Sometimes people ask me where "negative zero" (the name of my domain) comes from. Here's a quick computer science lesson to answer that question.

What is negative zero?

When we represent numbers in computers, we use binary. Let's suppose we're working with a single byte, which is 8 bits. A "bit" is a one or a zero, a single binary digit.

We can represent non-negative integers this way. For example...

Now, the question arises: How do we represent negative integers?

There are multiple options. One of them is called signed magnitude. In this representation, we reserve the first bit as the sign (0 means positive, and 1 means negative), and the rest of the bits represent the magnitude of the number (how far it is from zero, in either the positive or negative direction).

The positive examples above don't change, but now we also have...

As you might have noticed, 0 appears in both tables! That's right, with signed magnitude, we can represent both positive zero (0000 0000) and negative zero (1000 0000)!

Why did I choose the name "negative zero"?

Honestly, I just thought it was cool that the existence of a distinct negative zero was a consequence of this way of representing numbers. It's not much deeper than that.

So what's 0x80?

I use 0x80 as an account identifier online. It's short and easy to type and identify, but not easily pronounceable. (This is desirable since I don't really want it to be a "name".)

Working with binary is a pain. For that reason, we often represent numbers in hexadecimal (base 16) instead. Hexadecimal goes from 0-9, then A-F, for a total of 16 possibilities. Since 16 is a power of 2 (2⁴), binary and hexadecimal have a nice relationship: specifically, 4 bits can be represented as a single hexadecimal character, meaning that one byte can be represented by just 2 hexadecimal characters.

To indicate that hexadecimal is being used, we often precede hexadecimal strings with "0x". For example...

...and so on. As you can see here, 0x80 is just negative zero as a single byte signed magnitude integer.