Binary to Octal Converter [2025]

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Convert binary (base-2) numbers to octal (base-8) with step-by-step explanations. Essential for computer science and digital systems work.

✓ Direct 3-bit Grouping✓ Customizable Output✓ Educational Steps

Enter multiple binary numbers separated by spaces, commas, or new lines

Key Features

  • Convert binary numbers to octal using direct 3-bit grouping.
  • Customizable bit length output (24, 48, or 72 bits).
  • Optional zero padding for consistent width.
  • View step-by-step conversion process.
  • Automatic decimal representation.
  • Real-time input validation.
  • Copy functionality for quick result sharing.
  • Clear error messages for invalid inputs.

Common Use Cases

System Development

  • • File permissions
  • • Memory addresses
  • • System flags
  • • Debug outputs

Education

  • • Number systems
  • • Base conversion
  • • Computer science
  • • Digital logic

Digital Systems

  • • Data conversion
  • • Protocol analysis
  • • System testing
  • • Binary operations

Frequently Asked Questions

How does binary to octal conversion work?

Binary to octal conversion works by grouping binary digits into sets of three. Each group of three binary digits corresponds to one octal digit, since 2³ = 8. For example, the binary group '111' converts to octal '7', '110' to '6', and so on. This makes conversion straightforward and reliable.

Why use different bit lengths?

Different bit lengths are useful for different applications. The tool offers multiples of 3 (24, 48, 72 bits) to ensure clean octal conversion. This allows you to match your output to your system's requirements while maintaining proper alignment and grouping.

When is zero padding useful?

Zero padding ensures consistent output width and proper grouping for octal conversion. It's particularly useful when working with fixed-width systems or when you need to ensure your binary number can be properly grouped into sets of three bits for accurate octal conversion.

Why show the decimal value?

The decimal representation provides a familiar reference point and helps verify the conversion is correct. It's also useful when working across different number systems or when you need to understand the actual value being represented in a more conventional format.

Technical Details

Binary to Octal Conversion Process

The conversion follows these steps:

  1. The binary number is padded with leading zeros if needed to make its length a multiple of 3
  2. The padded binary number is divided into groups of three bits
  3. Each three-bit group is converted to its octal equivalent:
    • 000 → 0
    • 001 → 1
    • 010 → 2
    • 011 → 3
    • 100 → 4
    • 101 → 5
    • 110 → 6
    • 111 → 7
  4. The resulting octal digits are concatenated

Example conversion of binary 1101011:

  • Pad to 001|101|011
  • Convert groups: 001 → 1, 101 → 5, 011 → 3
  • Concatenate: 153 (octal)
  • Decimal: 107

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