Octal to Binary Converter Calculator
Octal (base-8) and Binary (base-2) number systems are integral in computing. While binary is native to digital circuits, octal offers a shorthand for binary numbers—grouping every 3 bits into a single octal digit. This tool instantly converts octal numbers into their binary equivalents with clarity.
What Is the Octal System?
Octal is a base-8 numbering system using digits 0 to 7. It is often used in computing to represent binary in a more compact and readable form, especially in UNIX file permissions and microcontroller programming.
157= 1×8² + 5×8¹ + 7×8⁰ = 111₁₀
What Is the Binary System?
Binary is a base-2 system with only two digits: 0 and 1. It forms the foundation of all modern computing. Each binary digit (bit) corresponds to an electrical signal being off (0) or on (1).
110111 = Octal 67How to Convert Octal to Binary
Each octal digit can be directly translated into a 3-bit binary number:
- Write down the octal number.
- Convert each digit into its 3-digit binary equivalent.
- Concatenate all binary triplets together.
- Remove leading zeros if needed.
1 → 001, 5 → 101, 7 → 111 → Binary = 001101111₂
Octal to Binary Conversion Table
| Octal | Binary |
|---|---|
| 0 | 000 |
| 1 | 001 |
| 2 | 010 |
| 3 | 011 |
| 4 | 100 |
| 5 | 101 |
| 6 | 110 |
| 7 | 111 |
| 157 | 001101111 |
Why Use Octal in Computing?
- Compact representation: Octal shortens long binary numbers, making code more readable.
- Direct mapping: Each octal digit maps cleanly to 3 binary bits.
- Use in system permissions: UNIX file permissions use octal to represent read/write/execute access.