## Understanding Binary, Hexadecimal and Octal Numbers

- None

### Understanding Decimal Notation

So, you know about decimal notation, right? It's the one you sue every day when working with numbers. Let's take it apart, to see if we can leverage what we find to understand the other types of notation-
$$123.45$$
This number is all we need to understand those mechanics. Okay, so what *does* this number mean? A hint would be to look at the "word"-form of this number - "A hundred and twenty three point four five". This number is a *representation, a notation* of the sum of the following numbers - $1\cdot 10^2,\space 2\cdot 10^1, \space 3 \cdot 10^0,\space 4\cdot 10^{-1},\space 5\cdot 10^{-2}$, which yes, are themselves are representations, but they're elementary enough for us to not need to break them down to know how they work. The exact same notation is used in every other number system

### A bit of terminology

OK, before we start learning about this stuff, we need a bit of terminology knowledge. It's not much, so here we go

- Number system $\implies$ A way of representing numbers
- Base $n$ $\implies$ A number whose digits go from $0$ to $n - 1$, with a total of $n$ digits. The numbers themselves should scale with powers of $n$ when going beyond the value $n - 1$
- When all existing numbers have been exhausted ($0, 1, ... 9$), usually, alphabets are used (but sometimes, Greek alphabets are used like in the case of the dozenal system which is arguably better than the decimal system)

## The numbering systems of digital logic

Now, strictly speaking, the numbering system for digital logic is binary (base 2), but octal(base 8) and hexadecimal(base 16) provide convenient ways of compacting the long binary numbers, so we study them as part of digital logic, in fact, you'll probably see hexadecimal the most. But either way, let's start with binary.