Maurits wrote:
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Sven Groot wrote:
That doesn't make their computations base 232 or 264 all of the sudden. |
That is the crucial question... I am still not entirely convinced...
Are digital clocks base ten, or base (24, 60, 60)? Maybe it's just a question of semantics.
The numbering system we use define the base by the number of symbols there are. Our normal decimal system is decimal (base 10), because it has 10 symbols (0,1,2,3,4,5,6,7,8,9). Once you run out of symbols, you increment the symbol to the left by one. Hexadecimal has 16 symbols (0-9,A,B,C,D,E,F) and octal has only 8 (0-7). Binary has just two symbols (0,1). The D'ni in the computer game Myst have a
base 25 numbering system, because they have 25 distinct symbols.
In computer terms, this means that internally, numbers are used by having elements (transistors) that can have two different states (on or off, switched/not-switched, true/false, whatever you want to call it) that represents the 0 and 1. Larger numbers are formed by combining multiple elements in the same way we combine elements (digits) when writing down a number larger than 9.
Computer are not base 2
32 or even base 2
8, because they do not use that number of states. They use only two states, and make larger numbers by combining multiple elements. Thus they are base 2.
EDIT: Converting any system to any other system is trivial. You keep dividing by the base of the destination system. The result of the division is the next number you need to divide, the remainder the next digit in the result number.