Overview
What octal to binary means
Converting octal to binary rewrites the same integer using a different digit alphabet and place-value system.
The absolute value does not change — only the representation does. Octal uses base-8 (0–7); Binary uses base-2 (0–1). This page treats the whole input as one number (whitespace is ignored), which matches how engineers usually convert machine values between bases.
Guide
How to convert octal to binary
- 1
Read the octal digits
Confirm every character is legal in base-8 (0–7). Optional whitespace is stripped before parsing so you can paste spaced nibbles or bytes.
- 2
Convert to an absolute value
Each digit is multiplied by 8 raised to its position, counting from the right starting at power 0. Summing those terms yields the same integer you would write in decimal.
- 3
Express the value in base-2
Repeatedly divide by 2 and collect remainders, or mentally group bits when moving between binary, octal, and hex. The remainders become the binary digits (0–1).
- 4
Preserve the sign if present
A leading minus sign is kept through the conversion. The magnitude is converted, then the sign is reattached to the result.
Example
Worked example
Take the octal sample 110 151. Walking through the conversion:
- Digits: 1 1 0 1 5 1 (base-8)
- Place values: 1×8^5 + 1×8^4 + 0×8^3 + 1×8^2 + 5×8^1 + 1×8^0 = 36969 (decimal)
- In base-2: 1001000001101001
Reference
Base reference (0–15)
Values zero through fifteen in decimal, binary, octal, and hexadecimal — the building blocks for larger conversions.
| Value | Dec | Bin | Oct | Hex |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 | 1 |
| 2 | 2 | 10 | 2 | 2 |
| 3 | 3 | 11 | 3 | 3 |
| 4 | 4 | 100 | 4 | 4 |
| 5 | 5 | 101 | 5 | 5 |
| 6 | 6 | 110 | 6 | 6 |
| 7 | 7 | 111 | 7 | 7 |
| 8 | 8 | 1000 | 10 | 8 |
| 9 | 9 | 1001 | 11 | 9 |
| 10 | 10 | 1010 | 12 | A |
| 11 | 11 | 1011 | 13 | B |
| 12 | 12 | 1100 | 14 | C |
| 13 | 13 | 1101 | 15 | D |
| 14 | 14 | 1110 | 16 | E |
| 15 | 15 | 1111 | 17 | F |
Basics
About these bases
base-8Octal
Octal is base-8, using digits 0–7. Each octal digit represents exactly three binary digits.
Octal was historically popular on systems with word sizes divisible by three, and still shows up in Unix file permissions (for example 755). Groups of three bits map cleanly to one octal digit.
Digits: 0–7
base-2Binary
Binary is base-2, using only the digits 0 and 1. It maps directly to the on/off states of digital circuits.
Every bit is a power of two. Reading from the right, positions are 2⁰, 2¹, 2², and so on. Contiguous binary is often grouped in 8-bit bytes so each group lines up with one character code.
Digits: 0–1
Practice
When to use a octal → binary converter
Debugging & inspection
Quickly check how a octal value looks when rewritten as binary without opening a calculator or REPL.
Learning place value
See the same quantity side by side in two alphabets — a concrete way to internalize powers of two, eight, ten, or sixteen.
Protocol & homework checks
Verify dumps, worksheet answers, or configuration values before you paste them into code or documentation.
Private, offline work
Everything runs in your browser. Nothing you type is uploaded, which keeps keys, snippets, and sample data on your device.
Notes
Tips and common pitfalls
- Whitespace inside numeric input is ignored, so you can paste grouped bytes or nibbles safely.
- When reading binary by hand, mark groups of 4 bits for hex or 3 bits for octal — those groupings eliminate most conversion mistakes.
- Unix permission bits are octal (for example 644 or 755). This converter uses the same digit rules.
- Invalid digits stop the conversion with a clear error instead of silently skipping characters.
Explore
Related converters
FAQ
Frequently asked questions
- Does octal to binary change the value?
- No. Both sides represent the same integer. Only the digit alphabet and place values change.
- Is my input uploaded?
- No. Conversion runs entirely in your browser. Nothing you type is sent to a server.
- How should I format multi-value input?
- Enter a single number. Spaces inside the digits are stripped before parsing.
- What digits are valid in octal?
- Octal accepts 0–7.