Number Base Converter: Convert Between Any Numerical Base (2-36)

Transform numbers instantly between binary, decimal, hexadecimal, octal, and any custom base from 2 to 36. This powerful number base converter simplifies base conversion for programmers, students, and professionals working with different numerical systems.

What is Base Conversion?

Base conversion (also called radix conversion) is the process of changing a number from one numerical base to another. Each base uses a specific set of digits to represent values:

• Binary (Base-2): Uses digits 0, 1
• Octal (Base-8): Uses digits 0-7
• Decimal (Base-10): Uses digits 0-9
• Hexadecimal (Base-16): Uses digits 0-9, A-F

How to Use the Number Base Converter

Converting between numerical bases is simple with our tool:

1. Enter your number in the input field
2. Select the source base (2-36) of your input number
3. Choose the target base (2-36) for conversion
4. View instant results as you type

The converter automatically validates your input to ensure it's valid for the selected base.

Common Base Conversion Examples

Binary to Decimal Conversion

• Binary: 1101 → Decimal: 13
• Calculation: (1×2³) + (1×2²) + (0×2¹) + (1×2⁰) = 8 + 4 + 0 + 1 = 13

Decimal to Hexadecimal Conversion

• Decimal: 255 → Hexadecimal: FF
• Process: 255 ÷ 16 = 15 remainder 15, 15 ÷ 16 = 0 remainder 15 → FF

Octal to Binary Conversion

• Octal: 17 → Binary: 1111
• Via decimal: 17₈ = 15₁₀ = 1111₂

Popular Use Cases for Base Conversion

Programming & Computer Science:

• Converting between binary and hexadecimal for memory addresses
• Working with octal file permissions in Unix/Linux systems
• Debugging assembly code and machine instructions

Digital Electronics:

• Analyzing binary data in circuit design
• Converting between different number representations in embedded systems
• Understanding digital signal processing values

Mathematics & Education:

• Learning positional notation systems
• Solving computer science problems
• Understanding how computers represent numbers

Understanding Numerical Bases

Each numerical base follows the same principles:

• Position value: Each digit position represents a power of the base
• Valid digits: Base-n uses digits 0 through (n-1)
• Extended notation: Bases above 10 use letters A-Z for values 10-35

Advanced Base Conversion Features

Our base converter supports:

• Custom bases from 2 to 36
• Real-time validation of input numbers
• Instant conversion as you type
• Error handling for invalid inputs
• Case-insensitive letter recognition for bases above 10

Frequently Asked Questions

What is the difference between binary and hexadecimal?

Binary (base-2) uses only 0 and 1, while hexadecimal (base-16) uses 0-9 and A-F. Hexadecimal is often used as a compact way to represent binary data since each hex digit represents exactly 4 binary digits.

How do you convert decimal to binary manually?

Divide the decimal number by 2 repeatedly, keeping track of remainders. Read the remainders from bottom to top to get the binary representation. For example: 13 ÷ 2 = 6 remainder 1, 6 ÷ 2 = 3 remainder 0, 3 ÷ 2 = 1 remainder 1, 1 ÷ 2 = 0 remainder 1 → 1101₂

What is the largest base this converter supports?

Our number base converter supports bases from 2 up to 36. Base-36 uses digits 0-9 and letters A-Z, making it the highest practical base using standard alphanumeric characters.

Why would I need to convert between different number bases?

Base conversion is essential in computer programming, digital electronics, and mathematics education. Programmers frequently work with hexadecimal for memory addresses, binary for bit operations, and octal for file permissions.

Can I convert negative numbers between bases?

This converter focuses on positive integers. For negative numbers, apply the conversion to the absolute value, then add the negative sign to the result.

How accurate is the base conversion calculator?

Our converter uses precise mathematical algorithms to ensure 100% accuracy for all supported bases (2-36). The conversion process follows standard mathematical principles for positional notation systems.

What's the difference between radix and base?

Radix and base are interchangeable terms referring to the number of unique digits used in a positional numeral system. Both terms describe the same concept in number theory and computer science.

How do computers use different number bases?

Computers internally use binary (base-2) for all operations. Hexadecimal (base-16) provides a human-readable way to represent binary data, while octal (base-8) is used in some systems for file permissions and legacy applications.

Start Converting Numbers Between Bases

Use our free number base converter to instantly transform numbers between any bases from 2 to 36. Perfect for students, programmers, and anyone working with different numerical systems. No registration required – start converting now!