446
Binary → octal
Type a binary number — 0s and 1s only, up to 512 bits — and get the octal value, the decimal value, and the 3-bit triad grouping that makes the conversion click.
CONVERTER · MATH · NUMBER SYSTEMS
Binary to Octal Converter — Two-Way With Worked Steps
101101 in binary is 0o55 in octal, which is 45 in decimal — pad the bits to a multiple of 3 (101 101) and read each triad as one octal digit. Convert either direction below: binary → octal with the triad grouping shown, or octal → binary, each with the decimal value alongside.
447
Octal → binary
Type an octal value — digits 0–7 only, with or without the 0o prefix, up to 512 digits — and get the binary expansion plus the decimal value.
The 60-second rule
Pad the binary to a multiple of 3 bits, split into triads, and read each triad as one octal digit (000=0, 001=1, 010=2, 011=3, 100=4, 101=5, 110=6, 111=7). For 101101: it’s already 6 bits → 101 | 101 → 5 | 5 → 0o55. Check: 5×8 + 5 = 45. Going the other way, expand each octal digit to 3 bits: 0o777 → 111 111 111 = 511.
The worked example, line by line
Setup: convert binary 101101 to octal (and decimal).
Pad to threes. 101101 is already 6 bits — two complete triads, no padding needed: 101 101. Leading zeros change nothing; they only complete the last triad when the bit count isn’t a multiple of 3.
Read each triad. 101 = 5, 101 = 5. So 0o55.
The decimal check. 5×8 + 5 = 40 + 5 = 45 — or from the bits directly: 32 + 8 + 4 + 1 = 45.
Branch — octal 777 to binary: 7 = 111, so 0o777 → 111 111 111 = 7×64 + 7×8 + 7 = 511 — every 1 in the input means every triad is maxed out.
Branch — binary 11011: 5 bits — pad to 6: 011 011 → 3 | 3 = 0o33 = 27 in decimal.
Branch — invalid input: “102” is rejected — “2” is not a binary digit. “89” is rejected as octal — “8” is not an octal digit. The converter names the offending character so you can fix it.
Output · formula · meaning
| Output | Formula | What it means |
|---|---|---|
| Octal value | each 3-bit triad → one octal digit | 0o55 at the defaults — the compact form of the bits. |
| Decimal value | ∑ digit × 8position | 45 at the defaults — the everyday number. |
| Triad grouping | pad to a multiple of 3, split in threes | 101 101 at the defaults — the visual proof of the conversion. |
| Binary expansion | each octal digit → 3 bits | 111111111 for 0o777 — octal is just shorthand for binary. |
Who uses this
- The CS student: the assignment says “convert 101101 to octal” — types it in, gets 0o55, and the triad grouping 101 101 shows why, not just the answer.
- The Linux admin setting permissions: knows chmod 755 means something — converts 0o755 → 111 101 101 and sees exactly which read/write/execute bits are on.
- The retro-computing fan: old DEC and PDP documentation is full of octal — expands 0o777 to 111 111 111 to read the machine’s native language.
- The exam crammer: the test asks binary → octal without a calculator — memorizes the 8-row triad table (000=0 through 111=7) and converts by sight.
Accuracy & limitations
The math is exact: conversion runs on arbitrary-precision integers (BigInt), correct up to the 512-digit cap — there is no floating-point anywhere, so even 2512−1 converts perfectly. Octal output uses the 0o prefix (0o55); input accepts it but doesn’t require it. Leading zeros are preserved in the triad display (011 011) but dropped from the value itself (0o33) — same number, cleaner notation. The converter handles unsigned integers only: no negatives, no fractions — a minus sign is rejected as an invalid character.
Cite this calculatorBright Side Kit. “Binary to Octal.” brightoolbox.com, 2026.
Bright Side Kit. "Binary to Octal." https://brightoolbox.com/binary-to-octal/ Accessed October 23, 2026.Frequently asked questions
Why do we group binary in 3s to get octal?
Because 23 = 8: one 3-bit group (a triad) holds exactly the values 0–7, which is exactly one octal digit’s range. That makes triads the natural bridge — no arithmetic needed, just an 8-row lookup: 000=0, 001=1, 010=2, 011=3, 100=4, 101=5, 110=6, 111=7.
What about leading zeros — do they change the answer?
No. Padding 11011 to 011011 (triads 011 011) gives 0o33 either way — the leading zero only completes the last triad. The converter keeps it in the grouping display (011 011) so the visual proof is complete, but drops it from the value (0o33, not 0o033).
Binary→octal vs binary→hex — what’s the difference?
Only the group size. Octal groups by 3 bits (2³ = 8 values per digit); hex groups by 4 bits (2⁴ = 16 values per digit). Hex is more compact — 101101 is 0o55 (2 digits) vs 0x2D (2 digits here, but 3 triads vs 2 nibbles on longer values). Hex won the computing wars, but octal lives on in Unix file permissions (chmod 755).
How long can my input be?
512 digits — 512 binary bits or 512 octal digits. The math uses arbitrary-precision integers (BigInt), so there’s no rounding or overflow — the cap is just a sanity limit. Longer input is rejected with the digit count, not silently truncated.
Where does octal still show up?
Unix/Linux file permissions — chmod 755 is three octal digits (owner/group/other), each digit being 3 permission bits: 7 = rwx, 5 = r-x. You’ll also find octal in legacy mainframe and DEC documentation, some embedded systems, and UTF-8 escape sequences like \101 (= “A”).