DIGITAL SIGNAL | Mediateca de EducaMadrid

Alright, let's jump right in. Have you ever stopped to think about how the world you actually experience, 00:00:00

you know, with all its smooth sounds and continuous colors, somehow gets crammed inside your phone? 00:00:05

It's because our world and our gadgets speak two totally different languages. 00:00:11

Today, we're going to crack the code and learn how to speak both. 00:00:15

So, let's start with a really simple question. How do computers even talk? 00:00:19

I mean, they don't understand sunlight or sound waves the way our brains do. 00:00:23

they need a translator, a way to turn our world into a language they can actually understand. 00:00:27

And that brings us to these two completely different worlds. On one side, you have analog. 00:00:33

Think of this as the language of nature. It's smooth, it's continuous, and it has an infinite 00:00:38

number of shades and tones. But on the other side, you've got digital. That's the language 00:00:43

of computers. It's chunky, it moves in distinct steps, and it only uses a limited set of values. 00:00:48

Okay, let's really dig into this. 00:00:54

How does this huge difference between a smooth, flowing reality and this kind of step-by-step data 00:00:56

actually work in the world around us and, you know, inside all the electronics we use every single day? 00:01:02

First up, let's talk about the analog signal. 00:01:07

The best way to think about it is like a ramp. 00:01:10

It's a perfect, smooth reflection of reality. 00:01:13

Its value changes continuously. 00:01:15

There are no breaks, no jumps. 00:01:18

Between any two points on that ramp, there's an infinite number of other points. 00:01:20

It's just a completely smooth, unbroken line. 00:01:24

And you are literally swimming in analog signals all day long. 00:01:27

I mean, the temperature doesn't just leap from 70 degrees to 71 degrees, right? 00:01:31

It flows through every single possible value in between. 00:01:35

And it's the same for the brightness of a light, the sound waves coming from a guitar, or the pressure of the wind. 00:01:39

It is all smooth, continuous change. 00:01:44

Now, let's flip the coin and look at the digital signal. 00:01:47

So if analog is a smooth ramp, think of digital as a staircase. 00:01:51

It's not a continuous flow at all. 00:01:56

It's just a series of very specific, separate steps. 00:01:57

It can only be one value or another. 00:02:01

You're either on this step or you're on that step. 00:02:03

There's absolutely nothing in between. 00:02:06

And this right here? 00:02:08

This is the heart of it all. 00:02:10

The simplest, most basic digital signal is called binary. 00:02:12

It's the native language of all electronics, and it has only two states. 00:02:16

That's it. 00:02:20

A high voltage, which we call a one, and a low voltage, which we call a zero. 00:02:21

It's just on or off. 00:02:25

That is the entire alphabet. 00:02:27

So hold on. 00:02:29

If computers can only understand on and off, just ones and zeros, how on earth do they 00:02:31

manage to represent a super complex photo or a beautiful piece of music? 00:02:36

Let's get into it. 00:02:41

Well, to understand how computers count, it really helps to first look at how we count. 00:02:42

We use the decimal system, right? Or base 10. It's probably because we have 10 fingers. 00:02:46

It gives us 10 symbols to work with, 0 through 9, to build any number we can possibly imagine. 00:02:51

And in our system, where you put the number is everything. Take 358. It's not just a 3, 00:02:57

a 5, and an 8 next to each other. We all know it's 300s plus 5 10s plus 8 1s. 00:03:03

Each position is a power of 10. We've been thinking this way our whole lives. 00:03:08

Okay, so computers take that exact same idea and they just simplify it, radically. They use binary 00:03:13

or base 2. So instead of 10 symbols, they only have 2, 0, and 1. We call each one a bit. And this 00:03:20

isn't just a random choice. It's brilliant, because it perfectly matches the physical reality of an 00:03:27

electrical circuit. Is there a low voltage? That's a 0. Is there a high voltage? That's a 1. Simple. 00:03:32

And, check this out, this chart is basically the translation guide. 00:03:38

On the left, you've got the decimal numbers we use every day. 00:03:42

And on the right, that's how a computer writes them. 00:03:45

So our number 2 becomes 0010. 00:03:48

Our number 7 becomes 0111. 00:03:51

It's a totally different alphabet used to write the exact same things. 00:03:54

So we have the analog world we live in, and we have the digital alphabet, computers speak. 00:03:57

So the next logical question is, how do we translate between the two? 00:04:03

This right here? 00:04:07

This is the aha moment where it all clicks. 00:04:08

And this magic trick? 00:04:11

It's called digitization. 00:04:12

This is the process, the bridge that connects the physical world to the world that exists 00:04:14

inside our computers. 00:04:18

It's how we translate that smooth, analog signal into a bunch of discrete digital numbers. 00:04:20

So how does this translation actually happen? 00:04:25

Let's just walk through it. 00:04:28

First, you start with that smooth, analog signal, like a sound wave. 00:04:29

Second, at super regular fixed moments in time, 00:04:33

you measure its value. 00:04:36

This is called sampling. 00:04:37

It's like taking thousands of little snapshots. 00:04:38

Third, each one of those snapshots gets converted 00:04:41

into its closest binary number. 00:04:43

And what you're left with at the end 00:04:45

is a clean, simple sequence of zeros and ones 00:04:46

that represents that original sound. 00:04:49

And here is the absolute key takeaway. 00:04:51

Just look at how that stepped blue line 00:04:53

tries to follow the smooth gray curve. 00:04:55

The digital signal is never a perfect, 00:04:58

identical copy of the analog wave. 00:05:00

it can't be. Instead, it's a very, very close approximation, one that's built from thousands 00:05:02

or even millions of those tiny, discrete snapshots. But you might be asking, why go through all this 00:05:08

trouble just to create an approximation? Why not stick with the original? Well, what makes this 00:05:14

whole process so incredibly powerful is the big payoff. And here it is. This is the whole reason 00:05:20

we do it. Once information is converted into a clear sequence of ones and zeros, it becomes 00:05:26

incredibly tough, incredibly robust. You can store it, you can copy it a million times perfectly, 00:05:32

and you can send it across the world without it getting easily messed up by noise or static. 00:05:37

And you have absolutely seen this for yourself. Remember the snow and static you'd get on an old 00:05:42

analog TV during a thunderstorm? Now think about a digital broadcast today. It's either perfectly 00:05:48

clear or it's just not there. It doesn't get fuzzy or degrade. And that's because the receiver 00:05:53

only has one job. Figure out if the signal is a one or a zero. It can completely ignore all that 00:05:59

messy static in between. And that leads us to a final, really fascinating question to think about. 00:06:05

We've seen that this digital world with all its perfect clarity is built on an approximation of 00:06:10

our real analog world. It's a world made of snapshots, not a continuous flow. So the question 00:06:15

to leave you with is this. 00:06:21

In that translation, 00:06:22

from the infinite to the finite, 00:06:23

what, if anything, 00:06:25

actually gets lost? 00:06:26

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