Eli5: What is the real difference between analog and digital?

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I tried looking it up, and my brain just wasn’t making sense of it, but I haven’t had coffee yet so.

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Digital defines a finite set of values something can be. Analogue on the other hand can be any of an infinite set of values, as for any two values you can always find one between them.

Example: your battery voltage is analogue – it can be 3.7, 3.71, 3.701, 3.70000 … 00001, point being you can keep adding zeroes to infinity and getting a new value. Your phone however displays it as a rounded percentage – a digital value with 101 possible states (0, 1, 2, … 99, 100).

What this means in the real world is that digital values can be stored/copied without further reducing the precision – if you want to write down that exact percentage you only need 3 digits, however if you want to write down the exact voltage you’d need infinite digits – not something feasible in the real world.

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