Binaryto Octal Converter
Our free numeral systems converter handles binaryto octal conversions. See tables, ratios, and examples for quick reference.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
Group binary into 3-bit triads; each triad = one octal digit (0-7)
Pad the binary number so its length is a multiple of 3. Group into triads (3 bits each) from right to left. Convert each triad to its octal digit: 000=0, 001=1, 010=2, 011=3, 100=4, 101=5, 110=6, 111=7. For reverse conversion, expand each octal digit to its 3-bit binary equivalent.
Worked Examples
Example 1: Binary to Octal Conversion
Problem:Convert binary 110101110 to octal.
Solution:Pad to multiple of 3: 110 101 110\n110 = 6\n101 = 5\n110 = 6\nOctal result: 656
Result:110101110 (binary) = 656 (octal) = 430 (decimal)
Example 2: Octal to Binary
Problem:Convert octal 752 to binary.
Solution:7 = 111\n5 = 101\n2 = 010\nBinary result: 111101010
Result:752 (octal) = 111101010 (binary) = 490 (decimal)
Frequently Asked Questions
How do I convert binary to octal?
Binary to octal conversion uses the fact that each octal digit corresponds to exactly 3 binary bits. Start by padding the binary number with leading zeros so its length is a multiple of 3. Then group the bits into sets of 3 from right to left. Convert each 3-bit group to its octal equivalent: 000=0, 001=1, 010=2, 011=3, 100=4, 101=5, 110=6, 111=7. Concatenate the octal digits for the final result.
Why does each octal digit map to 3 binary bits?
Octal is base 8, and 8 equals 2 to the 3rd power. This means exactly 3 binary bits can represent all 8 possible octal digit values (0 through 7). This power-of-two relationship creates a clean, direct mapping between the two number systems. Similarly, hexadecimal (base 16 = 2 to the 4th power) maps to groups of 4 bits. This mathematical relationship is what makes binary-to-octal conversion a simple grouping exercise.
What is the octal number system used for?
Octal was historically important in early computing when machines used 12-bit, 24-bit, or 36-bit words that divide evenly into groups of 3. Unix and Linux file permissions use octal notation extensively: for example, chmod 755 means rwxr-xr-x where each digit (7, 5, 5) represents 3 permission bits (read, write, execute) for owner, group, and others respectively. Octal is also used in some programming languages for character escape sequences.
What is the 0o prefix for octal numbers?
The 0o prefix (zero followed by lowercase o) is a modern convention for indicating octal numbers in programming languages like Python 3, JavaScript (ES6+), and Ruby. Older conventions include a leading zero (like 0755 in C), which can cause confusion with decimal numbers. The 0o prefix eliminates this ambiguity. Some assembly languages use a trailing q or o suffix instead. This converter supports both prefixed and unprefixed octal input.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy