You have a heap of apples. Here:

	O O OOO   OOO
	OO OO OO OOO OO
	 OOOO OOO OOOO
	OOO  OOOO  OOOO

You might want to count them, so you put them in clear groups.

You might count them in tens:

	O  O  O  O  O
	O  O  O  O
	O  O  O  O
	O  O  O  O
	O  O  O  O
	O  O  O  O
	O  O  O  O
	O  O  O  O
	O  O  O  O
	O  O  O  O

You get four tens and one. You decide to denote "four" by a scribble resembling "4",
and "one" by "1", and you get "41". 41 apples, in decimal (base-ten).

But wait, maybe you count them in eights!

	O  O  O  O  O  O
	O  O  O  O  O
	O  O  O  O  O
	O  O  O  O  O
	O  O  O  O  O
	O  O  O  O  O
	O  O  O  O  O
	O  O  O  O  O

You get five eights and one. You decide to denote "five" by a scribble resembling "5".
You get a "51". It is 51 apples, in octal (base-eight).

But wait, maybe you count them in sixteens!

	O  O  O
	O  O  O
	O  O  O
	O  O  O
	O  O  O
	O  O  O
	O  O  O
	O  O  O
	O  O  O
	O  O
	O  O
	O  O
	O  O
	O  O
	O  O
	O  O
	
You get two sixteens, and nine. You decide to denote "two" by a scribble resembling "2",
and nine by a scribble resembling "9".
So, it is a "29". You get 29 apples, in hexadecimal (base-sixteen).

But wait, you forgot about two apples that were on the chair!
Let's add them into the grouping by sixteens:

	O  O  O
	O  O  O
	O  O  O
	O  O  O
	O  O  O
	O  O  O
	O  O  O
	O  O  O
	O  O  O
	O  O  O
	O  O  O
	O  O
	O  O
	O  O
	O  O
	O  O

So you actually get two sixteens, and eleven. You decide to denote "eleven" by a scribble resembling "B".
So, the number is "2B". You get 2B apples, in hexadecimal (base-sixteen).



But wait, we just got a new delivery of apples! Suddenly we have a mountain of apples!

Let's count the apples, by grouping them in tens again. This is what we got!

	O  O  O  O  O  O  O  O  O  O  O  O  O  O  O
	O  O  O  O  O  O  O  O  O  O  O  O  O  O  O
	O  O  O  O  O  O  O  O  O  O  O  O  O  O  O
	O  O  O  O  O  O  O  O  O  O  O  O  O  O
	O  O  O  O  O  O  O  O  O  O  O  O  O  O
	O  O  O  O  O  O  O  O  O  O  O  O  O  O
	O  O  O  O  O  O  O  O  O  O  O  O  O  O
	O  O  O  O  O  O  O  O  O  O  O  O  O  O
	O  O  O  O  O  O  O  O  O  O  O  O  O  O
	O  O  O  O  O  O  O  O  O  O  O  O  O  O

Wow. That's MANY tens, and three. "3"
We can only count up to nine. There's definitely more than nine tens.
How many tens, exactly? Let's find out, by grouping the TENS in tens!

        OOOOOOOOOO    OOOO
        OOOOOOOOOO    OOOO
        OOOOOOOOOO    OOOO
        OOOOOOOOOO    OOOO
        OOOOOOOOOO    OOOO
        OOOOOOOOOO    OOOO
        OOOOOOOOOO    OOOO
        OOOOOOOOOO    OOOO
        OOOOOOOOOO    OOOO
        OOOOOOOOOO    OOOO

Ahh, so there's ONE "ten ten", and four "tens". Let's scribble down, "1" and "4".
So we got "143" apples, in decimal.



NOW we also have some kiwis.

        &  &  &  &  &  &

Let's group them in twos!

	&   &   &
	&   &   &

That's... MANY twos, and zero. Let's indicate the zero by scribbling down, "0".
We can only count up to one! There's definitely more than one twos.
How many twos were there, exactly? Let's find out, by grouping the twos in twos!

	&&    &
	&&    &

Ahh... so there's ONE "two two", and ONE "two". Let's scribble down, "1", and "1".
So we got "110" kiwis, in binary (base-two)!


Then there are a few plums.

	@  @  @  @  @  @  @  @  @  @

Let's group them in twos!

	@   @   @   @   @
	@   @   @   @   @

Bummer... That's MANY twos, and zero. Let's write down, "0" in any case.
Let's group the twos in twos!

	@@   @@   @
	@@   @@   @

Ahh, nice. So there's ONE "two". Let's write down "1".
But way too MANY "two two"s! Let's group THOSE in twos.

	@@@@
	@@@@

Ohh, I see. One "two two two". Zero "two two"s remain. Let's add, "1" and "0".

So we got "1010" plums, in binary.

Now we might also group those plums in groups of sixteen...

	@
	@
	@
	@
	@
	@
	@
	@
	@
	@

Looks like we've got ZERO sixteens, and ten. Let's denote the "ten" by scribbling down "A".
We've got "0A" plums, in hexadecimal! The "0" is of course redundant, so we've got just "A".



This was a gentle introduction to how different numeric bases work.


Our extensible scribble dictionary:
	"zero"      = 0
	"one"       = 1
	"two"       = 2
	"three"     = 3
	"four"      = 4
	"five"      = 5
	"six"       = 6
	"seven"     = 7
	"eight"     = 8
	"nine"      = 9
	"ten"       = A
	"eleven"    = B
	"twelve"    = C
	"thirteen"  = D
	"fourteen"  = E
	"fifteen"   = F
	"sixteen"   = G
	"seventeen" = H
When writing binary, only "zero" and "one" (0 and 1) are used. There is no "two". One+one is "10".
When writing octal, only 0 through 7 are used. There is no "eight". Seven+one is "10". Seven+two is "11". Seven+three is "12".
When writing decimal, only 0 through 9 are used. There is no "ten". Nine+one is "10". Nine+two is "11". Nine+three is "12".
When writing hexadecimal, only 0 through F are used. There is no "sixteen". Fifteen+one is "10". Fifteen+two is "11". Fifteen+three is "12".


-- 
Joel Yliluoma
http://iki.fi/bisqwit/