Binary to Octal Converter
Enter a binary number (0s and 1s), then click convert to get the octal value instantly.
What this binary to octal converter does
This calculator converts a binary number (base-2) into an octal number (base-8). It works for whole numbers and binary fractions, such as 1011.101. It also shows the grouping logic so you can understand exactly how the answer is produced.
Binary-to-octal conversion is common in computer science, digital systems, embedded programming, and low-level debugging, where compact number representation matters.
How to use the calculator
- Type or paste a binary value into the input box.
- Click Convert (or press Enter).
- Read the octal output instantly.
- Use Copy Result to copy the converted value.
How binary to octal conversion works
1) Group binary digits in sets of three
Each octal digit corresponds to exactly three binary bits:
- 000 = 0
- 001 = 1
- 010 = 2
- 011 = 3
- 100 = 4
- 101 = 5
- 110 = 6
- 111 = 7
For the integer part, grouping starts from the right. For the fractional part (if present), grouping starts from the left after the decimal point.
2) Pad with zeros if needed
If a group has fewer than 3 bits, add zeros:
- For integer side: add zeros to the left.
- For fractional side: add zeros to the right.
3) Convert each 3-bit group to one octal digit
After converting each group, concatenate the octal digits in order. That final sequence is your octal value.
Worked examples
Example 1: Integer value
Binary: 110101101
Group into 3s from right: 110 101 101
Convert groups: 110→6, 101→5, 101→5
Octal result: 655
Example 2: Binary fraction
Binary: 1011.101
Integer side: 1011 → pad left → 001 011 → 1 3
Fraction side: .101 → already 3 bits → 5
Octal result: 13.5
Why octal is useful
- It is more compact than binary, reducing visual clutter.
- Each octal digit maps cleanly to 3 bits, making conversion quick.
- It appears in systems work, permission notation, and legacy computing contexts.
Common input mistakes
- Using digits other than 0 and 1 (invalid for binary input).
- Including multiple decimal points.
- Leaving only a sign with no digits (like just “-”).
This tool validates input and tells you when something needs fixing.
FAQ
Does this support negative binary values?
Yes. You can enter values like -101101, and the sign is preserved in the octal output.
Can I include spaces?
Yes. Spaces and underscores are ignored, so inputs like 101 110_001 are accepted.
Is the conversion exact?
Yes. Binary and octal are both positional systems with powers of 2, so group-based conversion is exact.
Final takeaway
If you work with digital numbers, this binary to octal converter saves time and reduces manual errors. Use it for fast answers, and use the step breakdown to reinforce your number-system skills.