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Octal to Binary Converter
Convert any octal number to binary instantly — each digit becomes 3 bits. Free, fast, no sign-up.
Only octal digits allowed (0-7) — spaces, commas and dashes are ignored.
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Also equals
- Binary
- Decimal
- Octal
- Hex
Step-by-step calculation
| Octal digit | 3 bits |
|---|
How to convert octal to binary
- Write down the octal number.
- Replace each octal digit with its 3-bit binary form (0=000 … 7=111).
- Join the groups — that's your binary number (drop leading zeros).
Example: 175₈ → 1 7 5 → 001 111 101 → 1111101₂.
Background reading: the octal number system on Wikipedia.
Conversion table
Octal 0–17 expanded to binary, one 3-bit group per digit.
| Octal | Binary | Expansion |
|---|---|---|
| 0 | 0 | 0₈ → 000 → 0₂ |
| 1 | 1 | 1₈ → 001 → 1₂ |
| 2 | 10 | 2₈ → 010 → 10₂ |
| 3 | 11 | 3₈ → 011 → 11₂ |
| 4 | 100 | 4₈ → 100 → 100₂ |
| 5 | 101 | 5₈ → 101 → 101₂ |
| 6 | 110 | 6₈ → 110 → 110₂ |
| 7 | 111 | 7₈ → 111 → 111₂ |
| 10 | 1000 | 10₈ → 001 000 → 1000₂ |
| 11 | 1001 | 11₈ → 001 001 → 1001₂ |
| 12 | 1010 | 12₈ → 001 010 → 1010₂ |
| 13 | 1011 | 13₈ → 001 011 → 1011₂ |
| 14 | 1100 | 14₈ → 001 100 → 1100₂ |
| 15 | 1101 | 15₈ → 001 101 → 1101₂ |
| 16 | 1110 | 16₈ → 001 110 → 1110₂ |
| 17 | 1111 | 17₈ → 001 111 → 1111₂ |
| 777 | 111111111 | 777₈ → 111 111 111 → 111111111₂ = 511 |
Powers of 2
| Power | Value |
|---|---|
| 20 | 1 |
| 21 | 2 |
| 22 | 4 |
| 23 | 8 |
| 24 | 16 |
| 25 | 32 |
| 26 | 64 |
| 27 | 128 |
| 28 | 256 |
| 29 | 512 |
| 210 | 1024 |
| 211 | 2048 |
| 212 | 4096 |
| 213 | 8192 |
| 214 | 16384 |
| 215 | 32768 |
| 216 | 65536 |
Octal to binary in code
Python
bin(int("17", 8))[2:] # → '1111'JavaScript
parseInt("17", 8).toString(2); // → '1111'C
#include <stdio.h>
#include <stdlib.h>
int main(void) {
long v = strtol("17", NULL, 8); /* → 15 */
for (int bit = 3; bit >= 0; bit--) /* 15 needs 4 bits */
putchar(((v >> bit) & 1) ? '1' : '0');
putchar('\n'); /* → 1111 */
return 0;
}Common values
17₈ =1111₂10₈ =1000₂7₈ =111₂100₈ =1000000₂77₈ =111111₂0₈ =0₂
Key takeaways
- Expand each octal digit to its 3-bit binary form.
- 0→000, 1→001, 2→010, 3→011, 4→100, 5→101, 6→110, 7→111.
- 17₈ = 1111₂; 777₈ = 111111111₂.
- Drop unneeded leading zeros at the end.
Frequently asked questions
How do I convert octal to binary?
Replace each octal digit with 3 binary bits and join them together.
What is 17 in binary?
17₈ = 1111₂.
Do I keep leading zeros?
No — drop leading zeros from the final answer, e.g. 001 111 becomes 1111.
What is 17 in binary?
17₈ → 001 111 → 1111₂ = 15.
How do you convert octal to binary?
Replace each octal digit with its 3-bit binary form: 0→000, 1→001 … 7→111.
What is 777 in binary?
777₈ = 111111111₂ = 511.
Can the result have leading zeros?
Only if you keep the 3-bit groups padded — 10₈ can be written 001000 or 1000₂; the value is the same.
Need the reverse? Try our binary to octal converter.