Have you ever wondered why we use 10 numbers in our everyday numbering systems, represented by the numbers 0 through 9, instead of, say, 8 or 17 or why it's so easy for us to count by fives (5,10,15,20...) instead of by sevens? The bold fact is that humans have five fingers on each hand, totally 10 and our numbering system evolved from using our fingers to count up things. I'd happily bet that if we had six fingers on each hand, it would be quite natural for us to have 12 numbers in our base numbering system, say, zero through Þ. You've probably already groked this concept.
As just mentioned and you probably already knew, a number's base dictates how many numbers are used in the counting system. The most common bases are discussed next, but before that a brief detour on what --conceptually--a number means. Let's take the base-10 number, 28810
Note that I follow convention when a common base is not implied and explicitly state the base as a subscript to the number.
Decimal (base-10, or denary)
What does 28810 mean, exactly? This value explicates that this number encompasses two 100's, eight 10's, and 8 units. This can be succinctly shown as:
28810 = (2 * 100) + (8 * 10) + (8 * 1)
28810 = (2 * 102) + (8 * 101) + (8 * 100)
= 200 + 80 + 8
htun = (h * n2) + (t * n1) + (u * n0) where h=hundreds,t=tens,u=units
As read across left to right, each number increases the total value by that number * base to the power of its place. This notation will become useful when I show you how to convert any base into base-10/decimal in the next step. There's not much to say about denary until a few more steps.