Binary system explained (part 1)

Hi,
in the last post I showed cool trick, how to use your fingers to calculate to 1,023. It was based on binary system but I did not explain it much there. Here I will go through the conversion from binary to decimal system, that we normally use, and back.

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So all of these digits systems work with some number of symbols, 10 in decimal system for example. These digits means some number and when you run out of them you will just add another digit, for decimal system you have of course 0,1,2,3,4,5,6,7,8,9 and after 9 you have to start repeating previous symbols. Now if you think about it you could actually use this various ways, for example we write 10 but it could also be 00.

Binary system has 2 symbols only. 0 and 1. This means that you will have to use much more digits if you want to symbolise big number. Basically if you add one to number you display one higher symbol and you never skip any of them so there is given amount of numbers you can store in x number of digits. Because there are 10 symbols in decimal system you can display 100 different numbers (different combinations of these symbols) in two digits. From 0,1,2,3… to 97,98,99. This is 10² where the exponent is number of digits you have. For binary system the base will be two because you can store only two symbols in one digit. In two digits you can store 2² numbers.

This is good to know if we want to transfer from one system to the other, lets say that we have number in binary:

10011010

We want to change this number into decimal so that we understand it.
Every digit here stands for one of those exponents first digit (from the right) stands for 2º which is one and it either stores the number one or it does not. Since it is 0 and 0 is usually reffered to as empty, the first digit, again from the right, does not store any information[1].

2nd is for 2¹ and there is 1 which means that the information is there and we know that our final number (n) equals to the rest of the numbers plus 2.

We continue and there is no number on the next place but on the 3rd 2³ we have one which means that we remember this which equals 8. The next is 16 and the last one is even higher: 128. We now add all of them together to get 154 if I count right.

It is good to notice that with this system you can create any number you like because always this applies:

2ª=2^(a-1)+2^(a-2)+2^(a-3)..2^(1)+2^(0)+1

So
8=4+2+1+1

Because the post is quite long right now I will continue in the next post. I do not know when this will be because I am going on a trip this weekend and some days after but after I return there will definitely be new stuff 😉

Dragallur

[1]Same as zero in our system! If you have number: 00456 its just 456 of course that it is something different than 45600 where it moves the place where the numbers are but still it does not count to the final number!