What Is the Binary, Hexadecimal & Octal Base Converter?
Positional numeral systems represent numbers using distinct bases.
Binary (base 2) is the native language of digital electronics, Hexadecimal (base 16) provides human-readable shorthand for bytes, and Octal (base 8) is historically used in Unix file permissions.
How Does the Binary, Hexadecimal & Octal Base Converter Work?
The input string is parsed into its underlying decimal integer representation using radix decoding.
The integer is then formatted into base 2, base 8, base 10, and uppercase base 16 strings.
Binary, Hexadecimal & Octal Base Converter Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Positional notation evaluates each digit multiplied by the base raised to its position exponent.
How to Use the Binary, Hexadecimal & Octal Base Converter
- Enter the number you want to convert.
- Select the source base (Decimal, Hexadecimal, Binary, or Octal).
- View conversions across all four bases.
Step-by-Step Example Calculation
Convert Decimal 255 to All Bases
Input Values:
Understanding Your Result
Shows binary grouped in 4-bit nibbles, hex prefixed with 0x, octal prefixed with 0o, and byte lengths.
Factors That Affect the Result
- Signed vs unsigned representation (this calculator models unsigned whole integers).
When Should You Use This Calculator?
- Debugging memory dumps, setting Unix chmod permissions, color hex code analysis, and bitwise programming.
Assumptions & Limitations
- Limited to non-negative integers up to standard JavaScript safe integer precision (2^53 - 1).
Frequently Asked Questions
Calculation Accuracy & Reference Note
Lossless integer radix conversion.