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Convert octal numbers to binary. Useful for Unix file permissions and understanding how octal notation maps to binary bits.

What is the Octal to Binary Converter?

This tool converts octal numbers (base-8) to binary numbers (base-2). Each octal digit maps directly to exactly 3 binary bits.

Key relationship: each octal digit expands to exactly 3 binary bits, because 8 = 2³.

Why Convert Octal to Binary?

Understanding Permissions

chmod values like 755 and 644 become clearer in binary.

Legacy Systems

Some older systems still rely on octal notation.

Learning Number Systems

Octal is a stepping stone between binary and decimal.

The Conversion Method

Each octal digit converts to exactly 3 binary digits, so replace each digit with its 3-bit group.

Example: 755 = 111 101 101 = 111101101.

How to Use

1

Enter the Octal Number

Type using the digits 0–7 only.

2

View the Binary Result

Each octal digit becomes 3 bits, and the conversion is instant.

3

Copy the Result

Copy the binary value to use in your work.

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

Unix Permission Example

OctalBinaryPermission
7111read + write + execute
5101read + execute
4100read only

Frequently Asked Questions

Why does each octal digit become 3 bits?

Because 8 = 2³. A single octal digit can hold 8 values (0–7), exactly the range of 3 binary bits.

Can I enter 8 or 9?

No. Octal is base-8 and only allows the digits 0 through 7. The digits 8 and 9 are not valid.

How does this clarify chmod?

Expanding 755 to 111 101 101 shows the three permission triplets directly: rwx for owner, r-x for group, r-x for others.

Is the conversion always exact?

Yes. Each octal digit always produces exactly 3 binary bits, so the mapping is predictable with no rounding or ambiguity.

01234567
0o
01
0b

Octal to Binary

0 = 000
1 = 001
2 = 010
3 = 011
4 = 100
5 = 101
6 = 110
7 = 111

Octal (Base-8)

Used in Unix file permissions. Digits 0-7, where each represents 3 binary bits.

Binary (Base-2)

The fundamental language of computers. Each bit is 0 or 1.

Enter octal digits (0-7 only)
12 in octal = 001010 in binary
Each octal digit = 3 binary bits
Useful for Unix permission conversion
Want to learn more? Read documentation →
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