Number Base Converter

Using the Number Base Converter

1. Click an input base - Binary (2), Octal (8), Decimal (10), or Hexadecimal (16) - to tell the tool which numeral system you are typing.
2. Type your number. The input field filters keystrokes so only digits valid for the selected base are accepted; pasting a string with invalid characters shows a validation message.
3. Read all four representations at once. The output panel shows binary, octal, decimal, and hexadecimal side by side and updates on every keystroke.
4. Copy any single representation with the Copy button next to each row, or copy them all using the Copy All action.
5. Switch bases mid-session without losing your work; picking a new input base re-interprets the typed value if it is valid, or prompts you to clear it if not.

How the Conversion Actually Works

Conversion between bases goes through an integer intermediate. JavaScript's parseInt(string, radix) parses the input into a native number; (number).toString(radix) emits it into each target base. The radix parameter is the key: it tells the parser and formatter how many distinct digits to use (2, 8, 10, or 16 here). Hexadecimal uses case-insensitive A-F for 10-15; binary uses 0 and 1 only; octal uses 0-7. The conversion is mathematically exact for any integer up to Number.MAX_SAFE_INTEGER, which is 2⁵³-1, or 9,007,199,254,740,991 in decimal.

All four output rows are computed at once rather than piped from the current output, so if you change the input base the already-parsed integer regenerates all four strings from the same source. This avoids the subtle bug where repeated conversions accumulate rounding error, which matters at boundaries near the safe-integer limit. Everything runs client-side; there is no server involved, no analytics event carries the number, and the state is discarded on tab close.

Where Base Conversion Comes Up

• Reading or writing hexadecimal colour codes (#FF8800 is R=255, G=136, B=0) when you know the decimal RGB you want.
• Decoding file permission bits (chmod 755 = 111 101 101 in binary, three bits per octal digit).
• Debugging a protocol capture where packet fields are shown in hex and you want the decimal value.
• Understanding an embedded systems datasheet that expresses register defaults in binary and actual values in hex.
• Translating between IPv4 numeric ranges (decimal dotted quad) and their hex representations for CIDR math.
• Learning or teaching the positional notation that underlies every number system humans use.

Validation and Edge Cases

• Invalid digits for the current base are blocked at the input. Typing "9" when octal is selected does nothing; typing "G" when hexadecimal is selected shows an error.
• Leading zeros are preserved in binary display for readability but have no mathematical meaning; 0b00001010 and 0b1010 are both 10.
• Case-insensitive hex input. "FF", "ff", and "Ff" all parse to 255. Output is always uppercase because it is the more common convention in programming.
• Maximum safe integer is 2⁵³-1 (9,007,199,254,740,991) because JavaScript's number is a double. Larger values lose precision silently; the tool flags inputs beyond this bound.
• Negative numbers are displayed with a leading minus in each base; two's complement encoding is not applied because it depends on the bit width you are targeting.
• Fractional parts are not supported in this build. Converting 0.1 between bases is a famously surprising operation (0.1 decimal is an infinite repeating binary fraction 0.0001100110011...), which the tool sidesteps by accepting integers only.

A Primer on Positional Notation

Positional notation represents a number as a sum of digit-times-power-of-base terms. The decimal 437 is 4 * 10² + 3 * 10¹ + 7 * 10⁰. The binary 1011 is 1 * 2³ + 0 * 2² + 1 * 2¹ + 1 * 2⁰ = 11. The idea is Sumerian (base 60, around 3000 BCE) and Indian (base 10 with zero, codified by Brahmagupta in 628 CE); binary was studied by Gottfried Wilhelm Leibniz in 1703 in his Explication de l'Arithmétique Binaire, which he saw as mystically significant. Hexadecimal became a programming standard with the IBM System/360 in 1964 because 4 bits cover one hex digit and 8 bits (one byte) cover exactly two. ISO 80000-2 defines the standard notation: subscripts for bases (25₁₀, 11001₂) and prefixes (0b, 0o, 0x) for the programming conventions.

When to Use a Language or CLI Tool Instead

For one-off conversions in a terminal, printf "%x\\n" 255 (bash), (255).toString(16) (Node), hex(255) (Python), or bc -q <<< "obase=16; 255" all do the job with zero UI overhead. IDE plugins for hex-decimal conversion are common; macOS Calculator has a Programmer mode, Windows Calc has a Programmer mode with bitwise operations alongside base conversion. For arbitrary-precision base conversion (hundreds of digits), Python and GMP handle it natively while JavaScript's number caps out at 2⁵³-1; BigInt plus .toString(radix) is the right path in JS. The browser tool wins when you need to see all four bases at once - spotting that a value is a round number in hex but not decimal, for example - and you do not want to open a REPL.