How to Convert Binary to Octal (Step by Step, With Examples)
Converting binary to octal sounds technical, but it hides one of the nicest shortcuts in all of computing: every octal digit is exactly three binary digits. Once you know that, you can convert any binary number in seconds, with no calculator and no long division. This guide shows the method step by step, with worked examples you can check yourself.
The One Idea You Need: Groups of Three
Binary uses base 2 (digits 0 and 1). Octal uses base 8 (digits 0 to 7). Because 8 is 2 × 2 × 2 (2 cubed), each octal digit matches exactly one group of three binary bits. That gives us this complete conversion table — it is the only table you will ever need for this job:
| Binary | Octal |
|---|---|
| 000 | 0 |
| 001 | 1 |
| 010 | 2 |
| 011 | 3 |
| 100 | 4 |
| 101 | 5 |
| 110 | 6 |
| 111 | 7 |
The 3-Step Method
Step 1: Starting from the RIGHT side of the binary number, split it into groups of three bits. Step 2: If the last group on the left has fewer than three bits, add zeros at the front until it has three. Step 3: Replace each group with its octal digit from the table, and read the digits in order. That is the answer.
Worked Example 1: 101011
Split from the right: 101 | 011. Both groups already have three bits. From the table, 101 = 5 and 011 = 3. So 101011 in binary = 53 in octal. Quick check in decimal: 101011 is 43, and 53 in octal is (5 × 8) + 3 = 43. It matches.
Worked Example 2: 11010110
Split from the right: 110 | 101 | 10. The last group has only two bits, so pad it with a zero: 010. Now convert each group: 110 = 6, 101 = 5, 010 = 2 — wait, keep the order left to right: 011? No: after padding, the groups are 011? Let us redo carefully. Writing the number out: 1-1-0-1-0-1-1-0. Grouping from the right in threes gives: 11 | 010 | 110. Pad the left group to 011. Now convert: 011 = 3, 010 = 2, 110 = 6. So 11010110 in binary = 326 in octal. Check: 11010110 is 214 in decimal, and 326 octal is (3 × 64) + (2 × 8) + 6 = 192 + 16 + 6 = 214. Correct.
Worked Example 3: 11111111
Group from the right: 11 | 111 | 111, pad the first group to 011. Convert: 011 = 3, 111 = 7, 111 = 7. So 11111111 = 377 in octal — this is the famous 255 in decimal, the largest value in one byte.
Going Backwards: Octal to Binary
The reverse trip is just as easy: turn every octal digit into its three-bit binary group, then join them. Example: octal 47 becomes 100 | 111, so 47 in octal = 100111 in binary. Check in decimal if you like: 100111 is 39, and 47 octal is (4 × 8) + 7 = 39. Perfect.
Common Mistakes to Avoid
Grouping from the left. Always group from the right. Grouping from the left gives a wrong first group and a wrong answer. Forgetting to pad. A short left group needs leading zeros — 10 by itself is 2, but padded to 010 it is still 2; padding never changes the value, it just completes the group. Reading the digits backwards. After converting, the octal digits stay in the same left-to-right order as the groups. Mixing up the table. Remember 101 = 5 and 110 = 6; these two are the ones students swap most.
Why Octal Exists at All
Early computers grouped bits in threes, so octal became a compact way for programmers to read long binary strings: a 12-bit binary number becomes just 4 octal digits. You still meet octal today in Linux and Unix file permissions, where a setting like 755 is really three groups of binary read/write/execute bits. If you enjoy number systems, our guide on How to Convert Binary to Hex shows the sister method (groups of four), and How to Convert Hex to Binary covers the trip back.
Frequently Asked Questions
How do I convert binary to octal quickly?
Group the bits in threes from the right, pad the last group with zeros, and swap each group for its octal digit using the 000–111 table above.
What is 1010 in octal?
Group: 1 | 010, pad to 001 | 010, convert: 1 and 2. So 1010 in binary = 12 in octal.
Is there a binary to octal converter tool?
Our free Binary Translator converts between text and binary instantly, and it is the fastest way to check your homework answers after you have done the method by hand.
Practice with three numbers of your own, check them with the tool, and this conversion will never slow you down again.