Binary Fundamentals - Part 1 - Binary

Binary, most of you have heard of it, and relayed it to Hacking, Coding/Programming, or even Matrix.
I will not deny the fact that binary IS related to these topics in some ways, but binary's first purpose is to make computer be "alive".

To explain binary, we will first need to give example and understand what binary is:
Imagine a human that talks in a special language, its made out of two words, "yes" and "no", it doesn't know how to talk in any other language, so if you will ask him how much is 1 + 1, or even just write 1 + 1 = ?, he will not understand you, as he doesn't know such languages. Same works the computer, it can "talk" only in 0's and 1's while 0 is no and 1 is yes.
But, then, how does it calculates? As you might not imagine anything does "yes + yes = no" etc.
So let's look at binary in a new aspect, a mathematical aspect:
You'd probably know the regular numeric system (1 + 1 = 2, etc.), but what if I would tell you, there are other numeric systems, to show you that they exist and how do they work, let's yet again view the normal numeric system.
It might seem stupid, but to show how other numeric and our numeric system works, we will need to count to 10, starting from 0:
0, 1, 2, ..., 9, 10.
You might've ask yourself, why would we count to 10, especially when starting from 0, so let me explain you, our numeric system have different names: Decimal, Base 10, and a few more names, why do I tell you that? Because we need these names, to be exact, one of them, Base 10, now I will ask you a simple question, why does it called Base 10? Why not Base 1 or any other number?
Some answers might be "All the numbers are made out of 0 - 9", "Counting to 10 is the most basic math" etc.
But, to understand the real reason, we'll take a look at our counting (from 0 to 10), you must agree that 0 = 00, 01 = 1, 02 = 2, etc.
But then, when it comes to 10, a thing happens, instead of 0 and the number, there is 0 and two numbers, 0 10.
Same happens with 100 (0 100) etc.
Why does this happen? Because the digit increase, basically Base 10 means the amount of numbers per digit until the digit increases, to be more clear I will show an example: the numbers 0 - 9 are the first digit (1's digit), and then, 10 - 99 are the second digit (10's digit), and so on forever, basically, in every "new" digit, we have 10 numbers (including 0) till the digit change (from 1's to 10's etc.).

Now, why did we discuss all that? Exactly because binary works the same way, but with 2 numbers instead of 10 per digit (Base 2), so, per each digit, only two numbers needed to increase the digit (0 and 1):
0, 1 and the digit increase. But, before we continue, unless you really want to get confused, I need to explain another thing:
by splitting the 10's from the 1's and 100's from 10's from 1's etc we can see that the numbers repeat themselves: 0 0, 0 1, 0 2, ..., 0 9 and then 1 0 (we start counting from 0 again, but with 1 instead of 0 before the number, etc.)

So, in binary it works the same, 0 0, 0 1, and then 1 0 (the digit increases and the counting starts again from 0), then 1 1, and the digit increases again, so 1 0 0, 1 0 1, etc.
To make it more clear, I will just show a way how to use incerment in binary.
Let's take the number 1 (0 1) and the number 1 again. In Base 10, 1 + 1 would be 2, but in binary, 2 is not existing in one digit as the limit of numbers per digits is 2 numbers (0 and 1), so, 1 + 1 would be in the next digit, so we add 1 in the 10's row, now we need to think logical, if 1 in binary = 1 in Base 10, then 1 + 1 that equals 2 in Base 10, is basically greater in 1 than the number 1, which means we need to find the next number in the Binary Numerical System, and so we find 10, which equals to 10.
A conclusion we can make after testing a whole lot of numbers (about infinity) is that each 1 that added to 1 (in same digit), its being replaced with 0 and adding a 1 to the next digit, and 0 does not affect anything: 1 1 + 0 1, so 1 + 0 = 1 (10's  row), but 1 + 1 = 10, (because we replace 1 + 1 with 0 and add 1 to next digit) but then we have 1 + 1 again in the 10's row (11 + 01 = 10 + 10), so we yet again replace 1 + 1 with 0 and add 1 to next digit (100 = 10 + 10), fortunatley there is 0 (011) so we don't need to repeat this action again.

At last, I will teach you how to convert numbers from binary to Base 10:
You count the amount of digits (let's say we have the number 10101, we have 5 digits), then decrease it by 1, and powering 2 by the number you get, while decreasing the power by 1 each time, and multiplying by the number (1 or 0) that you have in that digit: (^ is power, n is the amount of digits, m is the number in the n digit) 2^n-1 * m + 2^n-2 * m...
For a more explained tutorial on how to convert binary to Base 10, check out this link: http://www.electronics-tutorials.ws/binary/bin_2.html

That's it for now, if you have any issues, be sure to E-Mail me at bekerman122@gmail.com

Made by Eldar Bakerman, please do not claim as yours and credit it as Eldar Bakerman's