Octal Explained: Convert Octal to Binary and Decimal

Octal is base eight and uses digits 0 through 7. Each digit corresponds to three binary bits, which makes it useful for Unix permissions such as chmod 755. This guide explains that mapping and shows how to convert between octal, binary, and decimal.

What Octal Is

Place values are powers of 8: …, 512, 64, 8, 1. The octal number 17 means 1×8 + 7 = 15 decimal. Write a leading 0 in some C dialects (0755), or use 0o755 in Python and modern JavaScript.

Why bother when hex exists? Because 8 = 2³, so one octal digit is exactly three bits. Hex wins for general byte work (four bits per digit). Octal wins when your natural group size is three bits, which is exactly the Unix rwx triplet.

Octal Digits to Binary (Three-Bit Groups)

Same idea as hex nibbles, but triples instead of fours.

Memorize 4=read, 2=write, 1=execute. Add them: 4+1=5 (read+execute), 4+2+1=7 (all). That arithmetic is why people say “chmod 644” instead of listing flags every time.

Unix Permissions: Owner, Group, Others

A common mode has three octal digits. Left to right: owner, group, others. Sometimes a fourth digit appears for setuid/setgid/sticky bits; ignore that until the basic three make sense.

In binary that is nine bits:

Mode 644 is the usual “text file” default: owner read/write, everyone else read-only → 110 100 100. Mode 600 keeps a private key readable only by you.

Convert Octal to Decimal

Expand by place value. Example: 755 octal.

You rarely need 493 when talking to chmod, but APIs sometimes want a decimal integer. Same bits either way.

Convert Decimal to Octal

Divide by 8, record remainders, read remainders bottom-up. Example: 493 → octal.

Or convert decimal → binary first, then group bits in threes from the right. 493 in binary is 1 1110 1101; pad and group as 111 101 101 → 7 5 5. Use whichever path you make fewer mistakes on. The binary converter checks both.

Octal ↔ Binary Directly

Binary to octal: pad on the left to a multiple of 3, split, map each triple with the table.

Octal to binary: expand each digit to three bits.

Octal vs Hex in Daily Work

Prefer hex for memory addresses, color codes, and file dumps. Prefer octal for Unix modes and a few legacy machine formats (some PDFs and old DEC documentation still show octal). Mixing them without a prefix is how bugs sneak into config files.

If you are already flipping hex and binary, the article on hex vs binary pairs well with this one. For dump reading, open the hex viewer rather than forcing octal onto byte streams.

Worked Permission Scenarios

The sticky bit on /tmp (often shown as 1777) lets everyone create files while blocking deletion of other users' files. That fourth digit is still octal; it just flags special mode bits beyond rwx.

Language Gotchas

In C, an integer literal starting with 0 is octal. So 010 is eight, not ten. That has ruined more than one “why is my loop short?” debugging session.

JavaScript used to treat leading-zero decimals as octal in non-strict mode. Strict mode and modern style prefer 0o10 for octal and plain 10 for decimal. When encoding text, octal is unrelated; use text to binary or the ASCII table instead.

FAQ

Practice and Convert

Choose a permission mode such as 755, 644, or 600. Write its nine permission bits, convert the result to decimal, then back to octal. The three representations should describe the same value.

Run the numbers through the Binary Converter on BinaryTranslator.org. Related reading: decimal to binary, how to read binary, and binary to hex for the four-bit sibling of this three-bit trick.