Binary system - الدحيح
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00:00I can't believe it! I'll see your fiancée who looks like Ahmed El Saqqa!
00:06Finally!
00:07I can't believe it! I found my dream girl!
00:12What's this?
00:13Mustafa!
00:14Good evening!
00:15Is this the one who looks like Ahmed El Saqqa?
00:17Yes, my girl!
00:18He looks like him in the way he looks!
00:20Look, he has a mustache, a moustache, and a hair like him!
00:24Okay, he doesn't have a lot of hair, but he's a genius!
00:29Right, Mustafa?
00:30He's a genius!
00:31Try asking him a difficult question!
00:33For example, how much is 2 plus 2?
00:374
00:38Wow!
00:39How much is 4 divided by 2?
00:422
00:43He's a human calculator! What do you think?
00:45Look, he really has unmatched computational abilities!
00:48Touch wood!
00:49But he doesn't look as handsome as us!
00:54By the way, I heard about you, Mr. Sagi!
00:56Yes, I know, but I'm not interested!
00:58Oh, I don't have any dignity at all!
01:00Go ahead!
01:01Sagi, it's not just math! It's anything else!
01:07Okay, what's Sheikh Zayed's capital?
01:10Arkambol, unfortunately!
01:11Oh! Okay, I can see!
01:14Sagi, I've always been proud of you!
01:17A rich, strong, handsome, and masculine groom!
01:21But it's time for you to accept the fact that he's a bit of a monster!
01:25He's ugly!
01:27He's a man-eater!
01:28Yes, that's right! I'm a man-eater!
01:30Also, Mustafa can't just split the cheque with his brain!
01:35Mustafa can read Arabic!
01:40No way!
01:42You can read Arabic?
01:43The series you're wearing is written on it!
01:46Mashallah!
01:48Oh my God!
01:49I've never been able to read this series!
01:53It's expensive!
01:54By the way, Mr. Sagi, can I marry two people?
01:58One plus one equals two!
02:02That's a lot of money!
02:12Hello, dear viewers, and welcome to a new episode of the show!
02:15This is a sports episode.
02:16It won't be as difficult as the previous episode,
02:19but there will be some small challenges.
02:21And it won't be difficult after you know it won't be difficult.
02:23Like I always say, it will be difficult in the end.
02:25Let me ask you a question.
02:26Before you ask yourself,
02:27why are our numbers made up of only 10 digits?
02:300, 1, 2, 3, 4, 5, 6, 7, 8, 9.
02:33Why?
02:34Because when we move on to the next one,
02:35we start to decide again.
02:361 and next to it, 0.
02:37If we're going to continue with them,
02:38we're going to have to put them next to each other in different ways
02:40to make bigger numbers.
02:41For example, 1967.
02:43The 10, the 100, the 80, the 50,000.
02:46They're all made up of the same numbers.
02:48According to some theories, humans made it easier.
02:50Why?
02:51Because we have 10 digits,
02:52so we can count on them.
02:5310 digits with 10 symbols,
02:54we're done.
02:55So if you're 33 years old,
02:56and you want to tell a stranger this information,
02:58but you don't speak the same language,
03:00you're going to put a 5 on his face,
03:01with both hands, three times,
03:02and he's going to ride a 10 like this,
03:03and then you're going to make him look like the king,
03:05and he's going to say,
03:06yeah, 63.
03:07Congratulations, you gave him the information.
03:09Even if you two don't speak the same language.
03:11What is this, my dear?
03:12You two used what's called the decimal system.
03:15My dear, the question I want to ask you here is,
03:17did all nations throughout history
03:19used this decimal system in their lives?
03:22The answer is no, my dear.
03:23Not all people throughout history
03:25used the decimal system.
03:26Many nations made different calculations
03:28for their lives and days.
03:29And many of them,
03:30we're going to continue with until today.
03:31Now, if you look, for example,
03:33you'll find that many of our calculations
03:34are not decimal.
03:35Where is this coming from, Abu Ahmed?
03:36I've always had decimal calculations.
03:37No, my dear.
03:38Look at the day, my dear.
03:39Today is 24 hours,
03:40not 10 hours.
03:41The minute is 60 seconds,
03:42not 10 seconds.
03:43The week is 7 days,
03:44not 10 days.
03:45All of this is not a decimal system.
03:46The week is a weekly system.
03:48The world cup is found every 4 years.
03:50If you look at history, my dear,
03:52you'll find that some nations,
03:53like the Babylonians for example,
03:54relied on what's known as
03:55the Sixth Decimal System.
03:57No, Abu Ahmed.
03:58The Sixth Decimal System.
03:59What is it in my country?
04:00It's the 60s system.
04:01Those, my dear,
04:02had 59 different numbers.
04:04And any number above 59
04:05needed,
04:06like we do in our dinner system,
04:08to rearrange the symbols
04:09next to each other
04:10to give us
04:11greater values than 59.
04:12According to some theories,
04:13the Babylonians found
04:14that 60 is a beautiful number.
04:15Joker's dream
04:16has many factors
04:17that accept many numbers.
04:19It accepts 1,
04:202,
04:213,
04:224,
04:235,
04:246,
04:2510,
04:2612,
04:2715,
04:2820,
04:2930,
04:30and 60.
04:31In the past,
04:32the Babylonians used to count
04:33in different ways.
04:34Look, my dear,
04:35you have a hand.
04:36The right hand.
04:37This week,
04:38we don't think of it
04:39as something that counts.
04:40So this hand counts 12,
04:41which is 1,
04:422,
04:433,
04:444,
04:455,
04:466,
04:477,
04:488,
04:499,
04:5010,
04:5111,
04:5212.
04:53So,
04:54for example,
04:55you have 25.
04:56What does 25 represent?
04:57It represents
04:58this,
04:59this,
05:0012,
05:01and a brain.
05:02If 5 is 7,
05:03it's 5 times 12,
05:04which is 60.
05:05It happens that
05:06every civilization
05:07has its own way
05:08of counting.
05:09Not all of them count
05:10the 10 or 60 symbols.
05:11These are
05:12completely optional symbols.
05:13It happens that
05:14people in certain places
05:15in a mathematical system
05:16know how to
05:17add,
05:18add,
05:19divide,
05:20divide,
05:21multiply.
05:22It doesn't matter.
05:23But how does a human
05:24know that
05:25a number of symbols
05:26can represent
05:27a large number
05:28with hundreds
05:29and thousands
05:30of symbols?
05:31No matter how large
05:32the number is,
05:33we are not talking about
05:34a limited number of symbols.
05:35A simple process
05:36breaks down
05:37this large number
05:38and makes
05:39a limited number
05:40enough to express
05:41a certain number.
05:42Abu Ahmed doesn't understand
05:43anything.
05:44Who's the one who wants to take you by the hand and go back to the days of your childhood?
05:48Do you remember, my dear, when you first came to learn math?
05:50Math class!
05:51The kids, when they came to learn the numbers,
05:53they used to take them from their hands to the library,
05:54and they would get the number, or the number of the plastic toy, do you remember?
05:57A plastic toy, with colorful balls.
05:59Our beautiful child, who hasn't seen it yet,
06:01would start dividing it, our number,
06:03into ones, tens, hundreds, and thousands.
06:05Suddenly, the child, who hasn't seen anything bad in his life,
06:07and his father tells him,
06:08Look, son, I want you to make a complicated number,
06:10like the number 1973.
06:12That's nice, Abu Ahmad, but how do you do that number?
06:14The child simply comes,
06:15one day, he puts a thousand,
06:16one day, he puts a thousand,
06:17and another day, he puts a nine,
06:18and another day, he puts a nine,
06:19and another day, he puts a hundred,
06:20and another day, he puts a seven,
06:21and another day, he puts a ten,
06:22and another day, he puts a three.
06:23Oh, good boy!
06:24If you brought me a colorful ball,
06:25because you were forced to do that,
06:26and you put it on a boring piece of paper,
06:27like a ball,
06:28you would find the number, like this,
06:29with exactly the same numbers,
06:30three ones,
06:31seven tens,
06:32nine hundreds,
06:33and a thousand.
06:34Think about it,
06:35it's like you're putting together cubes.
06:36You have cubes of the size of one,
06:42one condition.
07:13One ten, as it is.
07:14Until you get here, the nine,
07:15and here, you have a ten,
07:16it becomes like this,
07:17here, two.
07:18Now, you have nineteen.
07:19If you want to add one more,
07:20you will give us
07:21the nine cubes of the size of one,
07:22and you will take another cube
07:23of the size of the ten.
07:24So, you have two cubes,
07:25each one of them with a ten,
07:26and the one,
07:27you go back to zero again.
07:28So, the summary, dear,
07:29add one,
07:30you get nine,
07:31you give it up,
07:32and you take a cube with a ten.
07:33The same story,
07:34when you get to ninety-nine,
07:35give me nine cubes of the tens,
07:36you come and add one more,
07:37I tell you,
07:38wait a minute,
07:39tell me, my dear,
07:40the nine cubes of the size of one,
07:41and the nine cubes next to them
07:42of the size of the ten,
07:43and you take one cube
07:44of the size of one hundred,
07:45so you get one hundred,
07:46zero in the tens,
07:47zero in the tens,
07:48and one in the hundreds.
07:49Do you understand, dear?
07:50I hope you don't understand,
07:51because this is a disaster,
07:52and next time,
07:53it will be a disaster.
07:54If you focus, dear,
07:55you will find in the ten system,
07:56the cubes you have,
07:57either one, or ten,
07:58or one hundred,
07:59or one thousand,
08:00and so on,
08:01these are the units
08:02of your units.
08:03All of them
08:04are the bases of ten
08:05in the ten system.
08:06The smallest cube is the one,
08:07which is how many?
08:08Ten.
08:09The second cube
08:10is ten,
08:11which is one,
08:12and the third cube
08:13is ten times two,
08:14which is ten times ten,
08:15which is one hundred,
08:16and so on.
08:17One second, Abu Ahmed,
08:18you told us
08:19that humans can count
08:20with different numerical systems,
08:21not necessarily with the ten system.
08:22So, is this simple system
08:23that you explained to us
08:24what I understood?
08:25I will add the numbers.
08:26Can we get the same number
08:27with other cubes,
08:28other than the bases of ten?
08:29Or,
08:30is this an idea
08:31about the ten system?
08:32That's why people use it
08:33because it's a good system,
08:34and it produces the numbers
08:35we want,
08:36and that's why
08:37people wear it,
08:38and that's why people
08:39use the quadruple system.
08:40A number like four
08:41and its bases.
08:42Imagine you have
08:43four cubes.
08:44Four times zero
08:45equals one.
08:46Four times one
08:47equals four.
08:48Four times two
08:49equals sixteen.
08:50Four times three
08:51equals sixty-four.
08:52Four times four
08:53equals fifty-six.
08:54Four times five
08:55equals one thousand twenty-four.
08:56Let's look at this system
08:57and start trying
08:58to get our number,
08:59which is one thousand nine hundred seventy-three,
09:00with the quadruple system.
09:01Dear Abu Ahmed,
09:02the rule changes a bit here.
09:03In the ten system,
09:04we only use ten cubes,
09:05which means
09:06you can't have
09:07more than nine cubes
09:08of the same kind.
09:09As soon as you want
09:10ten cubes of the same kind,
09:11you immediately replace them
09:12with cubes of the larger kind,
09:13as we saw.
09:14In the quadruple system,
09:15we'll put a rule here
09:16that we'll only use
09:17four symbols.
09:18We want to count
09:19to four numbers only.
09:20You have from zero to three
09:21and you can't have
09:22more than three.
09:23If you have more than three,
09:24we'll take them from you
09:25and put them
09:26on the next cube.
09:27Now,
09:28our number
09:29translates to the following.
09:30It's not one,
09:31tens, and hundreds.
09:32No, it's one,
09:33four,
09:34sixteen,
09:35sixty-four,
09:36and twenty-four.
09:37I feel like I'm selling cream.
09:38Now, my dear,
09:39let's take our 1973
09:41and see how it will be
09:42in the quadruple system.
09:43First,
09:44let's go to the biggest thing
09:45and ask,
09:46how many 1024's
09:47does 1973 have?
09:48Welcome, Abu Ahmed.
09:49It has one, right?
09:50So, we need
09:511024.
09:52Okay,
09:53subtract from 1973.
09:54It will be 949.
09:57949
09:58has how many 256's?
10:00It has three.
10:01Bravo, my dear.
10:02So, you have one
10:03and three.
10:04Subtract them
10:05and it will be
10:06after you subtract
10:07those three 256's,
10:08you have 181.
10:09How many of those are there?
10:1064.
10:11Two, Abu Ahmed.
10:12Bravo, my dear.
10:13No one is with President Omar Harbi,
10:14you idiot.
10:15Now,
10:16we subtract
10:17two 64's.
10:18So, you have
10:19one,
10:20three,
10:21two.
10:22It will be,
10:23after we subtract
10:24the 64's,
10:25the 256's,
10:26and the 1024's,
10:27it will be 53.
10:28How many of those are there?
10:2916.
10:30Three, Abu Ahmed.
10:31God bless you, my dear.
10:32Who said that women
10:33are not good at math?
10:34Abu Ahmed,
10:35imagine the patient.
10:36Thank you, my dear.
10:37Indeed,
10:38there are three 16's.
10:39Subtract
10:40one.
10:41Now, my dear,
10:42you have five.
10:43These five
10:44have four.
10:45After all this,
10:46my dear,
10:47we will have one
10:48in the Sunday table.
10:49So, my dear,
10:50to express the number
10:511973
10:52from the quadratic system,
10:53we need
10:54what?
10:55I wrote it all down.
10:56We need
10:57one of the 1024's,
10:58three of the 256's,
10:59two of the 64's,
11:00available in any house,
11:01three of the 16's,
11:02one of the 4's,
11:03in the Sunday table.
11:04So, we have the number
11:05one, three, two, three,
11:06one, one.
11:07This hot line,
11:08my dear,
11:09in the 10th system
11:10is equal to
11:111973.
11:12In terms of simplification,
11:13this is mathematically
11:14subtracted by the equation
11:15in front of you.
11:16The equation, my dear,
11:17is that we get the same result
11:18but with two different
11:19numerical systems.
11:20Each one has its own laws
11:21that we must respect.
11:22Abu Ahmed,
11:23I have a small question
11:24about what you call
11:25mathematics.
11:26Oh, boy.
11:27Abu Ahmed,
11:28don't be mad at me
11:29because I'm going to
11:30embarrass you right now.
11:31Why should we respect
11:32the 4th system
11:33or more than 10 symbols
11:34in the 10th system?
11:35It's all in our hands
11:36and the symbols are our symbols
11:37and the cubes are our cubes.
11:38You're doing something
11:39that's correct
11:40but you're adding complexity
11:41to a simple system
11:42that can solve the whole thing.
11:43No one benefits from anything.
11:44For example,
11:45in the 4th system,
11:46we use six symbols.
11:47Now, we have two cubes.
11:48A 4th cube and a 5th cube.
11:49If I told you
11:50to convert the 20th number
11:51in the 10th system
11:52to the 4th system,
11:53you'd find us
11:54exaggerating like this.
11:55One, zero.
11:56Four, five.
11:57And 16's, zero.
11:58Because here,
11:59we're allowed to use
12:00a 5th cube,
12:01but here,
12:02we're allowed to use
12:03a 4th cube.
12:04So, the 20th number
12:05is a 5th cube
12:06in the 4th system.
12:07But you can also
12:08simplify it like this.
12:09Zero in the 7th system,
12:10one in the 4th system,
12:11and one in the 16th system.
12:12Now, you have a 16th cube
12:13and a 4th cube.
12:1420.
12:15Also, dear,
12:16you can simplify it like this.
12:17Four in the 7th system
12:18and four in the 4th system.
12:19If you go back, dear,
12:20and look at the table
12:21and look at how many values
12:22the 20th number has,
12:23in the case that you allowed
12:24to get out of the equation,
12:25you're adding cubes
12:26to the limit.
12:27If you allow this,
12:28you'll find that
12:29your 20th number
12:30can be represented
12:31in three ways.
12:32In the 4th system,
12:33five is zero,
12:34one is zero,
12:35and four is four.
12:36You're confusing the world.
12:37Why did you give me
12:38so many ways
12:39to get out of my equation?
12:40Why did you give me
12:41three numbers
12:42to get out of the equation?
12:43If you stick to this
12:444th system,
12:45you have three things
12:46that you can get
12:47out of the equation.
12:48Why?
12:49Don't listen to me.
12:50If you listen to me,
12:51you'll have one way
12:52to express
12:53the 20th number
12:54in the 10th system.
12:55Imagine that you give
12:56your son four names.
12:57What do you have?
12:58I have Amjad,
12:59and I'm going to tell you
13:00how to solve many problems.
13:01In mathematics,
13:02it will confuse the world.
13:03Without any justification,
13:04the sum, the sum,
13:05the multiplication,
13:06the multiplication,
13:07and the multiplication
13:08will be complicated
13:09without any benefit.
13:10Dear,
13:11we chose to suffice
13:12with four numbers
13:13in the 4th system.
13:14Don't go beyond
13:15four numbers.
13:16Zero, one, two, three,
13:17that's it.
13:18In the 10th system,
13:19only ten numbers.
13:20Zero, one, two, three,
13:21four, five, six,
13:22seven, eight, nine.
13:23We want less
13:24than the cube.
13:25In mathematics,
13:26the rule is always there.
13:27We impose a rule
13:28If a rule is not useful and does not facilitate the world, then it is not necessary.
13:32If we were born four weeks, the system we work with would be a quadruple system.
13:36And if we were born 13 weeks, the system would be a quadruple system.
13:40All have a system and all have a mathematical correctness.
13:42And all have a walking rule.
13:44The 10th system strengthened civilizations and benefited us a lot.
13:47But by entering the modern era and its inventions, such as electronics and computers,
13:51appeared a numerical system capable of being the language of this world.
13:54A system based on two symbols only.
13:56Zero and one.
13:58Two symbols that you can use to do all your calculations on your modern advanced device.
14:03Dear, allow me to introduce you to the binary system.
14:07Since you, dear, have reached this part of the episode,
14:10I mean, it seems that you understand so far,
14:12because from the moment I saw you and you shook your head like Yunus Shalaby in Al-Kibrit,
14:15I said, this boy is clever and genius, and after a while, he will become a heavyweight.
14:20Yes, dear?
14:21Nothing, Abu Ahmed, continue.
14:22Since you understand the game of binary systems,
14:24in the binary, you have a cube with a value of 1, which is 2-0,
14:27and a cube with a value of 2, which is 2-1,
14:29and a cube with a value of 4, which is 2-2,
14:31and a cube with a value of 8, which is 2-3,
14:33and so on and so forth, as you can see in the picture.
14:35Let's look at our number again.
14:371973 in the 10th system.
14:39How can we represent it in the Sinai system?
14:41It seems to us that there is no more than a cube,
14:43from any category, of 2-1 used.
14:45Come, dear, let's do what we did before.
14:47We will see 2-1, 2-2, 2-3, 2-4, 2-5, 2-6,
14:53up to 2-10.
14:55We will divide these 2-10 by 1024,
14:57and so on, as you can see in the picture.
14:59We will take our number, 1973,
15:02and we will do the same division that we did in the beginning.
15:051072, how many of them are there?
15:071024.
15:08One.
15:09How many of them are there?
15:10512.
15:11One.
15:12How many of them are there?
15:13256.
15:14One.
15:15How many of them are there?
15:16128.
15:17One.
15:18How many of them are there?
15:19064.
15:2032 are one, and 16 are one.
15:218, 0, 4, 1, 2, 0, 1, 1.
15:22The number in front of you will be 1, 1, 1, 1,
15:250, 1, 1, 0, 1, 0, 1.
15:28And of course, Abu Ahmed, if I like this cartoon,
15:30I will press a star.
15:31I told you not to be careful with the trigonometric system.
15:33It is true, dear, that the number appears long in front of you,
15:35but it is not vertical here.
15:36The real sum and the solution will appear
15:38if you try to combine two numbers together
15:40in the trigonometric system, not in the 10-system.
15:42Come, dear, let's try to combine these two numbers
15:45in a trigonometric shape, not in a 10-shape.
15:47Do you see the shape in front of you?
15:48The two numbers are placed on top of each other.
15:49Each number is supposed to be in the frame.
15:50But we will start by combining a number with a length,
15:52and we will start from the right.
15:53In the beginning, we will combine a normal number
15:55as we do with the 10-system.
15:56From the right to the left, starting with the 1-system.
15:591 plus 0 with how many?
16:01With 1.
16:02Clever.
16:03Let's go to the next number.
16:040 plus 1 with how many?
16:05With 1.
16:06Excellent.
16:07Until now, it has not come down to 0.
16:08Take care that the next number is in the shape.
16:091 plus 1 with how many?
16:11With 2.
16:12Ah!
16:13Take care that we are in the trigonometric system.
16:15In the trigonometric system,
16:16there should not be any symbols other than 2.
16:19Here, in our case,
16:20the two numbers are 0 and 1.
16:22These two numbers are strange.
16:23A number that we do not understand.
16:24What does this mean?
16:25What will happen here is that
16:26we will combine one number
16:28and we will put 1 on the next number.
16:30We do this in the 10-system.
16:31But when we pass the 9-system,
16:32do you remember?
16:33Let me explain to you what happened inside.
16:35If we think about it,
16:36where are we standing?
16:37We are standing in the fourth column,
16:38which is 2 plus 3,
16:39which is the 8-system.
16:41Now, we want two cubes from the 8-system.
16:43But these
16:44are equal to
16:45one cube from the 16-system.
16:47And 0 cubes from the 8-system.
16:49Right?
16:501 and 0.
16:51Now, we can say that
16:52in the binary system,
16:531 plus 1 is equal to 0.
16:54And we have 1.
16:55Important information, my dear.
16:56The 1 that we have after this,
16:57we call it carry out.
16:58Let's continue.
16:59We have now reached the last column.
17:00Now, we have 1 plus 1.
17:02But we still have one of the previous steps,
17:04which, if you remember,
17:05was carry out.
17:06Because it is one of the outputs
17:07of the sum function
17:08in the previous column.
17:09In this column, my dear,
17:10we call it carry in
17:11because it is one of the inputs
17:12of the sum function in it.
17:13Here, my dear,
17:14we have 1 plus 1 plus 1.
17:16And there are already
17:17two of them.
17:18There is one coming from
17:19the previous column.
17:20It was carry out.
17:21And God blessed it
17:22and it became carry in.
17:23Now, we are in the fifth column,
17:24which is 2 plus 4,
17:25which is the 16-column.
17:26Now, I want to combine
17:27three 16-systems together.
17:28But I do not have
17:29a symbol for the two
17:30or the three
17:31that are allowed
17:32in the other systems.
17:33But what can I do?
17:34I can take two of the 16-systems
17:35and get a cube
17:36from the 32-system
17:37and use one cube
17:38from the 16-system.
17:39In a way or another,
17:40my dear,
17:41and this will help us
17:42later,
17:431 plus 1 plus 1.
17:45So, any cube
17:46is equal to 1
17:47and we have 1.
17:48So, we use this rule
17:49to reach the following result.
17:50Now, we need
17:51to add an extra column
17:52to the left.
17:53We will put
17:54our carry out in it.
17:55This last one
17:56will not collect anything
17:57and it will go down
17:58as it is.
17:59We can say, my dear,
18:00that the process of
18:01combining in the last column
18:02is to combine
18:03carry in plus zero
18:04plus zero.
18:05So, you will have
18:06one that goes down
18:07as it is.
18:08So, it goes down
18:09in the sixth column
18:102 plus 5, 1.
18:11We can summarize
18:12what we did before.
18:13This is a number
18:14from the first number.
18:15We call it n0
18:16and we call it
18:17in the computer world
18:18the bit.
18:19This can be 0 or 1.
18:20The second input
18:21is a bit from the second number.
18:22We call it n1.
18:23This can also be
18:240 or 1.
18:25The third input
18:26is the carry in
18:27that comes from
18:28the previous column.
18:29This can also be
18:300 or 1.
18:31If there is no carry out,
18:32the carry in will be 0.
18:33If there is a carry out,
18:34the carry in will be 1.
18:35As for the outputs
18:36on the other side,
18:37they are the result
18:38of the process
18:39of combining
18:40three inputs together.
18:41We call it out0
18:42and we call it
18:430 or 1.
18:44The second input
18:45is the carry out
18:46that comes with us
18:47to go to the next column.
18:48As soon as it goes
18:49to the second column,
18:50it enters as a carry in.
18:51As we said,
18:52this can also be
18:530 or 1.
18:54In any of these
18:55binary numbers,
18:56we can apply
18:57these rules.
18:581 plus 0 is 1
18:59and 0 plus 1 is 1.
19:00This is a fixed rule.
19:011 plus 1 is 0
19:02and we have 1.
19:031 plus 1 plus 1
19:04equals 1
19:05and we have 1.
19:06We can write
19:07these rules
19:08in the form
19:09of a detailed table
19:10like the one in front of you.
19:11This table
19:12lists all the possible
19:13inputs
19:14which are
19:15exactly
19:168 possibilities.
19:17Also,
19:18this table
19:19lists the outputs.
19:20In all these possibilities,
19:21how will they look like?
19:22All the possibilities
19:23of the inputs
19:24are translated
19:25to this table.
19:26We call this table
19:27the truth table.
19:28According to Abu Ahmed,
19:29this table is a bit complicated.
19:30It looks like
19:31a complicated table
19:32but this table
19:33will be much more important
19:34than you can imagine.
19:35Because,
19:36God willing,
19:37we will move
19:38from the world of math
19:39to the world of computers.
19:40But,
19:41dear,
19:42take a deep breath.
19:43We are still here.
19:44Throughout this episode,
19:45we are with a person
19:46who is trying to choose
19:47a numerical system
19:48to solve his life problems
19:49and organize his mind.
19:50During this journey,
19:51you used your mind
19:52to understand
19:53how each system
19:54works,
19:55solve its problems
19:56and laws.
19:57Dear,
19:58when I tell you
19:59that we are now
20:00moving to the computer world,
20:01this means
20:02that we have
20:03replaced your mind
20:04with a device
20:05that combines
20:06and presents itself
20:07and gives results.
20:08How does this device work?
20:09We have another system.
20:10Why don't we use
20:11our own system?
20:12Let's start
20:13with the simplest
20:14possible operation.
20:15We agreed
20:16to combine a number
20:17into a number
20:18in the binary system
20:19like this column.
20:20And since
20:21the computer
20:22is a device
20:23that works
20:24with electricity,
20:25I want to combine
20:26this operation
20:27with electricity
20:28and not with my brain.
20:29I need to design
20:30a simple electric circle
20:31that does
20:32this combination
20:33for one bit
20:34plus one bit.
20:35This circle
20:36will be called
20:37the one bit other.
20:38How do we know
20:39that the house
20:40inside the circle
20:41is one or zero?
20:42The device
20:43doesn't understand it.
20:44What does one
20:45and zero mean?
20:46I need to talk
20:47to it in its language.
20:48The device
20:49doesn't understand
20:50other than
20:51the voltage
20:52or voltage.
20:53Now,
20:54in our language
20:55with the device,
20:56we will start
20:57translating it.
20:58We will say
20:59that each of us
21:00has five volts
21:01in the device
21:02and zero
21:03has zero volts.
21:04One has five
21:05and zero has zero.
21:06Sorry,
21:07he asked the device
21:08to bring the battery
21:09or still
21:10the zero volt
21:11as it is
21:12the negative pole
21:13of the battery.
21:14Take care
21:15my dear.
21:16Five and zero
21:17is not a λ.
21:18It can be
21:19two or ten volts.
21:20The point
21:21is
21:22that we only
21:23have
21:24two values
21:25of the volt
21:26in the system.
21:27You say
21:28two, ten,
21:29three, four.
21:30I don't care.
21:31The point
21:32is that
21:33there are two.
21:34One is the one
21:35and the other
21:36as we saw in the binary. You can add 1 and 0 and get carry out and so on.
21:41And since here the way of the sum is one, the electric circle will follow the same
21:46rules of the truth table that we talked about, which shows all possibilities.
21:50We will just replace the zeros with zeros and the ones with fives.
21:54That's it. Just do your operations at ease.
21:56If we have an electric circle like this, dear, then I will put the entire binary system
21:59in an electric circuit. I will put on any connected wire either 5 volts or 0 volts.
22:03As if I am writing 1 or 0. I enter it from the table and put it together.
22:06I look at the table, at the truth table, and I know the value of the sum.
22:09When I look at the volts on the output wires, the wire will tell me 0 or 0 volts or 1
22:13which is 5 volts, and also the value of carry out, 0 or 1.
22:16It will also be shown as 0 volts and 5 volts, as we agreed.
22:19Wait a minute, Abu Hamed. I need a genius circle like this to put one column together.
22:23What if I have four columns, Abu Hamed? How can I make the sum with electricity?
22:27Easy, dear. You will need several of the electric circles and put them together
22:31so that the carry out of each of them is equal to the carry in of the circle behind it.
22:35Just like what we did in the math table, where there is no need for electricity.
22:39What will happen, dear, is that we will simply keep repeating this electric circle.
22:43See, dear, the circle that has two inputs, the number here and the number that is put together
22:47will take carry in from the previous number. If we still start, then this number will be 0.
22:51It will give us two numbers. It will give us the carry out, the number that will be calculated
22:55with the next number, and it will give us the output, the number that will come down to us.
22:59As we explained, three inputs and two outputs. To put together several columns,
23:03we can put these next to each other. It's very simple.
23:05Abu Hamed, why did you make electricity so easy? Why didn't you write the number 5?
23:08Put this circle next to it. The carry out of each of them is equal to the carry in of the circle behind it.
23:12Thank you. Just like what we did a while ago in the math table,
23:16where there was no need for electricity yet. If you notice, dear, you will find that
23:20the largest number that we put as an input is 4 bits, i.e. in the binary, 1, 1, 1, 1.
23:25This, in our 10 system, will be 15. When we put together the shape in front of you,
23:28put together the four columns, put together the input in its place,
23:30the result will be 1, 1, 1, 1, 0 in the binary.
23:34Or, in our 10 system, 30. If you want to increase the range, or the machine's capabilities
23:38that calculates, increase the number of electric circles, where each circle represents
23:42one column. So you increase the number of bits, and you increase the throughput in the system.
23:45That's why, dear, sometimes you hear about computers that have 30 bits or 64 bits.
23:48Of course, we want a more complicated subject. That's why, dear, we need simplicity.
23:52Simplicity is almost impossible. I mean, it's a little bit impossible, but, I mean,
23:55so that you understand the idea. And this, dear, is the answer to the question,
23:58why did we use a binary system instead of a 10 or a 4?
24:03The truth is that everything I explained to you can be done in a 10 system.
24:06And we put 10 values of volts. But this will make the design of the electric circle
24:10and the entire computer, as a result, a very complicated thing without any need.
24:152 volts will make the design and execution easier. It will allow you to make a smart device
24:21that can calculate things and let you play Angry Birds and watch video games.
24:25Do you remember, dear? Our math is good, isn't it?
24:27We choose the system that makes life easier. That's why the binary system
24:30is the most popular system in electronic devices today.
24:33But what do I mean, Abu Ahmed? All that we applied to electricity is a theory.
24:36What do I mean? You took the pen and wrote it. You took the 1 and gave it 5 volts.
24:39You took the 0 and gave it 0 volts. What's wrong with you?
24:41And you think that we're in an electric circle, and you're drawing.
24:44Any circle, which is a few wires, will have enough intelligence to collect and
24:48display an output. How, Abu Ahmed? We take the theory from the bubble
24:53and transfer it to the real earth. To the real electricity.
24:57Now, dear, this transfer from the individual to the reality has a secret
25:01that all high school students hate. The transistor.
25:05What I just explained to you, dear, is theoretical.
25:07We understand how this binary system works, how we can calculate on it,
25:12and how, theoretically, we can do it on a computer.
25:15The most important technological tool, perhaps, in our history as humans,
25:20that helps us do this, is the transistor.
25:22Which, through it, and through the gates it makes, the logical gates
25:26that this tiny device makes, we were able to make electricity,
25:30like a math table behind you, you can insert logical inputs
25:33and get logical outputs.
25:35And so, dear, congratulations to you, civilization, the internet, the computer,
25:40Facebook, Snapchat, WhatsApp, and all that.
25:43The achievement of the transistor and the achievement of this method in the world.
25:46Do you want to know the details of the transistor and how?
25:48We made an amazing episode called The Transistor.
25:51In this episode, when the transistor is inserted,
25:53we close it, we close it, and then the party continues.
25:56And I also want you to watch the episode of Chip Wars,
25:58so you know what this transistor, at the level of world politics, does.
26:01What these logical gates can do in the world, and how wars are made.
26:06So watch these two episodes, the episode of the transistor,
26:08and the episode of Chip Wars.
26:10When Shakuntala Devi asked mathematicians,
26:12who used to calculate any complex operations with their genius,
26:15to the extent that they called it the human computer of the world,
26:18when they asked her, what is mathematics?
26:20In fact, she told them,
26:22it's only a systematic effort of solving puzzles posed by nature.
26:25Some, dear, consider mathematics to be a complicated science in a simple world.
26:28While actually, dear, in fact, it's the complete opposite.
26:31Nature is what is complicated, and it imposed challenges on us.
26:34Like, for example, we are required to count ourselves and the things around us.
26:38We are required to know how much everything around us is worth.
26:40And numerical systems were our attempt to solve a puzzle,
26:43a game imposed by nature on us.
26:45When a person's world is complicated,
26:47and he is greater than ten equations,
26:49he needs to invent numerical systems that add up bigger numbers.
26:51Then, when the effort is greater than our mind's ability,
26:53the person needs a machine to help him.
26:55And mathematics came with a system like the binary system,
26:58to make electricity, the energy that has no limits,
27:00subject to a law and simplify.
27:02Maybe, dear, I told you a lot of words in this episode.
27:04Maybe you learned from each other and added three quarters,
27:07but the most important thing I want you to learn in this episode
27:09is that mathematics came, according to the expression,
27:11mathematician Sam Goddard,
27:13not to make simple things complicated,
27:15but to make complicated things simple.
27:17Mathematics, dear, is not here to make things easy for you.
27:19It's not here to make the world difficult for you.
27:20The world is difficult.
27:21Mathematics is trying to make the world easier for you.
27:23Dear, I know that mathematics is a difficult science,
27:25and many of us hate it, because they consider it a complicated science,
27:27but it is one of the most important tools that helps us solve the puzzle of the world.
27:30Unfortunately, its challenges do not end.
27:32That's it, dear.
27:33If you didn't understand anything from this episode,
27:34you can understand from the previous episode,
27:35you can understand from the next episodes,
27:36you can look at the sources,
27:37or you can subscribe to the channel on YouTube.
27:39And trust me, dear, this topic is not difficult.
27:41It's not like the episode about imaginary numbers.
27:43This was a difficult episode.
27:44I'm sure.
27:45But this is easy.
27:46Watch it a few times and you'll understand.
27:47And indeed, this is a revolutionary system.
27:48A system of non-existence,
27:49but it allowed the existence of something like a transistor,
27:51which allowed the existence of something like a computer,
27:53which allowed the existence of something like the Internet,
27:54which allowed my existence.
27:55I'm trying to say that this is an important achievement.