Convert Octal to Binary
Need to convert an octal number to binary? Use our free calculator to instantly switch from base-8 to base-2. Just enter any octal digit (0 through 7) and let the tool handle the oct to bin conversion for you.
Octal to binary converter
Quick Reference
Octal to Binary Chart
Skip the calculator with our convenient octal to binary chart. Here is a handy reference showing the most common base-8 to base-2 conversions.
| Octal | Breakdown | Binary Result |
|---|---|---|
| 0 | 0 → 000 | 0 |
| 1 | 1 → 001 | 1 |
| 2 | 2 → 010 | 10 |
| 3 | 3 → 011 | 11 |
| 4 | 4 → 100 | 100 |
| 5 | 5 → 101 | 101 |
| 6 | 6 → 110 | 110 |
| 7 | 7 → 111 | 111 |
| 10 | 1 → 001, 0 → 000 | 1000 |
| 12 | 1 → 001, 2 → 010 | 1010 |
| 17 | 1 → 001, 7 → 111 | 1111 |
| 20 | 2 → 010, 0 → 000 | 10000 |
| 31 | 3 → 011, 1 → 001 | 11001 |
| 77 | 7 → 111, 7 → 111 | 111111 |
| 377 | 3 → 011, 7 → 111, 7 → 111 | 11111111 |
Step-by-Step
How to Convert Octal to Binary
Wondering how to convert an octal number to binary? The process is very straightforward once you understand how the two bases link together.
The Conversion Method
Octal is a base-8 number system containing digits 0 through 7. Binary is a base-2 system that runs entirely on 0s and 1s.
To manually perform a conversion from octal to binary, you just need to replace every single octal digit with its exact 3-bit binary equivalent. The mapping is simple: 0=000, 1=001, 2=010, 3=011, 4=100, 5=101, 6=110, 7=111.
How to Change Octal to Binary Manually
Write down the octal number
Take the exact octal value you want to convert. For instance, let's look at 17.
Match each digit to its 3-bit group
Look at the individual numbers. The 1 becomes 001 and the 7 becomes 111.
Combine and simplify
Put the bits together to form 001111, and then remove any leading zeros. You are left with 1111. So, 17₈ = 1111₂.
Octal vs Binary
Understanding Octal Binary Conversion
While both octal and binary are positional number systems used heavily in computer science, they serve slightly different roles. Converting octal to binary is popular because base-8 serves as a highly compact shorthand for base-2.
Instead of reading a long, confusing string of 1s and 0s, programmers can group bits into threes and read them as a shorter octal number. It saves space and reduces errors.
Because exactly three binary bits fit into a single octal digit, shifting between the two systems is much faster than dealing with standard decimals. You just need a reliable octal binary converter to double-check your work.
Worked Examples
Sample Conversions
Here is how you would convert octal to binary step by step for some of the most common values.
Converting 7 from octal to binary
The digit 7 translates to 111 in binary. So, 7₈ = 111₂.
Converting 10 from octal to binary
The 1 becomes 001 and the 0 becomes 000. Combine them to get 001000, then drop the leading zeros to get 1000.
Converting 12 from octal to binary
Change 1 to 001 and 2 to 010. You get 001010, which simplifies to 1010.
Converting 17 from octal to binary
The 1 maps to 001 and the 7 maps to 111. Smush them together for 001111, which equals 1111.
Converting 20 from octal to binary
Turn 2 into 010 and 0 into 000. Combine for 010000, leaving you with 10000.
Converting 31 from octal to binary
The 3 becomes 011 and the 1 becomes 001. Put together, it makes 011001, resulting in 11001.
Converting 77 from octal to binary
Both 7s turn into 111. Put them side-by-side to get 111111.
Converting 377 from octal to binary
Break it down: 3 is 011, 7 is 111, and the last 7 is 111. That results in 011111111, which trims down to 11111111.
FAQ
Frequently Asked Questions
Everything you need to know about changing base-8 values into binary.