Octal To Binary Converter
Enter the octal value to convert to binary or Binary to Octal.
Octal:
Octal (Base-8) digits each correspond to exactly 3 binary digits.
Binary:
Binary (Base-2) is the fundamental representation used by all digital systems.
How to Convert Octal to Binary — Formula:
Replace each octal digit with its 3-bit binary equivalent: 0=000, 1=001, 2=010, 3=011, 4=100, 5=101, 6=110, 7=111.
Example: Octal 377 → 3=011, 7=111, 7=111 → Binary 011111111 = 11111111.
Technical Details:
Direct digit-by-digit expansion. Used in: analyzing Unix permissions (755 → 111 101 101 = rwxr-xr-x), legacy computing systems, and PDP-11 assembly.
Octal To Binary Converter:
Convert octal to binary by expanding each octal digit into 3 binary digits.
Binary ↔ Hex ↔ Octal: Grouping Relationship
Binary → Hex (group by 4 bits):
Binary → Octal (group by 3 bits):
Frequently Asked Questions
How do I convert Octal to Binary?
Replace each octal digit with its 3-bit binary equivalent: 0=000, 1=001, 2=010, 3=011, 4=100, 5=101, 6=110, 7=111.
What is the Octal number system?
Octal (Base-8) digits each correspond to exactly 3 binary digits.
What is the Binary number system?
Binary (Base-2) is the fundamental representation used by all digital systems.
Where is Octal to Binary conversion used?
Direct digit-by-digit expansion. Used in: analyzing Unix permissions (755 → 111 101 101 = rwxr-xr-x), legacy computing systems, and PDP-11 assembly.
Can I convert large octal 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.