Something I found while reading about base systems, I can’t really wrap my head around it. Maybe it has to do with fractions?
In: 41
Individual bases are just different choices of when you have to “carry the one”.
For example, in Base-II “Binary” we can count: 0, 1… but we can’t write “2” because that isn’t a legal symbol in Base-II so we have to “carry the one” up to the next slot of 10, 11, 100, 101, 110, 111, 1000… etc.
In Base-III “Ternary” we can count: 0, 1, 2… but we can’t write “3” because that isn’t a legal symbol in Base-III so we have to “carry the one” up to the next slot of 10, 11, 12, 100, 101, 102, 110, 111, 112, 120, 121, 122, 200… etc.
In Base-IIII “Quarternary” we can count: 0, 1, 2, 3, but we can’t write “4” because that isn’t a legal symbol in Base-IIII so we have to “carry the one” up to the next slot of 10, 11, 12, 13, 20, 21, 22, 23, 30, 31, 32, 33, 100… etc.
So maybe you can see the pattern.
In every “Base-N” you get to use N-different symbols {0,1,2,3… N-2, N-1} in each number slot… but because 0 one of those N symbols that means that “N” itself doesn’t have one-slot representation in that number system… you have to carry the one to show it.
Which means that if we like Base-IIIIIIIIII and decide to call it “Base-10” because 10 is 9+1=N to us… then things will get confusing if we ever have to talk to some Base-III people who called *their* system “Base-10” because 10 is 2+1=N to them.
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