Number Base Converter

Convert numbers between binary, octal, decimal, hexadecimal, and any custom base.

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1. Select the input base: binary (2), octal (8), decimal (10), or hexadecimal (16). 2. Enter your number using valid digits for the selected base. 3. View the number converted to all four bases simultaneously. 4. Binary output is grouped in 4-digit clusters for easy reading. 5. Click the copy button next to any base conversion to copy it.

About This Tool

The Number Base Converter transforms numbers between different numeral systems - binary (base 2), octal (base 8), decimal (base 10), hexadecimal (base 16), and any custom base from 2 to 36. Enter a number in any supported base and instantly see its representation in all other bases. The tool handles both integer and fractional numbers.

Number base conversions are essential in computer science and digital electronics. Binary is the language of computers, hexadecimal is used for memory addresses and color codes, and octal appears in Unix file permissions. Understanding how to convert between these systems is a fundamental skill for programmers, engineers, and anyone working with digital technology.

The converter provides clear, formatted output with digit grouping for readability (such as spacing binary digits in groups of 4). It validates input for each base (ensuring you do not use invalid digits), supports copy-to-clipboard for each result, and shows the conversion process step by step for educational purposes.

Formula / How It Works

Value = sum of (digit x base^position) for each digit | Decimal to base b: repeatedly divide by b, collect remainders

Frequently Asked Questions

The most common bases are binary (base 2, using digits 0-1), octal (base 8, using digits 0-7), decimal (base 10, using digits 0-9), and hexadecimal (base 16, using digits 0-9 and A-F). Decimal is what we use in everyday life, while the others are critical in computing.
Multiply each binary digit by 2 raised to the power of its position (starting from 0 on the right), then sum the results. For example, 1101 in binary = 1x2^3 + 1x2^2 + 0x2^1 + 1x2^0 = 8 + 4 + 0 + 1 = 13 in decimal.
Hexadecimal is compact and maps cleanly to binary - each hex digit represents exactly 4 binary digits. This makes it much easier to read large binary values. For example, the binary number 11111111 is simply FF in hex, which is much more readable.
Hexadecimal uses 16 digits: 0-9 for values zero through nine, and A-F for values ten through fifteen. The letters can be uppercase or lowercase. For example, hex 2A = 2x16 + 10 = 42 in decimal.
Base 36 uses digits 0-9 and letters A-Z, making it the highest base that uses standard alphanumeric characters. It is sometimes used to create short, compact representations of large numbers, such as in URL shorteners or unique identifiers.

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