Octal to Binary Converter
Enter the octal number you want to convert to binary.
Table of Contents
- How does octal to binary conversion work?
- Octal to binary conversion formula
- Conversion process
- Examples
- Octal to binary conversion table
- Frequently Asked Questions
How does octal to binary conversion work?
The octal system is base 8 and the binary system is base 2. To convert an octal number to binary, replace each octal digit with its 3-bit binary equivalent. This method is straightforward because each base-8 digit corresponds exactly to a group of 3 binary digits.
Octal to binary conversion formula
For an octal number with n digits:
N₈ = ∑(oi × 8i) → N₂Where each octal digit oi (0–7) is converted into its 3-bit binary group. The final binary number is obtained by concatenating the groups in the same order.
Conversion process
- Write down the octal number.
- Convert each octal digit into its 3-bit binary equivalent (e.g., 0 → 000, 1 → 001, 7 → 111).
- Join all binary groups in the same order to get the full binary number.
Examples
7₈ to binary| Octal digit | Binary equivalent (3 bits) |
|---|---|
| 7 | 111 |
Result: 7₈ = 111₂.
25₈ to binary| Octal digit | Binary equivalent (3 bits) |
|---|---|
| 2 | 010 |
| 5 | 101 |
Reading the groups together: 25₈ = 010101₂.
Result: 25₈ = 10101₂.
Octal to binary conversion table
Quick reference values for short octal numbers.
| Octal | Binary |
|---|---|
0 | 000 |
1 | 001 |
2 | 010 |
3 | 011 |
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 |
30 | 11000 |
40 | 100000 |
Frequently Asked Questions
How do you convert an octal number to binary?
Each octal digit is replaced by its 3-bit binary equivalent. For example, the number 25₈ becomes 010 101₂, which gives 10101₂ when leading zeros are removed.
Why does each octal digit correspond to 3 binary bits?
Because the octal system is base 8, and 8 equals 2³. This means each base-8 digit can be represented exactly by three binary digits.
Cite this page
You can use the following citation format when referencing this calculator in academic or professional work.
Ramos, J., Octal to binary converter, Available at: https://calcuclub.com/convert/octal-to-binary/ (Accessed: 27 November 2025).