex.
Why can't I use digits 8 or 9 in octal?
Octal is base-8, using only digits 0-7 (like decimal base-10 uses 0-9). Each octal digit represents 3 binary bits, which can only encode values 0-7. If you see "8" in a supposed octal number, it's either a typo or the number is actually decimal.
What's the leading 0 prefix in C octal literals?
In C, a leading 0 indicates octal: int x = 0755; means octal 755 = 493 decimal (not 755 decimal!). To avoid confusion, modern code uses hex (0x1ED) or decimal (493). Always be careful with leading zeros in C—they change the number base.
Why do tar archives use octal in headers?
Tar format was designed in 1979 when octal was standard on Unix. The tar header stores file modes, UIDs, and sizes in octal ASCII strings. Modern tar implementations convert internally, but the on-disk format remains octal for backward compatibility with 40+ years of archives.
Is octal still relevant today?
Mostly for Unix permissions (chmod, umask) and legacy code. Modern programming favors hex for low-level work. However, understanding octal is essential for: system administration, archive file parsing, porting old C code, and working with historical computing documentation. It's niche but not obsolete.
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