Best uses
- Expand octal values into binary for study or debugging.
- Check permission-style octal values at the bit level.
- Practice base-8 to base-2 conversion.
Octal To Binary Converter
8
2
Calculation steps of octal to binary:
How to convert an octal number to binary
Converting an octal number to binary involves a systematic process where each digit in the octal number is replaced with its corresponding binary representation. In octal, each digit represents a power of 8, and in binary, each digit represents a power of 2. To perform the conversion, a table is utilized, mapping each octal digit to its binary equivalent. Starting from the leftmost digit of the octal number, each digit is substituted with its binary counterpart, ensuring that the binary representation is three bits long by adding leading zeros if needed. The binary representations of individual octal digits are then combined to yield the binary equivalent of the entire octal number. The final result may be further refined by removing any leading zeros. This method offers a step-by-step approach to manually convert octal numbers to binary, providing a clear understanding of the positional values and binary representations associated with each octal digit.
To convert octal to binary, replace each octal digit with its 3-bit binary equivalent. This works because
23 = 8. That means each octal digit can be written as a group of three binary digits.
Note: Leading zeros can be removed from the final binary result when they are not needed.
Example of octal to binary conversion:
(217.102)8 = (?)2
| Octal= | 2 | 1 | 7 | . | 1 | 0 | 2 |
|---|---|---|---|---|---|---|---|
| Arrow= | ↓ | ↓ | ↓ | . | ↓ | ↓ | ↓ |
| Chunk= | ______ | ______ | ______ | . | ______ | ______ | ______ |
| Binary= | 0 1 0 | 0 0 1 | 1 1 1 | . | 0 0 1 | 0 0 0 | 0 1 0 |
Result is = (010001111.001000010)2 or (10001111.00100001)2
Octal to binary conversion table:
| Octal | Binary |
|---|---|
| 0 | 000 |
| 1 | 001 |
| 2 | 010 |
| 3 | 011 |
| 4 | 100 |
| 5 | 101 |
| 6 | 110 |
| 7 | 111 |
| 10 | 001000 |
| 11 | 001001 |
| 12 | 001010 |
| 13 | 001011 |
| 14 | 001100 |
| 15 | 001101 |
Octal to binary guide
Octal to binary conversion is direct because each octal digit maps to exactly three binary bits. Replace every octal digit with its 3-bit equivalent.
Quality checks
- Convert each digit separately.
- Keep leading zeros inside each 3-bit group when they are needed.
- Confirm the octal input contains only digits 0 through 7.
Common mistakes
- Dropping zeros inside groups such as 001 or 010.
- Trying to divide the full octal number by 2.
- Entering digits 8 or 9.
Quick answers
Why does one octal digit equal three binary bits?
Three binary bits can represent values from 0 to 7, the full octal digit range.
Can octal 57 become 101111?
Yes. 5 maps to 101 and 7 maps to 111, so 57 becomes 101111.