How does octal convert to binary?

Because 8 equals 2 cubed, each octal digit corresponds to exactly three binary digits. You expand every octal digit into its three-bit pattern and concatenate the groups.

What three bits does each octal digit produce?

The mapping is fixed: 0 is 000, 1 is 001, up through 7 which is 111. Each of the eight octal digits has a unique three-bit code.

Why does the tool show two binary views?

The trimmed view drops leading zeros to give the number's true value, while the triplet-aligned view keeps each group of three bits so the octal-to-binary correspondence is visible.

Why is octal convenient for permission bits?

Unix permissions come in triplets of read, write and execute for owner, group and others. Each triplet is three bits, which is exactly one octal digit, so a mode like 755 maps cleanly to nine permission bits.

Can it handle long octal numbers?

Yes. Each digit expands independently, and the decimal cross-check uses exact big-integer arithmetic, so long inputs convert without rounding error.

Octal to Binary Converter

Converting octal to binary is a direct expansion that is especially useful when reasoning about Unix file permissions or any system that groups bits in threes. This converter turns any base-8 number into its full binary bit string.

How it works

Octal is base 8 and binary is base 2, and 8 equals 2 cubed. That power-of-two relationship means each octal digit maps to a unique group of exactly three binary digits, called a triplet. The conversion is a per-digit lookup: 7 becomes 111, 5 becomes 101, 0 becomes 000, and the triplets are joined in order.

No decimal intermediate is needed. The tool reads each octal character, expands it to its three-bit code, and concatenates. It then shows a trimmed value (leading zeros removed) and a triplet-aligned view that keeps each group intact.

Example

Convert the Unix permission 755. The digit 7 expands to 111, the first 5 to 101, and the second 5 to 101. Concatenated, that is 111101101, which equals 493 in decimal. Read as permission bits, the owner has all three (rwx) while group and others have read and execute.

Tips and notes

The triplet-aligned view makes octal-to-binary conversion transparent and is ideal for teaching the relationship between bases. Spaces, underscores and a leading 0o are accepted and ignored. All processing happens locally in your browser, so nothing you enter is transmitted anywhere.