Binary to Octal: Group Bits in Threes (With Full Table)
Binary to octal is easy: group bits in threes and look up each trio. Get the full table, worked examples including fractions, and the octal-to-binary reverse.
Binary to Octal Conversion: Group Bits in Threes (With a Full Table)
Converting binary to octal is one of the easiest base conversions there is, because of a neat coincidence: 8 is exactly 2 cubed. That means every group of three binary digits maps to exactly one octal digit, with no arithmetic beyond a tiny lookup. The whole method is: split the binary number into groups of three bits starting from the right, then replace each group with its octal value. That is it — no long division, no remainders.
Here is the direct answer with an example. To convert binary 11010 to octal, group from the right into 011 and 010 (pad the left group with a leading zero), then translate: 011 is 3 and 010 is 2, giving octal 32. Below we explain why the grouping trick works, give you a complete 3-bit-to-octal lookup table, walk through several worked examples including fractional binary, and show how this fits with the other number-base tools on our binary hub.
Why You Can Group Bits in Threes
Number bases that are powers of each other convert cleanly. Octal is base 8, and 8 equals 2 to the power of 3. Because three binary digits can represent exactly the values 0 through 7 (which is 000 through 111), and octal digits are also exactly 0 through 7, each trio of bits corresponds to one and only one octal digit. There is no overlap and no leftover — a perfect one-to-one mapping. This is the same reason binary-to-hexadecimal works by grouping in fours: 16 is 2 to the power of 4.
The shortcut works for any base that is a power of 2: group bits in 2s for base 4, in 3s for base 8 (octal), and in 4s for base 16 (hexadecimal).
The 3-Bit to Octal Lookup Table
Memorize or bookmark this table and binary-to-octal conversion becomes instant. There are only eight rows.
| 3-bit binary | Octal digit | Decimal value |
|---|---|---|
| 000 | 0 | 0 |
| 001 | 1 | 1 |
| 010 | 2 | 2 |
| 011 | 3 | 3 |
| 100 | 4 | 4 |
| 101 | 5 | 5 |
| 110 | 6 | 6 |
| 111 | 7 | 7 |
Notice the table never needs the digits 8 or 9 — octal has no such digits. Three bits top out at 7, which is exactly the highest octal digit. That tidy fit is the whole reason the method is so painless.
Binary to Octal in Three Steps
- Group from the right. Starting at the rightmost bit, split the binary number into chunks of three.
- Pad the leftmost group. If the final left-hand group has only one or two bits, add leading zeros to make three.
- Translate each group. Replace every 3-bit group with its octal digit from the table above.
Always group from the right, never the left. Grouping from the wrong end shifts the place values and gives a wrong answer — this is the single most common mistake.
Worked Examples
Example 1: 101110 to octal
Group from the right: 101 and 110. Translate: 101 is 5, 110 is 6. The result is octal 56. Check it: binary 101110 is decimal 46, and octal 56 is (5 × 8) + 6 = 46. They match.
Example 2: 1101 to octal
Group from the right: 101 and 1. Pad the left group to 001. Translate: 001 is 1, 101 is 5. The result is octal 15. Verify: binary 1101 is 13 in decimal, and octal 15 is (1 × 8) + 5 = 13. Correct.
Example 3: 11111111 to octal
This is the 8-bit maximum (255 in decimal). Group from the right: 11, 111, 111. Pad the left group to 011. Translate: 011 is 3, 111 is 7, 111 is 7. The result is octal 377, the classic octal value every programmer recognizes for a full byte.
Example 4: fractional binary 10.101
For a binary point, group the integer part leftward from the point and the fractional part rightward from the point. Integer part 10 pads to 010 = 2. Fractional part 101 = 5. The result is octal 2.5. The grouping direction flips around the point, but the lookup table is the same.
Octal vs Hexadecimal: Why Both Exist
Octal and hexadecimal solve the same problem — long binary strings are hard for humans to read — but they group bits differently. Octal packs three bits per digit; hexadecimal packs four. Since modern computers organize memory in 8-bit bytes, hexadecimal won out for most uses because two hex digits map exactly to one byte (4 + 4 = 8 bits). Octal needs an awkward 2.67 digits per byte, which is why you rarely see it outside file permissions. Still, the underlying trick is identical, just with a different group size.
| Target base | Bits per group | Digit range | Common use |
|---|---|---|---|
| Base 4 | 2 | 0–3 | Teaching, rare |
| Octal (base 8) | 3 | 0–7 | Unix permissions |
| Hex (base 16) | 4 | 0–F | Memory, color codes |
If you can group binary in threes for octal, you already know how to group in fours for hexadecimal — the only new thing is that hex needs the letters A through F for the values 10 through 15.
The Slow Way: Converting Through Decimal
You can also convert binary to octal by first turning the binary number into decimal, then dividing repeatedly by 8 and collecting remainders. For binary 101110: it equals decimal 46; 46 divided by 8 is 5 remainder 6; 5 divided by 8 is 0 remainder 5; reading remainders bottom to top gives 56. Same answer as the grouping method, but with far more steps and more room for error. The grouping trick exists precisely so you never have to take this detour — it is here only to show why the shortcut gives the right result.
Going the Other Way: Octal to Binary
The reverse is just as easy — expand each octal digit into its 3-bit group. Octal 56 becomes 101 (for 5) and 110 (for 6), giving binary 101110. You can drop leading zeros on the very first group if you like. This symmetry is what makes power-of-two bases so convenient for programmers working close to the hardware.
Where Octal Shows Up
Octal is less common than hexadecimal today, but it still appears in Unix and Linux file permissions (the familiar chmod 755 uses octal), in some older computing systems, and in certain programming literals. Knowing the binary-to-octal grouping trick means you can read a permission like 755 and immediately see its bit pattern: 7 is 111 (read, write, execute), 5 is 101 (read, execute). That direct mapping is genuinely useful day to day.
We do not currently offer a dedicated octal converter, but you can explore the related conversions and see how characters become bits with the Text To Binary tool, and find every base-conversion guide on the Binary Converter hub.
Common Mistakes to Avoid
- Grouping from the left: always start chunking from the right so place values stay correct.
- Forgetting to pad: the leftmost group must be padded with leading zeros to a full three bits.
- Using digits 8 or 9: octal only uses 0 through 7; if you ever write an 8 or 9, you have made an error.
- Mixing up the point rule: for fractions, group rightward from the binary point, not from the far right of the number.
Frequently Asked Questions
How do you convert binary to octal?
Group the binary digits into sets of three starting from the right, pad the leftmost group with leading zeros if needed, then replace each three-bit group with its matching octal digit using the lookup table. No long division is required.
Why do you group binary in threes for octal?
Because octal is base 8 and 8 equals 2 to the power of 3. Three binary digits represent exactly the values 0 through 7, which are precisely the octal digits, so each trio maps cleanly to one octal digit.
What is binary 111 in octal?
Binary 111 is octal 7. Three ones equal four plus two plus one, which is seven, and seven is the largest single octal digit.
Do you group from the left or the right?
Always group from the right. Starting from the right keeps the place values aligned. If the leftmost group ends up with fewer than three bits, pad it with leading zeros.
How do you convert octal back to binary?
Replace each octal digit with its three-bit binary equivalent. For example, octal 56 becomes 101 and 110, giving binary 101110. You can drop leading zeros on the first group.
Does octal use the digits 8 and 9?
No. Octal is base 8 and uses only the digits 0 through 7. If you ever end up with an 8 or 9 in an octal number, a mistake has been made in the conversion.
Where is octal still used?
Octal appears most often in Unix and Linux file permissions, such as chmod 755, and in some older systems and programming literals. The binary grouping trick makes those permission codes easy to read as bit patterns.
Curious how text turns into the bits you are grouping? Try the Text To Binary tool, then practice the binary-to-octal grouping on the output. For all base-conversion guides, visit the Binary Converter hub, or read our companion piece on how binary addition works.