Binary to Octal Converter

How to Convert Binary to Octal?

Binary to octal conversion transforms base-2 numbers (using only 0 and 1) into base-8 numbers (0-7). The conversion is done by grouping binary digits into sets of 3 (from right to left) and converting each group to its octal equivalent.

Conversion steps:
1. Group binary digits into sets of 3, starting from the right
2. Pad with leading zeros if necessary to make complete groups
3. Convert each 3-digit binary group to its octal equivalent
4. Combine the octal digits to get the final result

Example: Convert 101101 to octal:
101 101 → 5 5 → 55 (octal)

What is an octal number?

Octal is a base-8 numeral system that uses eight digits: 0, 1, 2, 3, 4, 5, 6, and 7. It was commonly used in early computing systems and is still used in some Unix file permissions. Each octal digit represents exactly 3 binary digits, making it convenient for representing binary data in a more compact form.

How do I convert binary to octal manually?

To convert binary to octal manually:
1. Group the binary digits into sets of 3, starting from the right
2. Add leading zeros if needed to complete the last group
3. Convert each 3-digit group to its octal equivalent using the table:
000 → 0 100 → 4
001 → 1 101 → 5
010 → 2 110 → 6
011 → 3 111 → 7
4. Combine the octal digits

Example for binary 110101:
Group: 110 101
Octal: 6 5
Result: 65 (octal)

Why is octal useful in computing?

Octal is useful in computing because:
1. Each octal digit represents exactly 3 binary digits
2. It's more compact than binary for representing the same data
3. It's easier to read and work with than long binary strings
4. It was used in early Unix systems for file permissions
5. It provides a middle ground between binary and decimal representations

What's the relationship between binary, octal, and hexadecimal?

The relationship between these number systems:
- Binary (base-2): Uses 0 and 1
- Octal (base-8): Uses 0-7, each digit = 3 binary digits
- Hexadecimal (base-16): Uses 0-F, each digit = 4 binary digits

This makes conversions between them straightforward:
- Binary to Octal: Group by 3 digits
- Binary to Hex: Group by 4 digits
- Octal to Hex: Convert to binary first, then group by 4

Binary to Octal Conversion Table