Octal to Binary Converter

Every octal digit expands into exactly 3 bits — the fastest way to read chmod permissions bit by bit. Digit mapping and decimal value included.

Written by Alex Rivera · Last verified: 2026-09-17

Result
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How Octal to Binary Works

No arithmetic at all: each octal digit is a stand-in for one 3-bit triple. Swap digits for triples, concatenate, done.

755 becomes 111 101 101 — 7 is 111, 5 is 101, twice. The converter shows the triple view by default because that is how the bits are actually used, and a continuous view for when you need to paste the bits elsewhere. The reverse direction (Binary → Octal, same card above) groups bits into threes; our binary to octal page covers that direction in depth, including why grouping starts from the right.

Everything about input is forgiving: spaces, commas, 0o prefixes and mixed separators are cleaned and counted in the report, and digits 8 or 9 — which cannot exist in octal — are flagged with their exact position instead of being silently reinterpreted as decimal.

Reverse Speed-Reading: The 3-Bit Anchors

Three anchors rebuild the whole 0–7 table from memory: 0 = 000, 7 = 111, 4 = 100 — then count off the 4-2-1 weights.

The three positions inside a triple are worth 4, 2 and 1. With the anchors 0 = 000 (nothing on), 7 = 111 (everything on) and 4 = 100 (only the 4), every other digit is one step away: 5 is 4 + 1 (101), 6 is 4 + 2 (110), 3 is 2 + 1 (011). After a day of chmod commands you will read the table without thinking — and the same 4-2-1-8 family extends to hex nibbles on our hex to binary page.

Reading chmod Permissions, Digit by Digit

The most common real-world octal you will ever expand is a Unix permission. Three digits, three audiences — owner, group, others — and each digit is one rwx triple where the three bits are read, write, execute in that order:

  • 755 → 111 101 101 → owner rwx, group r-x, others r-x. The standard for scripts and directories everyone may enter but only the owner may change.
  • 644 → 110 100 100 → owner rw-, everyone else r--. The standard for web files: writable by you, readable by all.
  • 700 → 111 000 000 → owner rwx, nobody else anything. Private keys and personal directories.

One honest limit: octal permissions pack neatly into triples, but general bytes do not — a byte is 8 bits, not a multiple of 3, which is why hex dominates everywhere except this one Unix habit. If you ever need the numeric value rather than the bit pattern, the decimal readout under the result has it (755 octal = 493), and the binary to decimal converter goes further with signed options.

Common Mistakes

  • Mistake: reading octal digits as decimal. Octal 755 is not seven hundred fifty-five — it is 7×64 + 5×8 + 5 = 493 in decimal. Correction: check the base before trusting a number; the converter shows both.
  • Mistake: dropping leading zeros inside a triple. 5 is 101, not 11 — losing the leading zero shifts every later bit. Correction: each octal digit is exactly 3 bits, zeros included; 10 octal expands to 001 000.
  • Mistake: typing 8 or 9 into octal. Correction: those digits do not exist in base 8. If they appear, the number was decimal — the converter flags the exact position rather than converting the wrong thing.

Practice

1. Expand octal 700. 7 = 111, 0 = 000 twice — answer: 111 000 000, owner rwx and nothing for anyone else.

2. What is octal 17 in binary and decimal? 001 111 — decimal 15 (1×8 + 7).

3. Read the permission 640. 6 = 110 = rw-, 4 = 100 = r--, 0 = 000 = --- — owner rw-, group r--, others no access. Verify all three in the converter above.

Octal to Binary FAQ

How do I convert octal to binary?

Expand each octal digit into exactly 3 bits: 755 becomes 111 101 101, because 7 = 111 and 5 = 101. Read the triples off the 0–7 table and concatenate — the converter above does it instantly, grouped or continuous.

How do you read chmod 755 in binary?

One digit per permission triple: 7 = 111 = rwx (read, write, execute all on), 5 = 101 = r-x (read and execute, no write). So 755 is owner rwx, group r-x, others r-x — 111 101 101 in bits.

What is octal 10 in binary?

001 000 — grouped by digit — or 1000 as a continuous string, which is decimal 8. Octal 10 is not ten: base 8 rolls over after 7, so octal 10 means one eight plus zero ones.

Is 9 allowed in octal?

No. Octal digits run 0–7 only; 8 and 9 do not exist in base 8. A number containing them is decimal, not octal — this converter flags the exact position instead of converting something wrong.

What is the difference between octal and decimal?

Base 8 versus base 10: octal uses digits 0–7 with place values of 1, 8, 64… while decimal uses 0–9 with 1, 10, 100…. The same digits mean different values — octal 755 is decimal 493 — so check which base the number is written in.

Why does one octal digit equal exactly 3 bits?

Because 8 is 2^3. An octal digit holds a value from 0 to 7, and 3 bits hold exactly 000 to 111 — the same eight values. It is the same trick as hex (16 = 2^4), just one bit narrower per digit.