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Base Conversion Question Generator

Converting between bases is arithmetic with a trap in it: the digits change, the number must not. Every question here is checked by parsing the answer back in its own base and requiring the original value, which is exactly what a conversion promises and what a mistyped hexadecimal digit breaks. Between binary and hexadecimal there is a shortcut worth knowing — group the bits in fours — and the working points it out where it applies.

What this generator does

Picks a value and two different bases from binary, octal, decimal and hexadecimal, and asks for the conversion. The working shows the repeated-division method and names the shortcut where the two bases are both powers of two.

How to use this tool

  1. Choose the level, which decides which bases are in play.
  2. Convert the number, either directly or through decimal.
  3. Reveal the answer to check your digits.
  4. Seed a question if you want the same one again.

Understanding the controls

Level
Gentle uses binary and decimal only with values under 64. Standard opens up all four bases, and stretch raises the values to four digits of hexadecimal.
Seed
Reproduces the same conversion question from a word you choose.
Show the answer
Reveals the converted digits along with the division working behind them.

Common use cases

  • Practice for a computing course where bases come up constantly
  • Drilling hexadecimal digits above nine, which is where most errors are
  • Showing the four-bit grouping shortcut on a real pair of numbers
  • Keeping to binary and decimal while the idea is still new
  • Setting the same conversions to a group from a seed

How this generator works

The value is drawn first and rendered in both bases, so the question and the answer are two views of one number rather than two calculations. The check parses each rendering back in its own base and requires both to give the original value.

Randomness and fairness

The value and the pair of bases are random; the digits follow exactly. Seeded questions reproduce and are therefore explicitly not cryptographically secure. Without a seed the browser's cryptographically secure generator is used.

For how randomness is produced across the whole site, see how Generate Random works.

Limitations and good to know

  • Only bases 2, 8, 10 and 16 — the ones a computing course actually uses.
  • Whole numbers only, so fractional binary and fixed-point representations are not covered.
  • Negative numbers are excluded, which means two's complement is out of scope.
  • One conversion per question rather than a chain through several bases.
  • A conversion set lasts only as long as the tab; seed one to keep it.

Privacy and your data

Values and conversions are computed in your browser. Your seed and settings are never transmitted or remembered.

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