Octal to Binary Converter

Convert octal numbers (integers and floats) to binary instantly with batch conversion support. Essential tool for programmers, students, and engineers.

When enabled, binary digits will be visually grouped in sets of 3 to show the conversion process.
Enter an octal number (digits 0-7 only). Use a dot (.) as decimal point. Positive and negative numbers supported.
12
12.4
17
15.5
0.4
0.2
0.1
0.7
-12.4
377
100.01

Batch Conversion: Convert multiple octal numbers at once. Enter one octal value per line, or separate values with commas, spaces, or tabs. Supports integers and floating-point numbers.

When enabled, binary digits will be visually grouped in sets of 3 to show the conversion process in batch results.
Enter octal numbers (digits 0-7 only). Each value will be converted separately. Maximum 1000 values.
Simple Octal List
Basic octal values for testing
12 12.4 17 15.5 0.4 0.2 0.1
Comma-Separated
Values separated by commas
12, 12.4, 17, 15.5, 0.4, 0.2, 0.1, 377
Unix Permissions
Common Unix file permissions in octal
755 644 777 750 600 755.0 644.0
Converting...

Understanding Octal to Binary Conversion

Octal is a base-8 numeral system that uses digits 0 through 7. Binary is a base-2 system using only 0 and 1. Converting octal to binary is straightforward because 8 is a power of 2 (2³ = 8).

Conversion Algorithm:

  • Direct Mapping: Convert each octal digit to its 3-bit binary equivalent
  • Integer Part: Convert each digit from left to right
  • Fractional Part: Convert each digit from left to right after the octal point
  • Negative Numbers: Convert absolute value, then add negative sign
  • Leading/Trailing Zeros: Remove unnecessary zeros for cleaner representation

Important Notes on Octal Float Conversion:

  • Octal floating-point numbers have an octal point (instead of decimal point)
  • Conversion is exact since each octal digit maps directly to 3 binary digits
  • The converter preserves all significant digits during conversion
  • Both positive and negative octal numbers are supported

Octal to Binary Conversion Table

Octal Digit Binary (3-bit) Decimal Value Octal Digit Binary (3-bit) Decimal Value
0 000 0 4 100 4
1 001 1 5 101 5
2 010 2 6 110 6
3 011 3 7 111 7

Conversion Examples

1

Octal 12 to Binary: 1₈ = 001₂, 2₈ = 010₂ → Combine: 001 010 → Remove leading zeros → 1010₂

2

Octal 12.4 to Binary: Integer part: 1₈ = 001₂, 2₈ = 010₂ → 1010₂, Fractional part: 4₈ = 100₂ → 12.4₈ = 1010.1₂

3

Octal 15.5 to Binary: Integer part: 1₈ = 001₂, 5₈ = 101₂ → 1101₂, Fractional part: 5₈ = 101₂ → 15.5₈ = 1101.101₂

Real-World Applications

  • Unix/Linux File Permissions: File permissions are represented as 3-digit octal numbers (e.g., 755 = 111 101 101)
  • Computer Programming: Octal to binary conversion used in low-level programming and debugging
  • Digital Electronics: Simplifies representation of binary states in circuits
  • Memory Addressing: Some systems use octal for memory address representation
  • Education: Teaching octal, binary, and hexadecimal number systems
  • Data Analysis: Converting octal-encoded data to binary for processing

Calculator Features:

  • Converts octal to binary with step-by-step mapping visualization
  • Supports octal integers, floating-point numbers, and negative numbers
  • Visual grouping of binary digits in sets of 3
  • Supports batch conversion of multiple octal values
  • Also shows decimal and hexadecimal equivalents
  • Export results as CSV or JSON
  • Validates octal input (only digits 0-7 and . allowed)

Frequently Asked Questions

Octal is base-8 (2³ = 8), which means each octal digit can represent values from 0 to 7. In binary, we need exactly 3 bits to represent values from 0 to 7: • 000₂ = 0, 001₂ = 1, 010₂ = 2, 011₂ = 3 • 100₂ = 4, 101₂ = 5, 110₂ = 6, 111₂ = 7 This direct 1:3 mapping makes conversion between octal and binary simple and exact.

Octal floating-point conversion follows the same direct mapping principle: 1. Separate integer and fractional parts at the octal point 2. Integer part: Convert each octal digit from left to right to 3-bit binary 3. Fractional part: Convert each octal digit from left to right to 3-bit binary 4. Combine results with a binary point 5. Remove unnecessary zeros (leading zeros from integer part, trailing zeros from fractional part)

Leading zeros in the integer part of a binary number don't change its value (just like leading zeros in decimal). The converter removes them for cleaner, more readable results. However, when the grouping visualization is enabled, you can see the full 3-bit groups including any zeros that were part of the conversion. For fractional parts, trailing zeros after the last 1 are also removed unless they're needed to complete a 3-bit group in the visualization.

Yes, the converter supports negative octal numbers. Simply prefix the octal number with a minus sign (-). The conversion process: 1. Convert the absolute value (without the minus sign) 2. Apply the negative sign to the result For example: -12.4₈ → Convert 12.4₈ to 1010.1₂ → Apply negative sign → -1010.1₂

The converter can handle very long octal numbers (up to several thousand digits in practical use). However, for performance reasons: • Single conversion: Virtually unlimited length • Batch conversion: Limited to 1000 values, each up to several hundred digits Extremely long numbers may slow down the browser, but typical octal numbers (up to 21 digits for 64-bit integers) convert instantly.