https://xkcd.com/2835

Alt text:

So what do we do when we get to base 10? Do we use A, B, C, etc? No: Numbers larger than about 3.6 million are simply illegal.

    • 22rw@feddit.deEnglish
      20·
      1 year ago

      According to this article, the factoradical system gets efficient for numbers larger than 20!, but i guess this here is a shining example of less is more is less

      • Sanyanov@lemmy.worldEnglish
        1·
        11 months ago

        It begins to improve related to regular base-10 after, well, 10!, but it takes a while to recover for lower base numbers before that.

      • Spuddaccino@reddthat.comEnglish
        19·
        1 year ago

        The idea is, each number is expressed as a sum of n factorials, with n being the number of digits in the number post-conversion. You start with the highest factorial that you can subtract out of the original number and work your way down.

        1 becomes 1, because 1 = 1!, so the new number says “1x(1)”.

        2 becomes 10, because 2 = 2!. The new number says “1x(2x1) + 0x(1)”.

        3 becomes 11, because it’s 2 + 1. The new number says “1x(2x1) + 1x(1)”.

        21 becomes 311: 4! is 24, so that’s too big, so we use 3!, which is 6. 3x6 = 18, so our number begins as 3XX.
        That leaves 3 left over, which we know is 11. The new number says “3x(3x2x1) + 1x(2x1) + 1x(1)”.

      • quindraco@lemm.eeEnglish
        10·
        1 year ago

        I appreciated them correcting Randall’s bad alt-text math - he was off by a power of ten!

  • notabot@lemm.eeEnglish
    21·
    1 year ago

    Good grief, it’s far too early in the morning for this sort of thing. My brain hurts now.

    • jasory@programming.devEnglish
      1·
      1 year ago

      Not really. The reality is that the only real metric for the utility of a notation is the speed of computation. A constant positional notation system is the most efficient, then you just optimise for a base whose multiplication table can be memorised (27 is a good one). Many people are under the impression that highly composite bases are better, but the reality is that it only optimises for euclidean division which is far out weighed by multiplication and addition (and can be easily computed using them).

  • Classy@sh.itjust.worksEnglish
    7·
    1 year ago

    0 = 0

    1 = 1

    2 = 10

    3 = 11

    4 = 20

    5 = 21

    6 = 100

    101, 110, 111, 120, 121,

    200, 201, 210, 211, 220, 221, 300, 301…

    Amidoinitrite