Octal to Binary Converter — Free, Instant, No Signup

To convert octal to binary, select Octal (Base 8) as the input in the free converter, type your octal number, and the binary result appears immediately. Each octal digit maps directly to exactly 3 binary bits — the same clean relationship that hex has with 4-bit groups, but with 3-bit groups instead. This makes octal-to-binary conversion fast and mechanical once you know the 8 digit patterns.

The 3-Bit Grouping Rule for Octal to Binary

Every octal digit has a fixed 3-bit binary equivalent. Because octal is base 8 and 2^3 = 8, each digit spans exactly one 3-bit group with no overlap or remainder.

Octal Digit	Binary	Decimal
0	000	0
1	001	1
2	010	2
3	011	3
4	100	4
5	101	5
6	110	6
7	111	7

To convert octal to binary manually: replace each octal digit with its 3-bit binary group. Octal 57 becomes 101 111 (5=101, 7=111) → binary 101111.

How to Use the Converter

1. Open the Number Base Converter
2. Select Octal (Base 8) from the "From Base" dropdown
3. Type your octal value — valid digits are 0 through 7 only
4. The Binary output appears instantly in the results panel
5. You also see Decimal and Hex equivalents at the same time
6. Click Copy next to Binary to copy the result

For binary to octal in reverse: select Binary (Base 2), type your binary digits, and read the Octal output.

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Binary to Octal — The Reverse Conversion

Converting binary to octal manually uses the same 3-bit grouping in reverse. Group binary digits into sets of three from right to left, then replace each group with the octal digit:

Example: Binary 110101011 to octal

• Group from right: 110 101 011
• 011 = 3, 101 = 5, 110 = 6
• Result: 653 (read left to right)

If the leftmost group has fewer than 3 digits, pad with leading zeros. Binary 10111 → 010 111 → 2, 7 → octal 27.

Octal to Binary Conversion Examples

Octal	Binary	Decimal
10	001 000	8
17	001 111	15
64	110 100	52
100	001 000 000	64
377	011 111 111	255
755	111 101 101	493
644	110 100 100	420

The last two rows — 755 and 644 — are the most common Unix file permission values. Seeing their binary expansion makes the permission logic clear: each 3-bit group represents read (1)/write (1)/execute (1) for owner, group, and others respectively.

Octal vs Hexadecimal — Why Hex Won

Octal and hex both exist as compact human-readable representations of binary. Octal uses 3-bit groups (one digit per 3 bits), hex uses 4-bit groups (one digit per 4 bits). The reason hex dominates today is byte alignment: one byte is 8 bits, which divides cleanly into two 4-bit hex digits. Octal requires 2.67 digits per byte — it does not align with the 8-bit byte standard.

Early 12-bit and 24-bit computing architectures did favor octal, since those bit widths divided by 3. Once 8-bit bytes became the standard, hex was more natural. Octal survives today primarily in Unix permissions and some academic computer science curricula.

Frequently Asked Questions

What octal digits are valid?

Octal uses only digits 0 through 7. Digits 8 and 9 do not exist in octal. If you enter an 8 or 9 when Octal is selected as the input base, the converter will show an error.

What is octal 755 in binary?

Octal 755 = binary 111 101 101. In Unix file permissions, this means owner has full permissions (rwx = 111), group can read and execute (r-x = 101), others can read and execute (r-x = 101).

Can I convert octal directly to hex without going through decimal?

Not directly with a simple pattern — the 3-bit (octal) and 4-bit (hex) groupings do not align neatly. The easiest method is to convert octal to binary first (using the 3-bit rule), then convert binary to hex (using the 4-bit rule). The converter does this automatically in one step.