Re: On Binary Digits

Ben Collver <bencollver@tilde.pink> wrote or quoted:

With them the computers can represent any finite quantity

  Computers /can/ represent /infinite/ quantities just as well,
  for example: "ℵ₀", "∞".

  Computers (and humans) /can't/ represent "any finite quantity".
  With the usual notation system for integers, like "0101"2 = "3"10,
  some finite numbers are just too large. To write down some
  finite numbers with that system, one would need to write more
  digits than there are elementary particles in the universe.

  However, what matters is not the value of a number, but how
  many of them you want to represent. Say, you use this code:

bit
state  meaning
0      the number 0
1      the number 100^100^100^100^100^100^100^100^100^100^100^100^100^100

  . Now, 100^100^100^100^100^100^100^100^100^100^100^100^100^100 is
  a very large number (^ is right-associative!). But using this code,
  it's represented by the bit "1". We need only one single bit,
  because we chose to represent just /two/ different values.

The number 31337 could be represented as:

  Ha, that's "Eleet"!

  Yeah, back then, binary numbers got a lot of attention - something
  we'd see as just a technical detail nowadays. It's kind of like
  trying to explain what people are, saying they're mostly made
  up of water, and then diving into hydrogen and oxygen.