Binary To Octal Converter
Enter the binary value to convert to octal or Octal to Binary.
Binary:
Binary (Base-2) numbers can be efficiently converted to octal by grouping bits in sets of 3.
Octal:
Octal (Base-8) provides a more compact representation than binary while maintaining easy conversion.
How to Convert Binary to Octal — Formula:
Group binary digits into sets of 3 from right: 000=0, 001=1, 010=2, 011=3, 100=4, 101=5, 110=6, 111=7.
Example: Binary 11111111 → 011 111 111 → 3 7 7 → Octal 377.
Technical Details:
This is a direct grouping conversion — no arithmetic needed. Pad with leading zeros to complete the leftmost group. 3 binary digits = 1 octal digit.
Binary To Octal Converter:
Convert binary to octal by grouping every 3 binary digits into one octal digit.
Binary ↔ Hex ↔ Octal: Grouping Relationship
Binary → Hex (group by 4 bits):
Binary → Octal (group by 3 bits):
Frequently Asked Questions
How do I convert Binary to Octal?
Group binary digits into sets of 3 from right: 000=0, 001=1, 010=2, 011=3, 100=4, 101=5, 110=6, 111=7.
What is the Binary number system?
Binary (Base-2) numbers can be efficiently converted to octal by grouping bits in sets of 3.
What is the Octal number system?
Octal (Base-8) provides a more compact representation than binary while maintaining easy conversion.
Where is Binary to Octal conversion used?
This is a direct grouping conversion — no arithmetic needed. Pad with leading zeros to complete the leftmost group. 3 binary digits = 1 octal digit.
Can I convert large binary numbers?
Yes. This converter handles numbers of any practical size. For very large numbers, the conversion is performed using arbitrary-precision arithmetic to ensure accuracy.
How to Convert Binary to Octal (Base-2 to Base-8)
Binary-to-octal conversion is used in Unix file permissions, older computer architectures, and digital electronics. Since 8 = 2³, every octal digit maps to exactly 3 binary digits. This makes the conversion a straightforward grouping exercise — no arithmetic needed beyond recognizing 3-bit patterns.
- Group the binary number into sets of 3 bits, starting from the right.
- Pad the leftmost group with leading zeros if it has fewer than 3 bits.
- Convert each 3-bit group to its octal digit (0-7).
- Write the octal digits together to form the final number.
- Example: 110101₂ → 110 101 → 6 5 → 65₈.
Binary to Octal: Key Values
Important binary-to-octal conversions used in permissions and systems programming:
| Input | Output |
|---|---|
| 000 | 0 |
| 001 | 1 |
| 010 | 2 |
| 011 | 3 |
| 100 | 4 |
| 101 | 5 |
| 110 | 6 |
| 111 | 7 |
| 111 101 101 | 755 |
| 110 100 100 | 644 |
| 111 111 111 | 777 |
| 000 000 000 | 000 |
Solved Examples: Binary to Octal
Question 1: Convert binary 11010110 to octal.
Solution:
Group into 3 bits from the right: 011 010 110
Convert each group: 011=3, 010=2, 110=6
Result: 326₈
Answer: 11010110₂ = 326₈. Verify: 3×64 + 2×8 + 6 = 192 + 16 + 6 = 214₁₀.
Question 2: A Unix permission is rwxr-xr-- in binary. Convert to octal.
Solution:
rwx = 111, r-x = 101, r-- = 100
Binary: 111 101 100
Convert each group: 111=7, 101=5, 100=4
Answer: 111101100₂ = 754₈ — this is chmod 754 (owner: full, group: read+execute, others: read only).
Question 3: Convert the 12-bit binary number 101011110001 to octal.
Solution:
Group from right: 101 011 110 001
Convert: 101=5, 011=3, 110=6, 001=1
Result: 5361₈
Answer: 101011110001₂ = 5361₈. Verify: 5×512 + 3×64 + 6×8 + 1 = 2560 + 192 + 48 + 1 = 2801₁₀.
Question 4: Convert binary 1111111 (7 bits) to octal.
Solution:
Pad to 9 bits: 001 111 111
Convert: 001=1, 111=7, 111=7
Result: 177₈
Answer: 1111111₂ = 177₈ = 127₁₀ — the maximum value of a signed 7-bit integer.
Practice: Binary to Octal
Try solving these on your own to test your understanding:
- Convert 101010 to octal. (Answer: 52)
- Convert 11111111 to octal. (Answer: 377)
- Convert 100000000 to octal. (Answer: 400)
- Convert 110110110 to octal. (Answer: 666)
- Convert 1010101010 to octal. (Answer: 1252)
- Convert 111000 to octal. (Answer: 70)
Why Unix Permissions Use Octal
Unix file permissions have exactly 9 bits: 3 for owner (rwx), 3 for group, and 3 for others. Since each 3-bit group maps perfectly to one octal digit, octal provides the most compact human-readable notation. chmod 755 instantly tells a sysadmin that the owner has full access (7=111=rwx), while group and others have read+execute (5=101=r-x). Using decimal (493) or hex (0x1ED) would obscure this clean structure.
Octal in Legacy Systems and C Programming
In C and C++, numeric literals prefixed with 0 are octal: 010 means 8 (not 10!). This is a common source of bugs. JavaScript's strict mode banned octal literals for this reason. However, octal escapes in strings (\012 for newline) remain in many languages. PDP-11 and other early computers used 18-bit words that split cleanly into six octal digits, making octal the natural base for those systems.
Key Takeaways
- Group binary digits into sets of 3 from the right, then convert each group (0-7).
- Pad the leftmost group with zeros if fewer than 3 bits.
- Unix permissions map perfectly: each rwx triplet = one octal digit.
- chmod 755 = 111 101 101 in binary (rwxr-xr-x).
- In C/C++, a leading 0 makes a number octal — a common bug source.
- Octal was historically important for 12-bit, 18-bit, and 36-bit word architectures.