Binary to Octal

Convert binary numbers to octal. Group binary digits into sets of 3 for easy octal conversion - useful for Unix permissions.

What is the Binary to Octal Converter?

This tool converts binary numbers to octal by grouping bits into sets of three.

Key relationship: exactly 3 binary bits map to 1 octal digit, because 8 = 2³. Octal is a compact, three-bit view of binary.

Why Convert Binary to Octal?

Unix Permissions

Each rwx triplet maps to one octal digit, the basis of chmod values.

Compact Notation

Shorter than binary and easy to read at a glance.

Historical Computing

Early systems relied on octal for memory and instructions.

Quick Mental Math

Easier than hex for small numbers and fast grouping.

The Conversion Method

Group the binary digits into sets of 3 from the right, then convert each group to its octal digit (0–7).

Example: 111 101 101 → 7 5 5 → 755.

How to Use

Enter the Binary Number

Type a sequence of 0s and 1s. The input is padded with leading zeros to form complete 3-bit groups.

View the Octal Result

The bits are grouped into threes and converted automatically, with the octal value shown instantly.

Apply the Value

Copy the result for file permissions, calculations, or your code.

Bidirectional: both fields are editable. Type an octal value in the result field to convert it back to binary, or use the swap button to flip the direction.

Permission Mapping

Binary	Octal	Permission
`100`	4	read (r)
`010`	2	write (w)
`001`	1	execute (x)
`101`	5	read + execute (r-x)
`111`	7	full access (rwx)

Frequently Asked Questions

Why is 3 bits exactly one octal digit?

Because 8 = 2³. Three bits can represent 8 distinct values (0 to 7), which is exactly the range of one octal digit.

How does this relate to chmod?

Unix permissions group bits as read (4), write (2), execute (1). Each set of three bits becomes one octal digit, so 111101101 reads as 755 (rwxr-xr-x).

What if the bit count isn't a multiple of 3?

The input is padded with leading zeros so it forms complete 3-bit groups. For example, 11 becomes 011, which is octal 3.

Is octal still used today?

Yes. Although hexadecimal is more common, octal remains the standard for Unix and Linux file permissions and appears in some programming languages as octal literals.