This tool converts numbers between different numeral systems like binary, decimal, octal, and hexadecimal.
It helps students, engineers, and programmers quickly verify calculations or understand data representation.
Use it for homework, debugging, or learning how computers process numbers.
🔢 Base Converter
Result:
Tip: Valid characters for each base are 0-1, 0-7, 0-9, and 0-9A-F (case-insensitive).
How to Use This Tool
Enter your number in the input field and select the base it is currently in. Then choose the base you want to convert to and click Convert. The tool will display the equivalent number in all four common bases for easy reference.
Formula and Logic
The conversion works by first parsing the input string into a decimal integer using the source base. For example, binary (base 2) uses powers of 2, octal (base 8) uses powers of 8, and hexadecimal (base 16) uses powers of 16 with A-F representing 10-15. The decimal result is then converted to the target base using repeated division and remainder logic.
Practical Notes
- For binary inputs, ensure only 0s and 1s are used. Octal uses 0-7, decimal uses 0-9, and hexadecimal uses 0-9 plus A-F (case-insensitive).
- Large numbers may exceed JavaScript's integer precision (up to 2^53 - 1). For extremely large values, consider using a library for arbitrary-precision arithmetic.
- Leading zeros are preserved in the output for clarity, but they do not affect the numeric value.
- Edge cases: Empty input or invalid characters trigger an error message. Zero converts correctly across all bases.
Why This Tool Is Useful
This calculator is essential for students learning computer science, engineers working with low-level data, and programmers debugging code. It provides instant, accurate conversions without manual calculation, saving time and reducing errors in homework, projects, or system design.
Frequently Asked Questions
What if my number has letters in it?
Letters are only valid in hexadecimal (A-F). If you enter letters in other bases, the tool will show an error and prompt you to correct the input.
Can I convert negative numbers?
This tool focuses on positive integers. Negative numbers require additional handling (like two's complement) and are not supported in this version.
Why does the result show multiple bases?
Displaying all four bases helps you see the relationships between numeral systems and verify your work, which is especially useful for learning and cross-checking.
Additional Guidance
Practice with common values like 10 (decimal) which is 1010 in binary, 12 in octal, and A in hexadecimal. Use this tool to explore how numbers are represented in different systems, which is foundational for understanding computer architecture and data encoding.