Let’s start with the basics: data stored is stored in bits – a bit can have two states: 0 or 1. When you combine these bits, you’ll inevitably end with a system that works in the powers of 2’s, as you put it.
Now, why 0 or 1? Because its the easiest way to express data through magnetic or electrical charge. This is where the material used in storage comes in: you can use magnetic disks, that retain a positive or negative charge over a long time, to store sequences of 1’s and 0’s. This can also be done with circuits that keep a charge, same principle.
Okay so how does that become a hdd, for example? Well, hard disk drives are relatively primitive, essentially its multiple disks of that magnetic material stacked over another, with a motor attached to spin them and an arm with a sensor on it for ever disk, swinging over it to read the disk – its as mechanical as it gets.
But how did we compress that tech into usb-sticks? We took the mechanical component and made it digital: microscopic transistors that can hold a charge, even when no power us applied, are used to simulate what the hdd does via its magnetic disks.
Bonus fact: thats why these solid state drives are faster than any hdd – there’s no physical step in the process of reading storage.
I hope this answers your questions somewhat.
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