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The most important concept is to recognize the difference between a number and the data that represents it.

A number is an abstract concept, such as a count of something. You have ten fingers. The idea of "ten" doesn't change, no matter what representation you use: ten, 10, diez (Spanish), ju (Japanese), 1010 (binary), X (Roman numeral)... these representations all point to the same concept of "ten".

Contrast this with data. Data is a physical concept, a raw sequence of bits and bytes stored on a computer. Data has no inherent meaning and must be interpreted by whoever is reading it.

Data is like human writing, which is simply marks on paper. There is no inherent meaning in these marks. If we see a line and a circle (like this: |O) we may interpret it to mean "ten".

But we assumed the marks referred to a number. They could have been the letters "IO", a moon of Jupiter. Or perhaps the Greek goddess. Or maybe an abbreviation for Input/Output. Or someone's initials. Or 10 in base 2, aka 2 in binary. The list of possibilities goes on.



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