Base Converter | Binary, Decimal, Octal, Hex & Custom Base

📖 How to Use This Base Converter

Enter the number - Type or paste the number you want to convert.

Select the source base - Choose the base of your input number (Binary, Decimal, Octal, Hex, or Custom).

Select the target base - Choose the base you want to convert to.

Click "Convert" - Get instant results with step-by-step conversion explanation.

🔢 Understanding Number Systems

A number system (or base) defines how many unique digits are used to represent numbers. Each position in a number represents a power of the base.

Binary (Base 2): Uses digits 0-1. Used in computers and digital electronics.
Octal (Base 8): Uses digits 0-7. Used in computing as shorthand for binary.
Decimal (Base 10): Uses digits 0-9. The standard number system for everyday use.
Hexadecimal (Base 16): Uses digits 0-9 and A-F (A=10, B=11, C=12, D=13, E=14, F=15). Commonly used in programming and web design (colors).
Custom Base (2-36): Any base between 2 and 36, using digits 0-9 and A-Z.

🧮 How to Convert Between Bases

Method: Convert to decimal first, then to target base.

To Decimal: Multiply each digit by (base^position) and sum.
Example: Binary 1011₂ = 1×8 + 0×4 + 1×2 + 1×1 = 11₁₀

From Decimal: Repeatedly divide by target base, read remainders backwards.
Example: 11₁₀ to binary = 1011₂

💡 Common Use Cases

Programming: Converting between binary, hex, and decimal for coding
Web Development: Hexadecimal color codes (e.g., #FF0000 = red)
Computer Science: Understanding how computers store and process data
Electronics: Binary and hexadecimal for circuit design
Mathematics: Learning different number systems and base conversions

❓ Frequently Asked Questions (FAQ)

What is the maximum base supported?

This converter supports bases 2 through 36. Base 36 uses digits 0-9 and letters A-Z (26 letters) for a total of 36 unique symbols.

Why do programmers use hexadecimal?

Hexadecimal is more compact than binary while still being easily convertible. One hex digit represents 4 binary digits (bits), making it ideal for representing memory addresses, color values, and machine code.

How do I convert a decimal to binary?

Divide the decimal number by 2 repeatedly, recording remainders. Read remainders from last to first. Example: 13 ÷ 2 = 6 remainder 1, 6 ÷ 2 = 3 remainder 0, 3 ÷ 2 = 1 remainder 1, 1 ÷ 2 = 0 remainder 1 → 1101₂.

What are valid digits for custom bases?

For base N (2-36), valid digits are 0-9 and A-Z, but only up to the base-1. For base 16, valid digits: 0-9, A-F. For base 20, valid: 0-9, A-J.

Does the converter handle negative numbers?

This converter handles positive integers. For negative numbers, convert the absolute value and add a minus sign. Fractional numbers are not supported in this version.

What is base 64 and why isn't it supported?

Base 64 is used in email encoding and data serialization, but it uses special characters beyond A-Z and 0-9. This converter focuses on bases 2-36 which use only alphanumeric characters.