Digital Wanderer

Северокорейский лидер Ким Чен Ир и вправду величайший в мире вождь! Согласен с ним по всем пунктам!
Курильщиков Ким Чен Ир называет "одними из трех типов дураков XXI века". Двумя другими он считает тех, кто ничего не знает о музыке и компьютерах.

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   Having sorted out the geopolitical situation, let's move on to the mathematical part. What does "good" or "bad" quality mean? Unlike the recent discussions about Esperanto and Film vs Digital, which I foolishly waded into, there are pretty strict criteria for evaluating blanks.
To start off - a little example from the world of digital data storage.
   Let's say we need to store eight numbers, each of which is a one or a zero (as we know, computers like ones and zeros, they have this weird quirk, they can't stand other digits). Let's take these: 0 0 1 0 1 0 1 1. How do we check that when reading from the disc we read exactly what we were supposed to, and didn't make a mistake? Add a ninth one, which will control the correctness of the previous ones. But how do we do that? Bright minds came up with this trick: we take all the previous numbers, add them up, do an integer division by 2 and take the remainder. This remainder will be that ninth number, verifying the correctness of the previous ones.
0+0+1+0+1+0+1+1=4
4 / 2= 2 and a remainder of 0
So we get : 0 0 1 0 1 0 1 1 0
Now suppose that one of the numbers was read from the disc incorrectly, namely the first one.
1 0 1 0 1 0 1 1 0
Let's run the operation described above.
1+0+1+0+1+0+1+1=5
5 / 2 = 2 and a remainder of 1
But the control number we read is 0! That means either the ninth (control) number, or one of the eight was read incorrectly.
   What I've provided above - is a primitive scheme for data integrity checking. It is capable of finding only single errors - if two numbers out of eight change at once, it will show that everything is in order. And it is not capable of correcting errors - to do that, you'll have to try reading the data one more time.
  On CDs, and especially on DVDs, complex schemes of redundant coding are used, allowing you not only to find errors, but also to correct them, if their quantity is within reasonable limits. This is done to mitigate the inevitable defects in the material of the blanks, errors in the DVD drive mechanics and laser operation. If the described schemes didn't exist, DVD drives and computers in general would cost colossal amounts of money, would work extremely unreliably and slowly, because producing perfect transistors, blanks, and lasers is incredibly expensive, and sometimes outright impossible. And of course, without error checking and correction, the emergence of our beloved internet would have become impossible.

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