Octal (base 8)
Octal (base 8) uses the digits 0 through 7. Each octal digit represents exactly three bits, which is why octal was widely used on early minicomputers and is still the conventional notation for Unix file-permission masks (e.g. 755).
Octal to Binary Converter
755 (oct) = 111101101 (bin)
Convert octal numbers to binary numbers exactly, for any size. Convertitive parses your input as a BigInt — so 64-bit values, 256-bit hex strings, and even larger numbers round-trip without rounding. For quick reference: 755 oct = 111101101 bin, and 100 oct = 1000000 bin.
Quick
How to convert octal numbers to binary numbers
Enter a value
Type a octal integer in the From field. Allowed characters: 0 through 7.
Read the binary result
The To field updates as you type. For example, the octal value 755 equals 111101101 in binary.
Copy or share
Use the copy button to grab the result. You can change either base from its dropdown without leaving the page.
Reference table
Fifty representative values. Every row is computed exactly by the same BigInt-based converter that powers the widget above.
| Octal (oct) | Binary (bin) |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 10 |
| 3 | 11 |
| 4 | 100 |
| 5 | 101 |
| 6 | 110 |
| 7 | 111 |
| 10 | 1000 |
| 11 | 1001 |
| 12 | 1010 |
| 13 | 1011 |
| 14 | 1100 |
| 15 | 1101 |
| 16 | 1110 |
| 17 | 1111 |
| 20 | 10000 |
| 21 | 10001 |
| 22 | 10010 |
| 23 | 10011 |
| 24 | 10100 |
| 30 | 11000 |
| 37 | 11111 |
| 40 | 100000 |
| 44 | 100100 |
| 52 | 101010 |
| 60 | 110000 |
| 62 | 110010 |
| 77 | 111111 |
| 100 | 1000000 |
| 144 | 1100100 |
| 177 | 1111111 |
| 200 | 10000000 |
| 310 | 11001000 |
| 377 | 11111111 |
| 400 | 100000000 |
| 764 | 111110100 |
| 777 | 111111111 |
| 1000 | 1000000000 |
| 1750 | 1111101000 |
| 1777 | 1111111111 |
| 2000 | 10000000000 |
| 4000 | 100000000000 |
| 10000 | 1000000000000 |
| 20000 | 10000000000000 |
| 40000 | 100000000000000 |
| 100000 | 1000000000000000 |
| 177777 | 1111111111111111 |
| 200000 | 10000000000000000 |
| 4000000 | 100000000000000000000 |
Frequently asked questions
- How do I convert octal numbers to binary numbers?
- Enter your octal value above. Convertitive parses it as an arbitrary-precision integer and reformats it in binary. The conversion is exact for any size — there's no float rounding.
- What is 755 in binary?
- 755 (octal) equals 111101101 in binary.
- Are negative numbers supported?
- No, only non-negative integers are supported for octal ↔ binary. Two's-complement encodings depend on a chosen bit-width, which this tool does not assume.
- What's the largest number I can convert?
- Any size. Convertitive uses JavaScript BigInt, which has no fixed upper bound — 256-bit hex strings, 512-bit and bigger all round-trip exactly.
- How many bits does the result take?
- An n-digit number in base 8 needs roughly 3.00 × n bits to store. The exact bit length equals ⌈log₂(value + 1)⌉.
- Is hex case-sensitive?
- Hexadecimal accepts letters in either case; this conversion doesn't involve hex.
- Are conversion factors exact?
- Yes. Base conversion is integer-to-integer; there are no factors, no rounding, no precision loss.
- Why would I convert octal numbers to binary numbers?
- Binary is what computers actually use internally. Converting from octal to binary is useful for low-level debugging, bit-mask design, and understanding how values are encoded at the hardware level.
About octal and binary
Binary (base 2)
Binary (base 2) represents numbers with two digits: 0 and 1. It is the native language of every digital computer because each digit maps directly to a transistor's on/off state. A group of 8 binary digits forms one byte, the smallest addressable unit in most modern hardware.