Binary to Octal Converter

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Binary to Decimal Decimal to Binary Binary to Octal Octal to Binary Binary to Hexadecimal Hexadecimal to Binary Octal to Decimal Decimal to Octal Octal to Hexadecimal Hexadecimal to Octal Decimal to Hexadecimal Hexadecimal to Decimal

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Understanding Binary and Octal

Binary is the base-2 number system used natively by computers: every value is stored as a sequence of bits, each either 0 or 1. Digital logic gates, boolean operations, and low-level memory all operate directly in binary — it's the only number system a CPU actually understands.

Octal is the base-8 number system, using digits 0–7. Because each octal digit maps exactly to 3 binary bits, it was historically popular for compactly displaying binary data on systems with word sizes divisible by 3. Today its main practical use is Unix/Linux file permissions, expressed as three-digit octal numbers like 755.

How to Convert Binary to Octal (Step by Step)

To convert binary to octal, group the bits into sets of 3 starting from the right (padding the leftmost group with zeros if needed), then convert each group to a single octal digit. For example, 11001010 splits into 011 001 010, which is 3, 1, 2 — giving 312.

Frequently Asked Questions

Find answers to common questions

Because each octal digit maps to exactly 3 bits with no remainder, converting binary to octal is a simple grouping operation you can do without any arithmetic — useful for quickly reading long bit strings, such as Unix file permission bits.

No — this converter uses arbitrary-precision (BigInt) math internally, so it produces exact results even for very long binary strings or huge decimal, octal, and hexadecimal values, unlike calculators limited to 32-bit or 64-bit integers.

Free online binary to octal converter. Convert binary numbers to octal instantly, with support for arbitrarily large values.

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Binary to Octal Converter