Free Binary to Octal Converter – Convert Binary to Base-8 Online

Convert binary numbers to octal (base-8) instantly with step-by-step 3-bit group visualization. See the complete conversion process. Perfect for programmers, students, and engineers. 100% free.

What Is Binary to Octal Conversion?

Binary to octal conversion transforms base-2 numbers (using only 0 and 1) into base-8 numbers (using digits 0-7). Since 8 is 2³, every 3 binary digits map directly to one octal digit, making this conversion straightforward.

Why Convert Binary to Octal?

Octal provides a compact way to represent binary values:

• File permissions: Unix/Linux uses octal (chmod 755)
• Assembly programming: Some architectures use octal opcodes
• Memory addresses: Octal notation in older systems
• Compact representation: 3 binary digits = 1 octal digit

How to Convert Binary to Octal

The 3-Bit Grouping Method

1. Group from right: Start from the rightmost bit
2. Make groups of 3: Each group becomes one octal digit
3. Pad if needed: Add leading zeros to complete the leftmost group
4. Convert each group: Use the reference table below

Conversion Reference Table

Step-by-Step Examples

Example 1: Convert 11010₂ to Octal

Step 1: Group from right in sets of 3

• 11010 → 011 | 010 (pad with leading 0)

Step 2: Convert each group

• 011 → 3
• 010 → 2

Result: 32₈

Example 2: Convert 11111111₂ to Octal

Step 1: Group from right

• 11111111 → 011 | 111 | 111

Step 2: Convert each group

• 011 → 3
• 111 → 7
• 111 → 7

Result: 377₈

Example 3: Convert 1000000₂ to Octal

Step 1: Group from right

• 1000000 → 001 | 000 | 000

Step 2: Convert each group

• 001 → 1
• 000 → 0
• 000 → 0

Result: 100₈

Common Binary to Octal Conversions

Unix File Permissions

Binary to octal is essential for understanding Unix permissions:

Each 3-bit group represents:

• Owner permissions
• Group permissions
• Others permissions

Understanding Number Systems

Binary (Base-2)

• Uses: 0, 1
• Each position: 2ⁿ
• Example: 101 = 1×4 + 0×2 + 1×1 = 5

Octal (Base-8)

• Uses: 0, 1, 2, 3, 4, 5, 6, 7
• Each position: 8ⁿ
• Example: 52 = 5×8 + 2×1 = 42

Why 3 Bits = 1 Octal Digit?

Since 2³ = 8, three binary digits can represent values 0-7, which are exactly the octal digits.

Programming Applications

JavaScript

const binary = '11010';
const octal = parseInt(binary, 2).toString(8);
// Result: '32'

Python

binary = '11010'
octal = oct(int(binary, 2))
# Result: '0o32'

C/C++

// Using bit manipulation
int decimal = 0b11010;  // Binary literal
printf("%o", decimal);  // Outputs: 32

Frequently Asked Questions

Why is octal used for file permissions?

Octal provides a compact way to represent 3-bit permission groups. Each digit represents read (4), write (2), and execute (1) permissions.

What's the largest octal digit?

7. Octal digits range from 0 to 7, corresponding to binary 000 to 111.

How do I convert large binary numbers?

Group from right in sets of 3 bits, then convert each group to its octal equivalent.

Is binary to octal conversion lossless?

Yes, the conversion preserves the exact value. You can convert back and get the original binary.

What if my binary doesn't divide evenly by 3?

Pad the leftmost group with zeros. For example, 1011 becomes 001 011.

Tips for Quick Conversion

1. Memorize the table: Only 8 values to remember
2. Group from right: Always start grouping from the least significant bit
3. Pad with zeros: Add leading zeros to complete groups
4. Check your work: Convert back to verify

Common Mistakes to Avoid

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