Convert Octal to Binary

Because 8 = 2³. Each octal digit (0-7) covers exactly 3 bits of information, so you can replace each digit with its 3-bit binary code without any cross-digit math: 0 = 000, 1 = 001, 2 = 010, …, 7 = 111. This is why historic computer systems used octal – humans could read register values as octal triples and “see” the binary without decoding. Hex (base 16 = 2⁴) won out because byte-aligned hex maps to nibbles cleanly.

For single-octal input, a grid below the main table shows each octal digit alongside its 3-bit binary mapping (e.g., for 755: 7 → 111, 5 → 101, 5 → 101). Educational – you can see exactly how the conversion happens digit by digit, not just trust the final result.

Those widths match standard integer types: byte (uint8), word (uint16), int (uint32), long (uint64). When you’re sizing memory or designing a register, you want to see “is this value 8-bit or do I need 16?” Bit-width padding shows the value as it would actually appear in that register. The tool warns if the value needs more bits than the chosen cap.

3-digit octals like 755 and 4-digit like 04755 are commonly Unix file permission modes. The decoder turns them into the rwxr-xr-x form ls -l shows. 755 = owner read+write+execute, group read+execute, other read+execute. 04755 = same with setuid bit on (the x in owner column becomes s). Saves you from doing the bit math in your head.

Just visual. Underlying bits are identical. Grouping every 3 bits makes it line up with the octal source (each group = one octal digit). Grouping every 4 bits aligns with hex digits. Grouping every 8 bits aligns with bytes. Pick whichever your downstream tool wants – Verilog testbenches usually want bytes; chmod docs use 3-bit groups; programmer logs use nibbles.

Cross-reference. If you don’t trust the binary, you can verify against decimal (the BigInt-exact base-10 value) or hex (compact representation). For 755 oct = 493 dec = 0x1ED – three different ways to write the same value. Useful when you’re comparing the converter’s output against a calculator or another tool.

Unlimited (BigInt). A 100-octal-digit input produces a 300-bit binary string. The result table cell scrolls horizontally for very wide values. Practical use is usually under 30 digits.

That JavaScript approach loses precision above 2^53 (16-17 decimal digits). This tool uses BigInt with the 0o prefix and toString(2) on BigInt, which handles arbitrary-size integers exactly. So parseInt('77777777777777777777', 8) in regular JS gives the wrong answer; this tool gives the exact 60-bit binary.

No. All BigInt arithmetic, per-digit lookups, and permission decoding happen in your browser. Open DevTools → Network and confirm zero requests fire after the page loads. Safe for proprietary file-mode dumps or competitive-programming inputs.

Yes. Total bundle is under 22 KB. Once loaded, disconnect and keep converting – useful for sysadmin scripting on air-gapped boxes or embedded firmware work.