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.