Number Base Converter
Convert between binary, octal, decimal, and hexadecimal numbers in real-time.
What is the Number Base Converter?
The Number Base Converter is an online tool that allows you to instantly convert numbers between different numeral systems (bases). It seamlessly converts between binary, octal, decimal, and hexadecimal numbering systems, supporting essential calculations for programming, computer science, and digital electronics.
Features of the Number Base Converter
- Real-time Conversion: Numbers entered in any base are instantly converted to all other supported formats
- Formatting Option: Long numbers can be displayed with separators for improved readability (e.g., 1111 1111)
- Error Detection: Immediately displays errors when invalid characters are entered for a specific base
- Copy Function: All conversion results can be copied to clipboard with a single click
- Large Number Support: Handles numbers within JavaScript's safe integer range (up to 9,007,199,254,740,991)
About Number Bases
Number bases (or radix) define the "weight" system for representing numbers. While decimal (base 10) is common in everyday life with each digit representing powers of 10, other bases are frequently used in computer-related fields.
Bases Supported by This Tool
| Base Name | Notation | Digits Used | Common Applications |
|---|---|---|---|
| Binary (Base 2) | 0, 1 | 0-1 | Computer internal representation, bit operations |
| Octal (Base 8) | 0-7 | 0-7 | UNIX file permissions, some programming languages |
| Decimal (Base 10) | 0-9 | 0-9 | Everyday calculations, standard numeric representation |
| Hexadecimal (Base 16) | 0-9, A-F | 0-9, A-F | Memory addresses, color codes, byte data representation |
How to Use the Number Base Converter
- Enter a value in any base: You can input values in any of the fields (binary, octal, decimal, or hexadecimal)
- Automatic conversion: As you type, the value is automatically converted to all other base formats
- Formatting options: Toggle the "Format Numbers" switch on/off to adjust the display format
- When on: Binary is separated every 4 digits, octal every 3 digits, decimal every 3 digits, and hexadecimal every 4 digits
- When off: Numbers are displayed as continuous digits without separators
- Copy results: Click the copy button next to any field to copy the converted result to your clipboard
Use Cases
Programming and Development
- Converting number representations in code: Interconvert between different numeral representations used in programs (e.g., 0x1A, 0b1010)
- Bit mask operations: Verify binary representations while performing bit-level operations
- Memory address calculations: Convert between hexadecimal memory addresses and decimal values
Important Notes
- Input limitations: Each base has restrictions on allowed digits (e.g., binary only accepts 0 and 1)
- Maximum value: Numbers exceeding JavaScript's safe integer range (2^53-1 = 9,007,199,254,740,991) cannot be accurately converted
- Separators: Spaces or separators in input (e.g., 1111 1111) are accepted but ignored during conversion
How Base Conversion Works
Base conversion is the process of transforming a number represented in one base to another base.
Example: Converting Decimal to Binary (10→2)
To convert decimal "42" to binary:
- 42 ÷ 2 = 21 remainder 0
- 21 ÷ 2 = 10 remainder 1
- 10 ÷ 2 = 5 remainder 0
- 5 ÷ 2 = 2 remainder 1
- 2 ÷ 2 = 1 remainder 0
- 1 ÷ 2 = 0 remainder 1
Reading the remainders from bottom to top: 101010 (binary)
The tool performs these mathematical conversion processes instantly, saving you the effort of manual calculations.