Base Numeral Systems

First things first, you have to be familiar with different number bases. We normally use the decimal number system to count, written in Arabic numerals. When counting you go…

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, “10” 

Add 9+1, and you get “10”.
You can do this at any scale, so 999999+1 = 1000000
Whereas in different base number systems, you would reach “10” after counting different amounts. These amounts can be bigger or smaller than “10”.

In  hexadecimal (16) you count to “16”
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, “10”
This means that instead of 9+1 = 10, now “F+1=10”.

Let’s go smaller now…
In binary (2) you only need to count to “2”.
0, 1, “10”

It can be confusing to think of ten as not ten. I couldn’t do it, it felt like trying to learn a new language while only being allowed to use old notebooks. Every new concept I tried learning was competing with one I already knew.  Creating the Neonumerals was my way of grabbing a new book, and starting with a blank slate.

Quarters are Base-4.

When telling time 60 seconds is a minute, 60 minutes is an hour. 24 hours makes a day. 7 days make a week, ~4 weeks a month, 12 months a year.

Another incredibly important base used in all technology is binary, or base-2.
The strings of 0s and 1s you see in hacker movies? That’s binary.
It’s a 0 or 1 value, an on or off condition. It’s written in strings of 4, which can be read up to 15. Each “place” is a power of 2, and you read it by adding the values of each space which go… 8 – 4 – 2 – 1. So you read 1001 as “8 + 0 + 0 + 1 = 9”.

I’ll be mostly talking about base-2, base-4, and base-16. Later on there will also be base-3 and base-7.

Binary will be the most important to understand, but I will use quite a few of them interchangeably.