Binary to Octal Converter

Enter any binary number into the Binary Input field and this Binary to Octal Converter will instantly convert it to its octal equivalent. You can also include a fractional part using a decimal point (e.g. 1100.11011). The tool shows you the octal result, the intermediate decimal value, and a step-by-step group breakdown of how each trio of binary digits maps to an octal digit. Also try the Big Number Calculator.

Enter a binary number using only 0s and 1s. Use a dot (.) for fractional values, e.g. 1100.101

Results

Octal Result

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Decimal Equivalent

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Group Breakdown

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Hexadecimal Equivalent

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Results Table

How do you convert binary to octal?

Group the binary digits into sets of three, starting from the binary point and working outward — left for the integer part and right for the fractional part. Pad incomplete groups with leading zeros (integer side) or trailing zeros (fractional side). Then convert each 3-bit group to its octal equivalent using the table: 000=0, 001=1, 010=2, 011=3, 100=4, 101=5, 110=6, 111=7. See also our calculate Number Base Converter.

Why are binary and octal so closely related?

Because octal is base-8 and 8 is exactly 2³, every single octal digit maps perfectly to exactly three binary digits. This makes the conversion straightforward and lossless — no arithmetic is required, just grouping and substitution.

Can I convert a binary number with a fractional part?

Yes. Enter the binary number with a dot separating the integer and fractional parts, for example 1100.11011. The integer portion is grouped from the dot to the left, and the fractional portion from the dot to the right, with trailing zeros added as needed to complete each 3-bit group.

What is the octal number system?

The octal system is a base-8 number system that uses digits 0 through 7. It was historically used in computing as a compact way to represent binary data, and is still seen in Unix/Linux file permission codes (e.g. chmod 755). You might also find our calculate Result (in Selected Base), Decimal (Base 10) & Binary (Base 2) — Base useful.

What is the binary number system?

The binary number system is a base-2 system that uses only two digits: 0 and 1. It is the fundamental language of all digital computers and electronics, representing off (0) and on (1) electrical states.

What happens if I enter an invalid binary number?

The converter only accepts digits 0 and 1 (plus an optional decimal point). If you enter any other characters such as 2–9 or letters, the tool will display an error message asking you to enter a valid binary number.

How is binary 1101100 converted to octal?

Split 1101100 into 3-bit groups from the right: 001, 101, 100. Convert each: 001=1, 101=5, 100=4. The result is 154 in octal, written as 154₈.

Is there a difference between binary to octal and binary to hexadecimal conversion?

Yes. For octal, you group binary digits in sets of 3 (since 2³=8). For hexadecimal, you group in sets of 4 (since 2⁴=16). The grouping-and-substitution method is the same in both cases.