== Learning Binary ==

Binary is a numeric system that uses the base 2 numeral system. There are only 2 usable digits 0 (or off) and 1 (or on). Binary is the heart of all electronic computers, including but not limited to personal computers, Macs, gaming controls, and cellphones. In computers the only thing it really does is switch between 2 states 0 or 1, from that many combinations we get our digital world as we have it today. In this portion I will be showing how to count in binary.
Take a look at the following:

Decimal	Binary
0	0
1	1
2	10
3	11
4	100
5	101
6	110
7	111
8	1000
9	1001
10	1010
11	1011
12	1100
13	1101
14	1110
15	1111
16	10000
17	10001
18	10010
19	10011
20	10100

Do you see the pattern?
   In the decimal system we start with 0, and there are 10 usable digits, 0-9. In binary like mentioned there are only 2 digits 0 and 1. In decimal once you get past 9 you simply increment the first digit to the left (if it doesn't exist then pretend its a 0) and start the sequence over. For example: 00,01,02,03,04,05,06,07,08,09 from here we increment to the next digit and start the sequence over again hence we get 10,11,12,13,14, etc.

 In binary its the same concept. 00,01 since 1 is our last usable digit we increment and start the sequence over hence 10,11 from here we repeat the same idea hence 100,101,110,111, etc. Now 100 shown here isn't actually 100 like we use in decimal its value is actually 4. Each place value is different, lets compare it to decimal system:

Note: the value 3,791 is randomly used in this comparison.
Decimal:

1000	100	10	1
3	7	9	1

Binary:

2048	1024	512	256	128	64	32	16	8	4	2	1
1	1	1	0	1	1	0	0	1	1	1	1

   In the decimal system you multiply the number of its place value, and then add the result of each multiplication. So you take (3x1,000) + (7x100) + (9x10) + (1x1) = 3,791.

   In binary it is the same process, just that the place values are different, and easy way to remember is it starts with 1 and is doubled each time. So (1x2,048) + (1x1,024) + (1x512) + (0x256) + (1x128) + (1x64) + (0x32) + (0x16) + (1x8) + (1x4) + (1x2) + (1x1) = 3,791. An obvious way to make this faster is ignore the multiplication part because if its 0 it doesn't add to the value and you can ignore it, and if its 1 just add the place value its because anything multiplied by 1 is equal to itself.

Here is a simple converter:

More information can be obtained here : http://en.wikipedia.org/wiki/Binary_number    

By the end of this lesson you will see there are 10 kind of people in this world those who know binary and those who don't.