Octal to Binary Converter
Convert octal to binary — each octal digit expands to three bits.
Each octal digit becomes exactly three binary digits: 7 is 111, 5 is 101, 4 is 100.
How the octal to binary converter works
Each octal digit becomes exactly three binary digits: 7 is 111, 5 is 101, 4 is 100. Join them in order.
The use everyone meets is file permissions: chmod 755 expands to 111 101 101, which reads as read-write-execute for the owner and read-execute for group and others.
Formula: value = Σ digitₖ × bᵏ
Worked examples
| Inputs | Converted | Note |
|---|---|---|
| 755 | 111101101 | 111101101 |
| 377 | 11111111 | 11111111 |
| 644 | 110100100 | 110100100 |
FAQFrequently asked questions
How do I convert octal to binary?
Expand each digit to three bits: 7 is 111, 5 is 101.
What does chmod 644 mean?
110 100 100 — read and write for the owner, read only for group and others.
How many bits is an octal digit?
Exactly three.
Why does octal only use 0 to 7?
Because three bits express eight values, 0 through 7. There is no octal 8 or 9.
What is 755 in decimal?
493.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Common Core State Standards — Mathematics — the terms and methods taught in US schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.