📖 How to Use This Base Converter
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Enter the number - Type or paste the number you want to convert.
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Select the source base - Choose the base of your input number (Binary, Decimal, Octal, Hex, or Custom).
3
Select the target base - Choose the base you want to convert to.
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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
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.