All Number Converter - Convert Between Binary, Decimal, Octal, Hexadecimal

All Number Converter - View All Number Base Conversions at Once

Our free online All Number Converter allows you to convert numbers between binary, decimal, octal, and hexadecimal number systems instantly. Unlike traditional converters that show one conversion at a time, this tool displays all conversions simultaneously, making it perfect for quick reference and comparison across different number bases.

What is Number Base Conversion?

Number base conversion is the process of changing a number from one number system (base) to another. Different number systems are used in various fields of computing and mathematics:

Binary (Base 2): Uses only digits 0 and 1. Fundamental in computer science, digital electronics, and binary logic operations.
Octal (Base 8): Uses digits 0 through 7. Commonly used in computing for file permissions and compact representation.
Decimal (Base 10): The standard number system using digits 0-9. Used in everyday mathematics and calculations.
Hexadecimal (Base 16): Uses digits 0-9 and letters A-F. Widely used in programming, web development (color codes), and memory addresses.

How to Use the All Number Converter

Enter your number: Type the number you want to convert in the input field
Select input base: Choose the current base of your number (Binary, Decimal, Octal, or Hexadecimal)
View all conversions: All four conversions (Binary, Decimal, Octal, Hexadecimal) will appear instantly in separate boxes
Copy results: Click the copy icon next to any conversion to copy it to your clipboard

Conversion Examples

Example 1: Decimal 255

Binary: 11111111
Decimal: 255
Octal: 377
Hexadecimal: FF

Example 2: Hexadecimal FF

Binary: 11111111
Decimal: 255
Octal: 377
Hexadecimal: FF

Example 3: Binary 1010

Binary: 1010
Decimal: 10
Octal: 12
Hexadecimal: A

Mathematical Formula

The conversion process involves converting the input number to decimal first, then converting from decimal to all other bases:

Convert to Decimal: \[ \text{Decimal} = \sum_{i=0}^{n-1} d_i \times b^i \] Where \(d_i\) is the digit at position \(i\) and \(b\) is the input base.
Convert from Decimal to Other Bases: Divide the decimal number by the target base repeatedly and collect remainders in reverse order.

Why Use All Number Converter?

This tool is particularly useful when you need to see how a number is represented across different number systems simultaneously. It's ideal for:

Quick Reference: See all conversions at a glance without multiple conversions
Learning: Understand how the same value appears in different number systems
Debugging: Compare number representations when working with different bases
Efficiency: Save time by viewing all conversions in one place

Common Use Cases

Computer Programming: Quickly check how a value appears in binary, octal, and hexadecimal
Web Development: Convert color values between decimal and hexadecimal formats
Digital Electronics: Understand binary representations and their equivalents
Mathematics Education: Learn and compare different number systems
System Administration: Convert file permissions between octal and other formats
Cryptography: Work with different base encodings and representations

Features of Our All Number Converter

Simultaneous conversions: View all four number bases at once
Real-time conversion: Results update instantly as you type
Input validation: Ensures valid characters for each number base
Error handling: Clear error messages for invalid inputs
Copy functionality: Easy copying of any conversion to clipboard with one click
Multiple input bases: Accept input in binary, decimal, octal, or hexadecimal
Educational content: Built-in guide and examples for learning

Number Base Reference

Base	Name	Valid Digits	Common Uses
2	Binary	0-1	Computer science, digital logic
8	Octal	0-7	File permissions, compact representation
10	Decimal	0-9	Everyday mathematics, standard counting
16	Hexadecimal	0-9, A-F	Programming, web colors, memory addresses

Frequently Asked Questions

What makes this converter different from other number converters?

Unlike traditional converters that show one conversion at a time, this tool displays all four conversions (Binary, Decimal, Octal, Hexadecimal) simultaneously. This makes it perfect for quick reference and comparison across different number systems without needing multiple conversions.

Can I input numbers in any of the four bases?

Yes! You can enter a number in binary, decimal, octal, or hexadecimal format. Just select the appropriate input base from the dropdown menu, and the tool will convert it to all other bases automatically.

What is the maximum number I can convert?

The converter can handle very large numbers, limited only by JavaScript's number precision (approximately 2^53 - 1). For extremely large numbers, you might see some precision loss in the least significant digits.

Can I convert negative numbers?

The converter currently handles positive integers. For negative numbers, you would need to work with their absolute values and apply the sign separately, as different number systems have different ways of representing negative values (like two's complement in binary).

What characters are valid for hexadecimal input?

Hexadecimal uses digits 0-9 and letters A-F (or a-f, case doesn't matter). The converter automatically converts lowercase letters to uppercase in the output. For example, "ff" and "FF" both represent 255 in decimal.

How accurate are the conversions?

The conversions are mathematically accurate. The tool uses JavaScript's built-in parseInt() and toString() methods, which provide precise base conversion for all supported number ranges within JavaScript's precision limits.

What if I enter an invalid number for a base?

The converter will display a clear error message indicating that the number contains invalid characters for the selected base. For example, entering "8" when converting from base 8 (octal) will show an error since octal only uses digits 0-7.

Can I copy the conversion results?

Yes! Each conversion box has a copy icon that allows you to copy that specific conversion to your clipboard with a single click. A notification will confirm when the value has been copied successfully.