Convert Decimal (decimal) to Octal (octal) instantly. Decimal to octal conversion.
| Unit | Name | Value |
|---|---|---|
| binary | Binary (Base 2) | — |
| hex | Hexadecimal (Base 16) | — |
| octal | Octal (Base 8) | — |
Example: 8 (Decimal) = 10 (Octal)
Method: Repeatedly divide by 8 and record remainders upward. E.g. 64÷8=8r0, 8÷8=1r0, 1÷8=0r1 → 100₈.
Decimal is base-10; Octal is base-8. Use the converter above for any value instantly.
Common values from 0 to 1,048,576 — powers of 2 and standard computing values
| Decimal (base 10) | Octal (base 8) | Notes |
|---|---|---|
| 0 | 0 | Zero |
| 1 | 1 | One |
| 2 | 2 | Two |
| 3 | 3 | |
| 4 | 4 | Four |
| 5 | 5 | |
| 6 | 6 | |
| 7 | 7 | |
| 8 | 10 | Eight |
| 9 | 11 | |
| 10 | 12 | Ten |
| 11 | 13 | |
| 12 | 14 | |
| 13 | 15 | |
| 14 | 16 | |
| 15 | 17 | Max nibble (4-bit) |
| 16 | 20 | One hex digit |
| 32 | 40 | 2⁵ |
| 64 | 100 | 2⁶ |
| 128 | 200 | 2⁷ |
| 255 | 377 | Max byte |
| 256 | 400 | 2⁸ |
| 512 | 1000 | 2⁹ |
| 1024 | 2000 | 1 KiB |
| 2048 | 4000 | 2 KiB |
| 4096 | 10000 | 4 KiB |
| 32768 | 100000 | 32 KiB |
| 65535 | 177777 | Max 16-bit unsigned |
| 65536 | 200000 | 2¹⁶ |
| 1048576 | 4000000 | 1 MiB (2²⁰) |
Divide by 8, note remainder (0–7). Read remainders bottom-to-top.
Powers of 8: 1, 8, 64, 512, 4096. Know these for quick conversion.
chmod 755 = 7(rwx), 5(r-x), 5(r-x). Octal perfectly encodes 3-bit permission groups.
Converts between binary, hex, and decimal daily for debugging, bitmasking, and memory address analysis.
Learns number base conversions as a fundamental concept in computer architecture and digital logic courses.
Works with IP addresses, subnet masks, and MAC addresses in binary, decimal, and hex representations.
Programs microcontrollers using binary bit patterns and hex register values for hardware configuration.
Designs logic circuits using binary truth tables and checks hex values on oscilloscopes and analyzers.
Reads hex dumps, analyzes binary data, and decodes encoded strings during reverse engineering and forensics.
The decimal (base-10) number system uses ten digits (0–9) and is the universal numeral system for human mathematics, commerce, and everyday life. It is almost certainly based on the ten fingers of the human hand — 'digit' comes from the Latin digitus meaning finger.
The decimal system with positional notation and zero was developed in India (5th–7th century CE) and transmitted to Europe via Arabic mathematicians — which is why it is also called the Hindu-Arabic numeral system. It replaced Roman numerals in European commerce by the 16th century.
Interesting fact: Not all cultures chose base-10. Babylonians used base-60 (preserved in our 60 seconds, 60 minutes, 360 degrees). The Mayans used base-20. The Yuki people of California used base-8, counting the spaces between fingers rather than the fingers themselves.
The octal (base-8) system uses digits 0–7 and was historically important in early computing because it maps cleanly to 3-bit groups (2³=8). Before hexadecimal became dominant, octal was the standard shorthand for binary in many early computer systems.
Unix and Linux file permission codes use octal: chmod 755 sets read/write/execute (111=7) for owner, read/execute (101=5) for group and others. Unix file permissions are still one of the main reasons programmers encounter octal today.
Interesting fact: The DEC PDP series computers (1960s–1970s) — among the most influential minicomputers ever built — used octal throughout their documentation and front-panel displays. Many 1970s programming books use octal; older UNIX documentation assumes octal fluency.
Decimal to octal is used primarily for Unix/Linux file permissions. chmod 755 = rwxr-xr-x: each octal digit encodes 3 permission bits. 8=10₈, 64=100₈, 512=1000₈. Leading zero in C code signals octal (e.g. 0755).
Use the converter above for any value. Results are exact — numeral base conversions involve no rounding or approximation.