## Sunday, November 15, 2009

### Binary code

Hello lads!!! No time no see... Read this article to find out how to convert a number into a binary code or reverse...
First, let's say that binary code is a line of n numbers 1 or zero...
e.g. this 1001100...
If we take it logically 1 represents true and 0 false. If we had an electronic circuit, 1 means that electricity runs through it and 0 it's not...
So, let's go to the mathematical part now... Think about a calculator... How does it understand numbers and how does the calculations? With binary code... We are now going to see how the binary code represents a number leaving the engineering part out of this unit.
Think about a table of one column or row that has n cells... In that cells we put 1 (one) or 0 (zero). The function that returns the decimal (normal) number is working like this:
The first cell represents the 2^0, the second 2^1 the third 2^2.... It's like this:
the table:
index
0
1
2
3
4
.
.
.
n
If in a cell there's the number 1 we add 2^index and we add nothing if there's a zero.
Remember that in a line the index 0 represents the last number we see...
Let's look an example.
example 1. Find the decimal number that is represented by the binary : 1001110
1001110=0x2^0+1x2^1+1x2^2+1x2^3+0x2^4+0x2^5+1x2^6=0+2+4+8+0+0+64=78
In the above example we see a zero in the cell with index 0 so we ignore it or we multiply 2^0 with zero (it is the same thing, duh!).
Now if we have a number e.g 100 we do reverse work. we found the number power of 2 that is the closest to our number. In this case it is the number 64 i.e 2^6. 100-64=36. 32 is the closest, 32=2^5. 36-32=4. 4=2^2. So we are going to put the number 1 in the cells with index 6, 5 and 2. 100=1100100