Octal To Binary and Binary To Octal Converter

Seamless Octal & Binary Conversion

Effortlessly convert numbers between the octal (base-8) and binary (base-2) systems. A fast, accurate, and free tool for developers and students.

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Octal & Binary Converter

Enter a number, select the conversion direction, and get the result instantly.

Octal To Binary & Binary To Octal

Input

Output

Why Use Our Converter?

Our tool provides an intuitive and fast way to convert numbers directly in your browser.

Direct Conversion

Leverages the direct 1-to-3 digit relationship between octal and binary for fast, accurate conversions.

Client-Side Speed

All calculations are performed instantly in your browser, ensuring maximum speed and efficiency.

Privacy Focused

No uploads to servers. All conversions happen locally on your device, respecting your privacy.

How It Works

Converting your numbers is simple with our straightforward three-step process.

1. Enter Number

Type or paste the number you want to convert into the 'Input' text area on the left.

2. Choose Conversion

Click the appropriate button for the conversion you need: 'Octal to Binary' or 'Binary to Octal'.

3. Get Result

The result appears instantly in the 'Output' box. Use the 'Copy' button to save it to your clipboard.

The Bridge Between Octal and Binary

Understand the fundamentals of base-8 and base-2, and why they are so closely linked in computer science.

Understanding Number Systems

In computing, we work with different number systems beyond the everyday decimal (base-10) system. The most fundamental is Binary (base-2), which uses only two digits: 0 and 1. Another important system is Octal (base-8), which uses eight digits: 0, 1, 2, 3, 4, 5, 6, and 7.

The magic of converting between octal and binary lies in their mathematical relationship: 8 is a power of 2 (8 = 2³). This means that every single digit in the octal system can be represented by exactly three digits in the binary system. This creates a simple and direct bridge for conversion, making octal a convenient shorthand for representing long binary strings.

The Octal-to-Binary Mapping

Here is the direct conversion for each octal digit:

• Octal 0 = Binary 000
• Octal 1 = Binary 001
• Octal 2 = Binary 010
• Octal 3 = Binary 011
• Octal 4 = Binary 100
• Octal 5 = Binary 101
• Octal 6 = Binary 110
• Octal 7 = Binary 111

How to Convert Octal to Binary

Converting from octal to binary is incredibly straightforward. You simply replace each octal digit with its corresponding 3-digit binary equivalent from the table above.

Let's convert the octal number (347)₈ to binary:

• Break down the octal number into its digits: 3, 4, 7.
• Convert each digit to its 3-bit binary representation:
  • 3 → 011
  • 4 → 100
  • 7 → 111
• Combine the binary groups: 011 100 111.

So, the octal number (347)₈ is equal to the binary number (011100111)₂. Our tool automates this process for you.

How to Convert Binary to Octal

Converting from binary to octal is the reverse process. You group the binary digits into sets of three, starting from the right. If the leftmost group doesn't have three digits, you pad it with leading zeros. Then, you convert each 3-digit binary group into its corresponding octal digit.

Let's convert the binary number (11010110)₂ to octal:

• Start from the right and group the digits in threes: 11 010 110.
• The leftmost group, 11, has only two digits. Pad it with one leading zero to make it a full group of three: 011.
• Now our groups are: 011, 010, 110.
• Convert each binary group to its octal equivalent:
  • 011 → 3
  • 010 → 2
  • 110 → 6

Thus, the binary number (11010110)₂ is equal to the octal number (326)₈.

Why is This Useful?

While modern programming rarely requires manual binary manipulation, understanding this relationship is crucial for computer science fundamentals. In the past, octal was widely used as a compact, human-readable representation of binary machine code.

• Readability: It's much easier for a person to read and transcribe (326) than 11010110, reducing the chance of errors.
• File Permissions: A classic example still in use today is in Unix/Linux file permissions. The chmod command often uses a 3-digit octal number to set read, write, and execute permissions for the owner, group, and others. Each digit (0-7) represents a 3-bit setting.

Frequently Asked Questions

Find answers to common questions about our Octal & Binary Converter.

Why convert between Octal and Binary?

Converting between Octal (base-8) and Binary (base-2) is common in computing because Octal provides a human-friendly shorthand for long binary numbers. Since 8 is a power of 2 (2^3), one octal digit perfectly represents three binary digits, making conversions direct and simple.

What does this tool do?

This tool allows you to instantly and accurately convert numbers between the Octal (base-8) and Binary (base-2) number systems directly in your web browser.

Is my data stored anywhere?

No, all calculations happen locally in your browser. Your data is not sent to or stored on any server, ensuring your complete privacy.

How do I use the converter?

Simply enter a valid octal or binary number into the 'Input' box. Then, click either the 'Octal to Binary' or 'Binary to Octal' button. The converted result will instantly appear in the 'Output' box.

What is an 'Invalid binary string' error?

This error occurs if you try to convert from binary to octal and your input contains any characters other than 0 or 1. The binary system only uses these two digits.

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