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Base: In mathematics, a base is the number of single digits denoting different values in a positional numeral system, including zero. For example, the decimal system, the most common system in use today, uses base ten, hence the maximum number a single digit will ever reach is 9, after this it is necessary to add another digit to achieve a higher number.
Base 256 does indeed exists... and it would be represented by a system of 256 unique symbols... wether math can accurately allow them to be ASCII's or if there is limitations to this kind of thing, I don't know.
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