Numeral systems history

  1. #2010-08-16: First version on my old website. Had positional notation; English, Spanish, and German number names; scientific notation, Roman numerals, medieval numbers, sexagesimal, and upside-down.
  2. #2013-11-18: Limited the length of unary numbers (to prevent crashes)
  3. #2013-12-24: Converting negative numbers to Spanish now says it's not supported rather than incorrectly converting to English. This version is still available, in case later versions don't work.
  4. #2015-03-03: Added fractions and English ordinals. Changed everything to use rational numbers.
  5. #2015-05-17: Added factorial base (and recursive factorial)
  6. #2015-07-08: Added Fouriest transform, Chinese numbers, and more buttons to change the current number
  7. #2015-08-04: Added factors. First version on
  8. #2015-11-11: Changed the title from "Numeric Representations" to "Number representations".
  9. #2016-04-22: Changed external links from http: to https: throughout my site whenever possible
  10. #2017-06-15:
    • Added quote notation, Fibonacci coding, and continued fractions
    • Changed the ordinary positional notation section to allow each row's options to be changed (instead of having everything be fixed and just one "other" row)
    • Moved sexagesimal to the ordinary positional notation section and made it so any base above 36 will act like sexagesimal
    • Removed "upside down" (which was just calculator writing)
  11. #2018-12-02: Reorganized my site so that this page is available from the new math page (and changed the breadcrumb)
  12. #2020-06-07: Changed xkcd forum links to point to the web archive :(. This version is still available
  13. #2021-05-22: Many changes including: added Gray code, general mixed base, Stern-Brocot coding; changed some things about the interface
    • Changed how the interface works. Previously, all options were just on the page. Now, you can click the name of the numeral system to see a list of options, and you can put any numeral system anywhere. My reasoning for doing it this way:
      • If you want to compare two numeral systems, it's now easier to put them next to each other.
      • I can now add more options without cluttering up the UI.
      • Hopefully now standard positional systems will fit horizontally on small screens (e.g. mobile).
      • When a numeral system has options, you can now always show different versions of that numeral system at the same time; e.g., you can see both Traditional and Simplified Chinese, or both directions of the Fibonacci coding, at the same time, whereas you couldn't before.
      • I can now make numeral systems available without making them visible by default. Upside down (calculator writing) is now available again (but not visible by default), and I've removed Fouriest and Medieval by default (but they're still available).
    • New numeral systems:
      • Gray code
      • General mixed base
      • Stern-Brocot coding
    • Added more options to fixed-base positional systems:
      • Repeating decimals can now be represented with parentheses (so 0.1(6) for 0.1666666666…).
      • There are options for how to display digits (these apply to some other systems as well).
      • Bases 0 and -1 now work.
    • Fixed some things relating to quote notation:
      • Fixed a bug where it gave incorrect results where there were multiple zeros after the decimal point.
      • The decimal point is now always visible, and quotes are now shown at the end of the number when possible (so -1 is now 9! instead of 9'9).
    • Moved some things around:
      • Split standard and nonstandard fixed-base systems into separate sections. Also added bases 6 and 20 by default.
      • There's now a section for mixed-base systems; previously, they were in "Other".
      • Moved continued fractions from "Other" to "Fractions".
      • Like I mentioned above, I removed Fouriest and Medieval Roman numerals by default.
    • Changed how numbers are represented, so it now gives more precise or exact results for more cases (especially if your browser supports bigints).
    • Changed the URL from /convert/numbers to /numerals/ (a bit shorter)
    • Some fields that used to be of type "number" are now of type "text". This means that up and down arrows won't appear on desktop, and mobile devices might default to the wrong keyboard. This is because "number" is too inflexible (doesn't support bigints, and some of these fields now accept fractions and square roots).
    • When inputting numbers, some not-quite-valid numbers may be interpreted differently.
    • Decimals now have a 0 in front (so 0.5 instead of .5); this made the code for mixed-base systems simpler, and it seems most programming languages and calculators do it that way.
  14. #2021-08-23: Added some more binary-related systems and square root representations, and an options to enter/display infinitely-repeating continued fractions
    • New numeral systems:
      • Floating point
      • Complements (ones' complement and two's complement are shown by default, and other bases are available)
      • Sign-magnitude (binary)
      • Square root representations (and minimal polynomials for square roots)
    • Moved gray code to the "binary" section
    • More options for a couple existing systems:
      • Gray code: for base 2, there's now an option to then convert it to some other base (which there also is for the new binary systems)
      • Continued fractions now have the option to use parentheses to indicate infinite repetition
    • Switch to a monospace font
    • Maybe fix some bugs