Number System Converter - Convert Between Hex, Binary, and Decimal
Free online number system converter. Convert between hexadecimal, binary, and decimal number systems instantly with precision.
Convert between decimal, binary, and hexadecimal number systems with this powerful and accurate converter. Perfect for programming, electronics, and computer science applications.
Common Number System Conversions
Decimal to Binary
10 = 1010
Decimal to Binary
15 = 1111
Decimal to Binary
20 = 10100
Binary to Decimal
1010 = 10
Binary to Decimal
1111 = 15
Binary to Decimal
10100 = 20
How This Tool Works
Our Number System Converter tool makes it easy to convert between different number systems:
- Enter the value you want to convert in the input field
- Select the number system you are converting from (Decimal, Binary, or Hexadecimal)
- Select the number system you want to convert to
- Click the "Convert" button to see the result
- Use the "Swap Systems" button to quickly switch between systems
- Copy the result to your clipboard by clicking the copy button
The converter supports the following number systems:
- Decimal - Base 10 number system (0-9)
- Binary - Base 2 number system (0-1)
- Hexadecimal - Base 16 number system (0-9, A-F)
This converter is useful for:
- Programming and software development
- Electronics and digital circuit design
- Computer science education
- Debugging and troubleshooting
Frequently Asked Questions
What's the difference between decimal, binary, and hexadecimal?
Decimal, binary, and hexadecimal are different number systems used in computing:
- Decimal - The standard base-10 system we use in everyday life, using digits 0-9.
- Binary - The base-2 system used by computers, using only digits 0 and 1.
- Hexadecimal - The base-16 system, using digits 0-9 and letters A-F, commonly used in programming and memory addresses.
Each system has its own advantages and use cases in computing and electronics.
How accurate is this number system converter?
This converter performs precise mathematical conversions between number systems using standard algorithms:
- For decimal to binary/hex: Division by the target base and collecting remainders
- For binary/hex to decimal: Positional notation and power of the base
- For binary to hex and vice versa: Grouping bits into 4s and converting each group
The results are mathematically accurate and can handle large numbers within the limits of the system.
Why do we need different number systems in computing?
Different number systems serve different purposes in computing:
- Binary - Essential for computer hardware as it represents the on/off states of electronic circuits
- Hexadecimal - Provides a more compact representation of binary data and is commonly used in memory addresses and color codes
- Decimal - Used for human-readable output and input, as it's the most familiar number system
Each system has its own advantages in different contexts, making them all important in modern computing.
What are some practical applications of number system conversion?
Number system conversion is essential in many computing and electronics applications:
- Programming and debugging - Understanding memory addresses and bit manipulation
- Digital electronics - Designing and troubleshooting circuits
- Network administration - Working with IP addresses and subnet masks
- Color representation - Converting between RGB and hexadecimal color codes
- Data compression - Understanding binary representations of data
These conversions are fundamental to many aspects of computer science and technology.