How do binary and hexadecimal numbers work?

This post is from a series I'm writing in which we'll learn how computers work, by writing a computer simulator in Javascript. However, I figured an explanation of binary and hexadecimal numbers is useful enough by itself, so here it is!

Before explaining how computers load data into their working space and process it, it's valuable to understand binary and hexadecimal numbers. This is because computer hardware only understands binary values due to the physical characteristics of the electronic circuitry used to implement them. I won't go further into explaining the reasons why computer hardware works with values in binary form, but you can read more about it here.

So what is binary? Binary is a 'base-2 number system'. But what does that mean?

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