Convert between binary and octal number systems—each octal digit represents exactly 3 binary bits.
2026-03-28T00:00:00Z
Binary to octal conversion translates numbers between base-2 (binary) and base-8 (octal) systems. Octal is useful because each octal digit represents exactly 3 binary digits (bits), making it a more compact representation than binary while still being easy to convert mentally.
The relationship is straightforward: binary groups of 3 bits map directly to single octal digits. For example, 111₂ = 7₈, 101₂ = 5₈, 000₂ = 0₈. This direct mapping makes conversion simple—group binary digits into sets of three and replace each group with its corresponding octal digit (0-7).
While octal is less common than hexadecimal today, it still appears in Unix/Linux file permissions (chmod 755), some assembly languages, legacy systems, and certain technical contexts. Understanding binary-octal conversion helps when working with systems that use base-8 notation and provides insight into how different number bases relate to binary.
Convert 11101001₂ to Octal:
Octal provides a middle ground: more compact than binary but simpler than hex. Each digit = 3 bits (vs 4 for hex), making some calculations easier. It's still used in Unix permissions and legacy systems.
In Unix/Linux, 755 is octal notation for file permissions. Each digit represents permissions for owner, group, and others. 7 = 111₂ (read+write+execute), 5 = 101₂ (read+execute).
Because 8 (octal base) = 2³ (binary). Three binary bits can represent 8 different values (000-111), which perfectly matches the 8 octal digits (0-7).
Less common than hex, but still used in: Unix file permissions, some assembly languages, embedded systems documentation, and as a teaching tool for understanding number bases and bit groupings.
Add leading zeros to the left until you have a multiple of 3 bits. For example, 11 becomes 011, which converts to 3 in octal. Trailing zeros after grouping don't affect the value.
Replace each octal digit with its 3-bit binary equivalent. For 755: 7→111, 5→101, 5→101. Result: 111101101, which shows exactly which permission bits are set.
Not directly—bits don't align. Convert octal→binary (3 bits per digit), then binary→hex (4 bits per digit). Or go through decimal: octal→decimal→hex.
Understanding octal reinforces number base concepts, helps with Unix permissions, and shows why bit-grouping matters. It's also historically significant in computing.
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