I just decided yesterday that I would try to make a lesson on binary; I don’t think anyone is that interested in binary but I’m just going to make it for future reference and for fun . (Note: I will have the tutorial in parts, each will have its own thread, this will leave plenty of space for questions)
Ok…(gathering thoughts), Before the days of languages, such as C++, C, Visual Basic etc., there was actually Intellectual people slaving away at computers typing up unending pages of machine code. So back then the average computer programmer had done Degrees in mathematics. 80% of the time the programmers had degrees anyway, this degree in mathematics helped a lot when it came to understanding the way a computer works.eg. The computers output of 1's and 0's. This being Binary.

At the core, Computers understand only one language, the binary code of 1's and 0's that represent on-off electric pulsations. Because this code is so difficult for people, programmers have built more concise ways of expressing the binary numbers that constitute, for example the contents of a computer's memory or the address in memory of each piece of data. Two numbering systems that can serve as convenient short hand for the binary (base 2) are octal (base 8 ) and Hexidecimal (base 16).

Because 8 is raised 2 to the third power (8 = 2 * 2 * 2), one octal digit is the equivalent of three binary digits, similarly, one hexidecimal digit represents 4 binary digits (16 is raised to the forth power). Also normal counting e.g. 0,1,2,3,4,5,6,7,8,9, is called (base 10), the reason why I didn’t write 0 to 10 is because 10 is just 1 and a 0 put together. This will make sense later

Now how to count in binary, it’s kind of like normal counting how we reach the maximum of 9 then we go back to 0, move over one space and put on a 1. But with just 1 and 0 it same concept you reach the max the move over one space and add something. I will first add a table of binary from 0 to 10 then I will explain after how it works out
Decimal | Binary
------- ------
0 | 00
1 | 01
2 | 10
3 | 11
4 | 100
5 | 101
6 | 110
7 | 111
8 | 1000
9 | 1001
10 | 1010
See binary is easy enough and if you leave out the first column you will notice that 4 - 7 looks like 0 – 3 and remember it’s just like going from 9 to 10 in decimal, except move over 1 place and add on a 1.