Octal to Binary Converter
Instantly convert any octal number into its binary equivalent.
Octal Input
Binary Output
Why Use This Tool? ✅
Fast & Accurate
Converts octal to binary instantly and precisely as you type.
Perfect for Computing
An essential tool for anyone working with file permissions, digital logic, or computer architecture.
User-Friendly Interface
A simple, clean two-panel layout makes converting from octal to binary effortless.
Ideal for Learning
Helps students and developers visualize the relationship between octal and binary number systems.
From Base-8 to Base-2: A Bridge in Computing 🔢
The octal (base-8) number system uses eight unique digits (0-7). In the early days of computing, it served as a more human-friendly way to represent binary numbers, much like hexadecimal does today. While less common now, it still has important applications, especially in legacy systems and certain computing contexts like file permissions in Unix-like systems.
The Link Between Octal and Binary
The octal system is convenient because there is a very direct relationship between it and the binary system. Each octal digit corresponds to a unique three-digit binary number.
For example, to convert the octal number `755` to binary, you simply convert each digit to its 3-bit binary equivalent and join them together:
- Octal `7` = Binary `111`
- Octal `5` = Binary `101`
- Octal `5` = Binary `101`
So, the octal number 755 becomes the binary string `111101101`. This tool automates that direct translation, making it easy to see the binary representation of any octal value.
Unix File Permissions: A Common Use Case
One of the most common places you'll still see octal in use is for setting file permissions on Unix-based systems (like Linux and macOS). The `chmod` command often uses a three-digit octal number to define read, write, and execute permissions for the owner, group, and others. For example, the permission `755` (which this tool converts to `111101101`) gives the owner full permissions (read, write, execute), while the group and others have read and execute permissions. Understanding the octal-to-binary conversion is key to understanding how these permissions work at a low level.