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Octal to Decimal Converter
Convert octal (base 8) numbers to decimal. Interpret Unix chmod values like 755.
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ASCII Letter A
Convert the ASCII code for uppercase A (65) across all bases.
Key values: Decimal 65 · Binary 1000001 · Hex 41
Byte Maximum
The largest value a single byte can hold (255).
Key values: Decimal 255 · Binary 11111111 · Hex FF
Hex Color Code
Convert a common hex color code (deep sky blue) to other bases.
Key values: Hex 00BFFF · Decimal 49151 · Binary nibbles
The Octal Number System
Octal (base-8) uses digits 0–7. Each position represents a power of 8:
Worked Example
Convert to decimal:
Unix File Permissions
The most common modern use of octal is Unix file permissions. The command chmod 755 file sets three octal digits — one each for owner, group, and others:
| Octal | Binary | Permissions |
|---|---|---|
| 0 | 000 | No access |
| 1 | 001 | Execute only |
| 2 | 010 | Write only |
| 4 | 100 | Read only |
| 5 | 101 | Read + execute |
| 6 | 110 | Read + write |
| 7 | 111 | Read + write + execute |
So chmod 755 means: owner gets full access (7 = rwx), group gets read+execute (5 = r-x), others get read+execute (5 = r-x).
Why octal works here: Each permission group has 3 bits (read, write, execute), and — so one octal digit maps perfectly to one 3-bit permission group. This is the same reason hex maps to 4-bit nibbles.
Octal ↔ Binary Shortcut
Just as hex groups 4 bits, octal groups 3 bits:
This 3-bit grouping is why octal was popular on machines with 12-bit, 24-bit, or 36-bit word sizes (all multiples of 3). Modern 32-bit and 64-bit machines favor hex (4-bit grouping) instead.
Historical Context
Octal was the dominant shorthand for binary in early computing (1950s–1970s). The PDP-8 and other DEC machines used 12-bit words, which divide evenly into four octal digits. The C programming language's octal literal syntax (0755) dates from this era. Hex eventually replaced octal for most purposes as 8-bit bytes and 16/32-bit words became standard.
Frequently Asked Questions
How do you convert octal to decimal?
Multiply each octal digit by its positional power of 8 and sum. For example, 755 in octal = in decimal.
What does chmod 755 mean in Unix?
Each digit represents permissions for owner, group, and others. 7 (binary 111) = read+write+execute, 5 (binary 101) = read+execute. So chmod 755 gives the owner full access and read+execute access to group and others.
Why is octal used for Unix file permissions?
Each permission group has 3 bits (read, write, execute), and , so one octal digit maps perfectly to one 3-bit permission group. This is the same reason hex maps to 4-bit nibbles.
How do you convert between octal and binary?
Each octal digit corresponds to exactly 3 binary digits. For example, 755 in octal becomes 111 101 101 in binary. Just convert each digit independently using the 3-bit groups.
Why has hexadecimal largely replaced octal in modern computing?
Modern computers use 8-bit bytes and 16/32/64-bit words, which are all multiples of 4 (not 3). Hex groups 4 bits per digit, aligning perfectly with byte boundaries. Octal was more natural for older machines with 12-bit or 36-bit word sizes.
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