Binary to Octal Converter
3-Bit Grouping
Convert binary numbers to octal by grouping bits into 3-bit sets. See step-by-step how each group maps to an octal digit — commonly used in Unix file permissions and legacy systems.
5Number Systems
∞Precision
0msLatency
Interactive Tool Module
Visualizing 3-Bit Octal Boundaries
Octal numbers natively map perfectly to sets of 3 binary logic gates. Type binary below to see the parser pad the stream leftward with zeroes and precisely chunk elements into 3-bit arrays.
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FAQ
Frequently Asked Questions
How do you convert binary to octal?
Group the binary digits into sets of 3 starting from the right (pad with leading zeros if needed). Then convert each 3-bit group to its octal equivalent: 000=0, 001=1, 010=2, 011=3, 100=4, 101=5, 110=6, 111=7. Example: 110101₂ → 110 101 → 65₈.
Why does binary to octal use 3-bit groups?
Octal is base 8, and 8 = 2³. This means exactly 3 binary digits map to 1 octal digit. This direct power-of-2 relationship makes conversion a simple grouping-and-replacement process without any arithmetic.
What is the octal number system?
The octal number system is a base-8 numeral system using digits 0 through 7. Each position represents a power of 8. It was historically popular in computing because early computers used 12-bit, 24-bit, or 36-bit words that divide evenly into 3-bit (octal) groups.
Where is octal used today?
Octal is primarily used in Unix/Linux file permissions (e.g., chmod 755), some programming languages (C/C++ octal literals like 0755), and in aviation transponder codes (squawk codes). It was historically important in early computing but has largely been replaced by hexadecimal.
What is the octal equivalent of binary 111111?
Binary 111111₂ = octal 77₈. Grouping into 3-bit sets: 111 111 → 7 7. This is equivalent to decimal 63. In Unix permissions, 77₈ would represent read, write, and execute permissions.
How is octal different from hexadecimal?
Octal is base 8 (digits 0-7, groups of 3 bits), while hexadecimal is base 16 (digits 0-F, groups of 4 bits). Hexadecimal is more common in modern computing because it maps cleanly to bytes (2 hex digits = 1 byte). Octal was more popular with older computer architectures.