What's a Bit? Binary Numbers
 
Ok, When I said I wouldn't have to explain binary numbers and how the computer counts ,,, I lied.
Below is my quick and dirty binary number explanation. Very quick and very dirty. I've included some links to other web sites at the bottom of this page that may explain better.
 
The confusion is that the computer doesn't use the standard base 10 number system. The computer only uses the numbers 0 and 1. It counts in the base(2) or binary system.
 
This is a complicated topic but I'll try to be brief.
Remember back to when you learned to count numbers. The number 1251 was taught as
1 in the    1's column
5 in the   10's column
2 in the  100's column
1 in the 1000's column
--------------------------
1+50+200+1000 = 1251

This is called the Base(10) system because each column is 10 times greater than the last

Read numbers in the Binary, Base(2) system in the same maner

Read the number from RIGHT to LEFT.
The first  column is the number of 1's
The second column is the number of 2's
The third  column is the number of 4's
The fouth  column us the number of 8's
Etc, Etc
Each column is 2 times greater than the last.

8's 4's  2's  1's

So the binary number 1011 would be
1 in the 1's
1 in the 2's
0 in the 4's
1 in the 8's

or 1+2+0+8 = 11 in base(10)


Here are the numbers 1-10 in Base(10) and Base(2)

Base  Base
 10     2
----------------
 0      0
 1      1
 2     01
 3     11
 4    100 
 5    101
 6    110
 7    111
 8   1000
 9   1001
10   1010

Another way to look at this data is to assume that you have an 8 bit number, then
determine how high can you count using this many bits of data.

# of 
bits		Example				Base 10
-------------------------------------------------------------
 1		1				1
 2		11				3
 4		1111				15
 8		11111111			255
16		11111111 11111111		65,535
24		11111111 11111111 11111111	16,777,215

This chart is more commonly shown as below, where the number zero is included in the total.
The number of bits is called the "Bit Depth".

Bit	Total 
Depth	Numbers
------------------
1	1
2	4
4	16
8	256
16	65,536
24	16,777,215
32	4,294,967,296
The only special case is the TIFF file which can be stored as a 32 bit color file. This is not a file with 4 billion colors. Rather it is a file with 16 million colors and each pixel has a 8 bit number added to show 256 variations of transparency. This is called the Alpha channel.
 
For More detailed information
Binary Number Tutorial
Binary Number Systems