Binary to Octal
Convert binary to octal and see the working. Enter a binary number, whole or fractional, and the converter returns the octal value with a step-by-step solution that shows how the bits were grouped. It checks your input as you type and flags any digit that is not 0 or 1. It is free, with no signup.
How to Convert Binary to Octal
1. Enter your binary number. Use only 0 and 1, and a point for any fractional part.
2. Watch the live validation, which flags any invalid digit.
3. Read the octal result and the step-by-step solution beneath it.
4. Follow the breakdown, or copy it, to check your own work.
How Binary to Octal Conversion Works
Octal is base 8, and 8 is 2 to the power of 3. That means three binary digits cover exactly the values 0 to 7, which is one octal digit. So the whole conversion is grouping:
1. Split the binary number into groups of three bits, starting from the right.
2. If the leftmost group has fewer than three bits, add zeros on its left.
3. Replace each group with its octal digit using the table below, and join the digits.
| Bits | Octal | Bits | Octal | Bits | Octal |
| 000 | 0 | 011 | 3 | 110 | 6 |
| 001 | 1 | 100 | 4 | 111 | 7 |
| 010 | 2 | 101 | 5 |
Take 1101010. Grouped from the right and padded, it is 001 101 010. Those groups are 1, 5 and 2, so the octal result is 152.
| Binary | Grouped in threes | Octal digits | Octal |
| 1101010 | 001 101 010 | 1, 5, 2 | 152 |
| 10101110 | 010 101 110 | 2, 5, 6 | 256 |
| 11111111 | 011 111 111 | 3, 7, 7 | 377 |
The last row is worth remembering: 11111111 is 377 in octal, FF in hexadecimal and 255 in decimal.
Fractional Binary to Octal
Fractions follow the same rule, but you group outward from the point. Group the whole part from the point leftward, and the fractional part from the point rightward. If the last fractional group is short, add zeros on its right.
For 1101.101: the whole part 1101 becomes 001 101, which is 15, and the fractional part 101 is already a full group, which is 5. The octal result is 15.5.
For 10110.01: the whole part becomes 010 110, which is 26, and the fractional part 01 is padded on the right to 010, which is 2. The result is 26.2.
Octal to Binary
This tool converts binary to octal only. To go the other way by hand, replace each octal digit with its three-bit group from the table above. For octal 752, the digits 7, 5 and 2 become 111, 101 and 010, so the binary number is 111101010.
Binary vs BCD: Why It Matters for Octal
BCD, or binary-coded decimal, writes each decimal digit as its own 4-bit group. The decimal number 10 is 0001 0000 in BCD. If you read those same bits as ordinary binary, you get 16, and the octal answer is 20. The correct octal for decimal 10 is 12.
So a BCD value cannot be converted to octal by grouping its bits. First decode the BCD digits into the decimal number, then convert that number to octal. This tool converts ordinary binary and does not decode BCD.
Where Octal Is Used
Octal is a compact way to write binary, and its best-known use is Unix and Linux file permissions. Each permission set is three bits: read is worth 4, write is worth 2 and execute is worth 1. In chmod 755, the owner gets 7 (rwx, binary 111), the group gets 5 (r-x, binary 101) and others get 5 (r-x, binary 101).
Common Mistakes to Avoid
❌ Mistakes to Avoid
✓ Solution:
Grouping from the left instead of the right. Start at the right of the whole part. Grouping from the left pads the wrong end and gives a different number.
Including invalid digits. Binary has only 0 and 1. The converter flags anything else as you type.
Dropping the point in a fractional number. 10110110 and 1011.0110 are different numbers, and the point decides where grouping starts.
Confusing octal output with decimal. Octal digits run from 0 to 7 only. The octal number 377 is not three hundred and seventy-seven. It is 255 in decimal.
Padding the fractional part on the wrong side. Zeros added to a short fractional group go on the right. Adding them on the left changes the value.
Frequently Asked Questions
Group the bits in threes from the right, pad the leftmost group with zeros if needed, and replace each group with its octal digit. For 1101010, that is 001 101 010, which gives 152.
Because 8 is 2 to the power of 3. Three bits can represent the eight values 0 to 7, which are exactly the digits of octal.
Yes. Use a point. For example, 1101.101 is 15.5 in octal.
No. This tool converts binary to octal only. To reverse it, replace each octal digit with its three-bit group.
No. BCD is a different encoding from ordinary binary. Decode the BCD digits to a decimal number first, then convert that number.
Each permission set has three flags: read, write and execute. Three bits make one octal digit, so a three-digit number such as 755 describes the owner, group and others in a compact way.
They are number bases 2, 8 and 16. Octal groups binary digits in threes and hexadecimal groups them in fours, so both are shorthand for binary.
Yes. It is free to use, with no signup.
Convert Binary to Octal
Enter your binary number and read the octal result and the working. Use the breakdown to check your own homework or code.
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