This number base converter is a powerful utility for converting numbers between any bases from 2 to 36. Here is a detailed guide on how to use it:
Type the number you want to convert into the input field, then select its current base from the dropdown menu (such as binary, decimal, or hexadecimal). The tool instantly converts your number to binary, octal, decimal, hexadecimal, and base-36, displaying all results in the cards below. Each result has a "Copy" button next to it—click to copy that value to your clipboard.
Below the input field are five quick-select buttons for the most common bases: Binary, Octal, Decimal, Hexadecimal, and Base-36. Click any button to instantly switch the source base without using the dropdown. The active button is highlighted so you always know which base is currently selected.
Click the "Clear" button to erase the input field and reset all results. The input supports standard keyboard shortcuts such as Ctrl+A to select all text, making it easy to replace your input and perform new conversions quickly.
Number base conversion is essential in many technical fields. Here are some typical scenarios where this tool proves invaluable:
Software Development: When working on embedded systems, low-level drivers, or network protocol parsing, developers frequently switch between binary, hexadecimal, and decimal. For example, parsing memory addresses, handling bitmasks, or analyzing packet headers. This tool helps verify conversion results quickly and speeds up debugging.
Education and Learning: Computer science students need to understand how different numeral systems relate to one another. By entering any number and seeing its representation across multiple bases, students can build intuition for how positional numeral systems work. Teachers can also use it to check students' manual homework.
Hardware and Electronics: In digital circuit design and FPGA development, binary and hexadecimal are the dominant representations. Engineers use this tool to convert between bases when verifying logic designs, calculating data path widths, or reading register maps in datasheets.
The Nature of Number Bases: A numeral system (or base) is a way of representing numbers using a specific set of symbols. Decimal uses ten symbols (0-9), while binary uses only two (0 and 1). Any integer can be expressed in any base, and conversions between bases follow well-defined mathematical rules that work for all integers.
Why Computers Prefer Binary: Modern computers rely on binary because electronic components can most reliably distinguish between two states: high voltage (1) and low voltage (0). Binary logic gates (AND, OR, NOT) map directly to transistor circuits. Although humans prefer decimal, every computation inside a computer is ultimately performed in binary.
The Power of Hexadecimal: Hexadecimal is a compact representation of binary because 16 equals 2 to the 4th power. Every four binary digits map to exactly one hexadecimal digit, reducing binary string length by 75%. This is why memory addresses, color codes, and cryptographic hashes are almost always displayed in hexadecimal notation.
This tool supports conversions between any bases from 2 to 36. The most commonly used are binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16). Other bases like base 3, base 12, and base 36 are also fully supported. Valid digits are 0-9 and A-Z (case-insensitive), where A=10, B=11, ..., Z=35.
To convert from another base to decimal: work from right to left, multiply each digit by the base raised to the power of its position (starting from 0), then sum the results. For example, binary 1011 = 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8+0+2+1 = 11. To convert from decimal to another base: repeatedly divide the decimal number by the target base, record the remainders, then read the remainders in reverse order. For example, converting 11 to binary: 11÷2=5 remainder 1, 5÷2=2 remainder 1, 2÷2=1 remainder 0, 1÷2=0 remainder 1. Reading remainders in reverse gives 1011.
In hexadecimal, the letters A through F represent decimal values 10 through 15. Specifically: A=10, B=11, C=12, D=13, E=14, F=15. This is necessary because hexadecimal needs to represent 16 different states per digit (0-15), but the digits 0-9 only cover the first 10 values. The letters A-F provide the remaining six symbols. For bases greater than 16 (such as base 36), the pattern continues with G=16, H=17, all the way up to Z=35.
Binary and hexadecimal have a direct relationship because 16 equals 2 to the 4th power. This means every 4 binary digits map exactly to 1 hexadecimal digit: 0000→0, 0001→1, ..., 1111→F. For example, the binary number 11110110 can be grouped as 1111 and 0110, which map to F and 6 respectively, giving the hexadecimal value F6. This one-to-four relationship makes hexadecimal an extremely compact way to represent binary data, which is why it is so widely used throughout computer science.
No. This tool runs entirely in your browser. All calculations are performed locally on your device, and no data is ever uploaded to a server. Once the page has loaded, you can use it offline without any internet connection. This ensures both speed and privacy.
Computers use binary because electronic circuits can most easily represent two stable states: on (1) and off (0). These states can be implemented using voltage levels, magnetic polarization, or physical pits on optical media. If computers used decimal, the hardware would need to reliably distinguish between ten different states, which would dramatically increase complexity and error rates. Another advantage of binary is its simple arithmetic rules—for example, addition has only four possible combinations (0+0=0, 0+1=1, 1+0=1, 1+1=10), compared to one hundred combinations in decimal.
Hexadecimal is widely used in programming for: 1) Color codes (e.g., #FF5733 for red); 2) Memory addresses (e.g., 0x7FFF); 3) Representing byte data (75% shorter than binary); 4) Hash values and UUIDs; 5) MAC addresses; 6) Port numbers. Nearly all programming languages support hexadecimal literals with a 0x prefix (such as in C/C++, Python, Java, and JavaScript). Understanding hexadecimal is essential for low-level programming, debugging, and working with binary data.