Base Conversion Calculator

A base conversion calculator converts numbers from one positional numeral system to another — for example, turning the decimal number 255 into binary (11111111), octal (377), or hexadecimal (FF). Every number we write is implicitly in a base: decimal is base 10, using digits 0–9. Computers use binary (base 2), programmers use hex (base 16) for compactness, and theoretical math explores bases like ternary (base 3) or duodecimal (base 12).

This calculator converts any number from a source base (2 through 36) to its decimal equivalent using positional notation (Σ digit × base^position), then converts the decimal to the target base via repeated division — the two-step process used by parseInt() and toString() in JavaScript. It displays all five standard conversions (binary, octal, decimal, hex, and custom target base) simultaneously, so you can see a single number in every common representation at a glance.

Any number in base b is a sum of digits multiplied by powers of the base. To convert from decimal to base b, repeatedly divide by b and collect remainders in reverse order.

The calculator uses JavaScript's parseInt(input, fromBase) and toString(toBase), which handle bases 2–36. For bases above 10, letters A–Z represent values 10–35. If the input contains invalid digits for the selected source base, an error message is displayed.

1. Enter the number: Type the number in the input field. Use digits 0–9 for bases up to 10; for hex and higher bases, use letters A–F (or A–Z for bases up to 36). The input is automatically uppercased.
2. Select source base: Choose the base that your input number is expressed in from the dropdown (binary, octal, decimal, hex, or custom).
3. Select target base: Choose the base you want to convert to. All five standard conversions are always displayed, but this controls the "custom" result card.
4. Read all conversions: Binary, octal, decimal, hexadecimal, and your custom target base are all shown simultaneously.

Base conversion is essential in computer science and programming. Binary is the native language of hardware; hex provides a compact, human-readable shorthand (two hex digits = one byte). Debugging memory dumps, configuring network masks, and setting file permissions all use base conversion. In digital electronics, octal was historically used for 12-bit and 36-bit computer architectures because groups of three bits map cleanly to octal digits.

Beyond computing, different bases have cultural and mathematical significance. The Babylonians used base 60 (sexagesimal), which survives in our measurement of time (60 seconds, 60 minutes) and angles (360 degrees). The Maya used base 20 (vigesimal). Understanding how positional notation works in any base deepens mathematical literacy and makes the decimal system less arbitrary.