Binary to Octal Converter

One octal digit is exactly 3 bits — group from the right and read. Digit mapping and decimal value included, with forgiving input for messy pastes.

Written by Alex Rivera · Last verified: 2026-09-16

Result
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How Binary to Octal Works

Octal is binary in shorthand, three bits at a time: 8 is 2^3, so one octal digit abbreviates exactly three bits.

Group from the right — for 111101101:

  1. Split into triples from the right: 111 101 101.
  2. Read each group off the table: 7, 5, 5.
  3. Result: octal 755.

If the bit count is not a multiple of three, the converter left-pads and says so (11111111 becomes 011 111 111 → 377, decimal 255). No multiplication, no division — pure grouping, exactly like hex except the groups are one bit smaller. The reverse direction expands each digit back into its 3-bit triple.

The same 8-4-2-1 family of ideas powers the neighboring pages: hex to binary expands 4-bit nibbles, binary to hex compresses them, and binary to decimal handles the base where digits stop lining up with bits.

Three Bits or Four: Why Octal and Hex Both Exist

Octal and hex are the two branches of the same idea — pick a base that is a power of two, and each digit becomes a fixed-width group of bits. Hex packs 4 bits (16 = 2^4) and fits bytes perfectly: one byte is always two hex digits. Octal packs 3 bits (8 = 2^3), which divides bytes unevenly — that is the honest reason hex won for general byte work, and octal is rarer today.

Octal survives exactly where the world is three bits wide: Unix permissions. chmod 755 is octal, and each digit expands into one read/write/execute triple — 7 = 111 = rwx, 5 = 101 = r-x — so 755 is 111 101 101, owner rwx, everyone else r-x. The web's default file permission 644 is 110 100 100 = rw-r--r--. Paste either into the converter above (Octal → Binary direction) and the bits spell the permission string directly. Need to do arithmetic on the bits once you have them? The binary calculator adds, subtracts, multiplies and divides with the working shown.

OctalBinary (3 bits)As rwx
0000---
1001--x
2010-w-
3011-wx
4100r--
5101r-x
6110rw-
7111rwx

Common Mistakes

  • Mistake: grouping from the left. 111101101 grouped left-to-right reads 111-10-1101 and falls apart mid-number. Correction: always group from the right — the converter left-pads the short group for you.
  • Mistake: writing 8 or 9 in octal. Correction: octal digits run 0–7 only. If your “octal” number contains an 8 or 9, it was decimal — the converter flags the exact position instead of guessing.
  • Mistake: dropping leading zeros inside a group. 5 is 101, not 11. Correction: every octal digit is exactly 3 bits, zeros included — 17 expands to 001 111.

Practice

  1. Convert 11111111 to octal. Left-pad to 9 bits: 011 111 111 → 3, 7, 7 — answer: 377 (decimal 255).
  2. Expand octal 644 to binary. 6 = 110, 4 = 100, 4 = 100 — answer: 110 100 100, the rw-r--r-- permission.
  3. What is octal 17 in decimal? 1×8 + 7 = 15. Check all three in the converter above.

Binary to Octal FAQ

How do I convert binary to octal?

Group the bits into 3s starting from the right, then read each group as one octal digit: 111101101 splits into 111 101 101, which is 7-5-5 — octal 755. The converter above does it instantly and shows the group-by-group mapping.

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, where 16 = 2^4 makes one hex digit equal 4 bits.

What is the difference between octal and hex?

Both are shorthand for binary, just with different group sizes: octal packs 3 bits per digit (digits 0–7), hex packs 4 (0–F). Hex won for byte-oriented work because a byte is exactly two hex digits; octal survives where fields are naturally 3 bits wide, like Unix permissions.

Where is octal used today?

Mostly in Unix file permissions — chmod 755 is octal, and each digit expands to an rwx triple (7 = 111 = rwx). Beyond that, octal lives in legacy systems like PDP minicomputers and a few C-style escape sequences; for general byte work, hex has replaced it.

Is 8 a valid octal digit?

No. Octal digits run 0–7 only — 8 and 9 do not exist in base 8, just as there is no digit 2 in binary. If you see an 8 or 9, the number was decimal all along; this converter flags it with the exact position.

What does chmod 755 mean in binary?

Each octal digit is one 3-bit permission triple: 7 = 111 = rwx, 5 = 101 = r-x. So 755 expands to 111 101 101 — owner rwx, group r-x, others r-x. Read each bit as read / write / execute, on or off.