Convert octal numbers to binary by expanding each octal digit into its three-bit equivalent with a step-by-step breakdown.
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Number Systems
The octal to binary converter translates octal (base-8) numbers into their binary (base-2) equivalents. Enter an octal value and see the binary result with each octal digit expanded to its three-bit representation.
Each octal digit maps to exactly three binary digits. Replace each octal digit with its three-bit binary equivalent and concatenate the groups to form the full binary number.
For example, octal 75 becomes 111 101 in binary. The digit 7 maps to 111 and 5 maps to 101.
This conversion is particularly useful when analysing Unix file permissions at the bit level. Each permission digit (such as 7 for rwx) expands to three bits that represent read, write, and execute flags individually.
Frequently asked questions
Yes. Every octal digit maps to exactly three binary bits, including leading zeros (for example, octal 1 becomes 001).
No. Octal uses only digits 0 through 7. The digits 8 and 9 are invalid in base 8.
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