Lecture 02

Let's start from where we left off last time. Last time, we talked about the same story with A. B. Strouzer, how she started losing her business. Because a telephone operator, who was a woman, would route her husband to all the calls for Undertaker. I am narrating this story because I don't know if it is true or not. But after that, she decided that she wanted to make an automatic exchange. At that time, electronics were not that advanced. We did not have vacuum tubes, transistors or computers. So how did she make it? There was a problem in front of her. She and her nephew designed the first Strouzer exchange. Actually, A. B. Strouzer was not a technical person. But ultimately, his relative designed it. And gradually, it became quite popular. And it became quite popular. The biggest thing was that the operator did not know what was being discussed. Of course, there was no secrecy. If you could connect your headphones to the wire, you could hear what was being discussed. But since there was no human operator, no man or woman was managing it or setting the connection, so it was quite automatic. And the biggest thing was that the man's value was reduced. Basically, it was an automatic exchange. So it was more reliable and more secretive compared to manual telephony. So the biggest thing to make it was... Those of you who have seen old-fashioned telephones, we used to use rotary dial phones, if you have ever noticed. The dial used to be made like this. I think I have not changed the number here. So it used to be like this. You used to put your finger on it and rotate it. And after that, a pulse would be generated. If you wanted to dial 0, 10 pulses would be generated. If you wanted to dial 1, 1 pulse would be generated. So once you dialed 1, 1 pulse would be generated. There was a time gap. Then you used to dial another number. So these pulses were basically called pulse-driven exchanges. They were also called step-by-step exchanges. In every step, there was a corresponding connection setup of a particular number. So three main things were designed in this. A director, a uniselector, and a dual motion selector. So that was there. And in this, relays were used. So relay, timer circuits, basically analog circuits were used. Relay was a digital circuit. It was a mechanism for information processing. So the entire logic was hardwired in this. All the wires and all the relays were connected and the entire logic was made. There was no computer program in this at that time. So normally, it is very simple. How would a uniselector work? So in a uniselector, there used to be a gear like this. This diagram is not correct, but you will understand. It should not rotate back. It should only rotate in one direction. There used to be a stent to stop it. And we put a spring in it. And this spring is fixed to the shell of the body. So it can rotate in one direction, but not in the opposite direction. There used to be an arm in this. This arm could go over many connectors. Now how would we operate this? Before dialing your number, it used to be in the home position. Home means zero position. There is no connection there. If you send a pulse, there will be an electromagnet here. A pulse will come here. When an electromagnetic pulse comes, it will rotate once. So one position will move forward. It will come from here to here. If there are two pulses, it will move forward twice and come to this position. If there are ten pulses, it is in the zero position at the end. So I can divide it from the first digit to zero. When I dialed the first number, the first unisector worked. After this, the relay has to cut this input here and take it to the other device. In this way, I can create an exchange by creating a cascade. It was not that easy, but it was the main principle on which it worked. Normally, there will be an arm on top of this. It can rotate. This is its hinge. We have put a metal piece here. Whenever there is a pulse in the electromagnet, it will be pulled down. When it is pulled down, it needs to be operated. This is a system like a hook. When it is pulled down, it can go down easily. There is a hinge here too. It can move this side. It should always go up. A spring will be installed here. Whenever there is a pulse, it will go down. It will engage itself on the next tooth. When the pulse is over, it will go up again due to the spring. Because this spring will always pull this side, it will engage on the next tooth. When it goes down, it engages on the next tooth. When the spring goes back, it will rotate one pulse. This was the basic simple mechanism. This is a return type mechanism. There are many other mechanisms through which uniselectors were made. But you will notice one thing. This is an electromechanical system. This is a thing that moves. When it moves, it is slowly pulled down. It has wear and tear. The material is slowly reduced. The contact of the copper is also worn out. After some time, there will be a big problem. It will wear out and a mechanic will have to repair it. Similarly, another system was made. This is a very simple system. There is one input and there are 10 outputs. It is used for 1 to 10 expansion. If I want to do 1 to 100, what should I do? It needs a two-motion selector. We will put a rod like this. There will be an arm in it. There will be a total of 10 levels above each level. There will be a total of 10 times 10, which is 100. A small gear can be installed here. This was the basic principle. There will be gears here. It can be moved up and down. If there is a pulse of the electromagnet, it can go up and down. There is a gear like this and another gear like this. This gear is used to rotate it. It will rotate with a circular gear like this. There will be another gear mechanism to go up and down. There will be a rotary wheel here. It will be a system like the one we have made above. It will move it up and down. It converts the rotary motion into linear motion. It will convert the rotating motion into a straight line. Similarly, this linear will also move in this direction. We will move it up and down for the first time and rotate it for the second time. It can be connected to any of the 100 output connections. Before setting the connection, these two devices need to be moved to their home position or basic position. There was a special circuit for this. It was called the homing circuit. If you have ever heard of a homing circuit. This is a very complicated system. It was made by A. B. Strausser. It was very successful. But the problem with this is that it is very slippery. It is mechanical. Dust accumulates on top of it. No matter how much you cover it with a cover, there was no air conditioner at that time until it was invented. Electricity was invented because it is based on that. It used to be dusty. It had to be repaired. The material used to get scratched. This was a big problem. Maintenance was very expensive. Many people needed it. It had to be trained. But it was very popular. It was better than manual telephony. It involved men and women. In return, this system was better. This was also changed. People thought this was not right. We should do something else. One more thing we knew. Oxidation contact occurs in this. Copper becomes copper oxide. If there is aluminum contact, it becomes aluminum oxide. Oxidation contact was a big problem in this. After this, a new thing was invented. It was a crossbar. Crossbar switch. The biggest thing in a crossbar is a glass bulb. In this, inert gas can be filled. Oxygen can be extracted from this chamber. When we break the glass, the oxygen that is not there will be found in the environment. But when it is made, oxygen will be extracted. Till the time we had the technique of making a bulb, Edison's bulb had been invented. The same thing was used in this. Two arms are inserted here. This is called a crosspoint. There is no word for it in Hindi. Google gives the correct word for it. We call it a crosspoint. I have written X point. It should be called a crosspoint. We make a crossbar exchange from a crosspoint. There are two ends here. This is a metallic contact. Mostly copper or silver or gold should be there. Whenever we can bring them close to each other, our connection will be formed. Between A and B. When we leave it, the connection will break. How will we make this connection? There was still time for electromagnets and relays. We put a piece of metal here. We put an electromagnet here. We call one as a row and the other as a column. This will be clear when I draw a crossbar. If I apply a current in both of them, that is, if I pass a current through them, then this will pull it to its side. This will pull it to its side. These two will join together. The crosspoint will snap. It will join together. This is a basic crosspoint. We can make a switch with this basic unit. Compare a uniselector or a two-motion selector with this. It is so easy and simple. There is no oxygen in it. If we fill inert gas in it, there will be no oxidation. The life of the contact will increase. My maintenance of the exchange will be very less. Gradually, the electromechanical exchanges, the Strausser exchanges, were over. All of them were converted into crossbar exchanges. Because they were more reliable, they could be made in a larger size at a lower price. It was a reliable service. But how do we make it? We can make it very simply. Suppose I have four outputs, four inputs. We have given the numbers 1, 2, 3, and 4. 1', 2', 3', and 4'. The dots above are called prime. This point I have made here. I have given this to A and this to B. I have put a crosspoint here. This is wrong. It should have been here. This is here and this is here. This input will connect to an output whenever this crosspoint snaps. We can show this with a small ball. Of course, there is a problem here. If I have n inputs and n outputs, how many crosspoints do I need? This is a question. Can we reduce this? Here, you can see that n times n. You will need n square crosspoints. As n increases, the crosspoints will increase in the form of n square. This is called crosspoint complexity. Quadratic complexity will be there. Quadratic complexity is not a good thing. If my size increases, my resources should also increase in the proportion of n. I will not like it in the proportion of n square. It is good if log n increases. It is bad even if n is log n. It is not a good thing. Everything is fine as long as n is equal. It should increase in the proportion of n or decrease in the proportion of n. This is my complexity of anything. Whether I need time to execute an algorithm, I can say it for time. Or, I can say it for crosspoint. This is called crosspoint complexity crossbar. O n square. O n is a notation. So, crosspoint complexity is O n square. When we make a switch here, when we talk about an analog telephone, the sound goes to this side and this side. What will I do with this one? Normally, when I am talking to 2, 2 connects to 1 and 1 connects to 2. This is also possible in this way. If it was in one direction, it would have been fine if it was coming here and we would have sent 2. We would have sent the one coming from 2 here and 1 would have gone here. So, we need these two wires for the connection of 2 and 1. For the communication between 1 and 2. But, since the sound can go in both directions on one wire, we can connect it. So, the value of the number of crosspoints in this will be reduced. So, how do we do this? It is very easy. We have taken 1 and 1. We have brought it here and connected it here. So, it is in both directions here. But, we have put this device here. We call it a duplexer. It is not a duplexer. It is called a duplexer. So, the coming sound will go this way and the outgoing sound will go this way. So, it can be mixed. For 2 like this. So, when we have to talk to 1 and 2, we will have to send only one wire. We will talk to both of them. And through this switch, how will we set the connection? Here, we can set the connection in two ways. One possibility is to set the connection from here. And the other possibility is to set the connection from here. And 1 will never connect to 1. And 2 will never connect to 2. We never talk to ourselves in the loop. So, this means that these two are redundant. That is, we have one redundant and one extra. So, we do not need that. Actually, we are so much below the rule. We can put a cross point in them and run our work. So, the correct cross point, we just need to put a cross point here. We will leave the middle one. We will need this much cross point. And what is the number of this cross point? This is an easy mathematics. It will be this much. This is the same number that we found for the mesh network. How many wires do we need if we want to connect n people? Here also, we have to connect n people. We will need this much cross point. So, the complexity of the wire at that time has now become the complexity of the cross point. Now, we only need n wires. We do not need wire n into n minus 1 by 2. So, we have converted the complexity of the wires into the complexity of the cross point. So, after making the network, we said that we will put a switch in the middle and connect all the people there. There has been no change in the complexity. Only its form has changed. Now, instead of wires, it has become a cross point. It is better to make so many bulbs than to lay so many wires a few kilometers long. This will reduce the cost. Later, as we move forward, we will see how we can reduce this number also. We want to reduce this complexity from O n square. We do not want O n square. Now, before going further, before reducing the cross point complexity, we have to know how to control the switch. We saw in the diagram at the back that there were two electromagnets, one R and one C. When we give current to both, this connection will snap. So, how will we control this? So, let us think about controlling this. We have taken four here. Now, let us take all the cross points. Let us not take it in the lower triangular form. Let us take the entire cross point. The complexity is O n square. There is no difference between the two. If we have to find its complexity, it becomes n square by 2 minus n by 2. Whenever there is a polynomial like this, we remove all the terms of the lower order. The highest order term determines its complexity. So, this complexity is also O n square. So, how will we control this? How will I decide which row and which column I have to connect? We will call this row and this column. So, we can do one thing. We can connect the two switches that I had created there. We connect these two, A and B. There is one wire. Whenever we pass current through this wire, this connection will snap. If we leave the current, it will turn off. We can do this. What will we do if we can do this? 1, 2, 3, 4. 4 control points. 5, 6, 7, 8. You will need 4 times 4. You will need 16 control points. You will need 16 wires to control this. If I use a computer, a logic or a microprocessor, it will control these 16 wires, the physical wires. So, of course, at this time, by putting a number in 4 lines, it can do this. We can take log216. There are 4 lines, basically a 4-bit number. A microprocessor can decide which one to switch on and which one to switch off. But at the same time, different switches can be switched on and off. We do not want to switch on one of the 16. We want to switch on or off any combination. But all combinations will not be valid in this. So, we do not want to switch on an invalid combination. We only want to allow a valid combination in this. So, in this, either the microprocessor gives a separate address to each line and says switch it on, then give the address and say switch it off. Either we can do it this way. But this number will keep increasing. Again, my control complex has also become O n square. Can I do something about this? So, maybe, if you observe this, there are 4 rows and 4 columns. Maybe you will get the idea. Let us activate one row. Let us make a control and connect all the rows. Let us connect all the columns. If we do one row and one column, then the row and column which is activated will get activated. What will happen in that? How many control wires will we need? For 4 rows and 4 columns, we will need a total of 8. So, how many will we need? 2 n for n by n switch. What will be the complexity of this? If we apply the same principle, then its complexity will become O n. So, I can convert the control complexity from O n square to O n. So, let us do this and see whether it will work or not. We made the same 4 switch. What did we do next? We made a row line in it. We called it R 1 control. Row number 1. Row number 2 control. Row number 3 control. Row number 4 control. So, we thought that we will have to make a column like this. So, let us make a column. We connected the column. We made a column 1 control. We made a column 2 control. We made a column 4 control. So, I want to make a connection from 1 to 2. If we want to make only one connection, then it is very easy. First, I moved R 1 up. I increased its voltage. As a result, the current went to the electromagnet. After that, I increased the voltage of C 2. Only row 1 and column 2 will activate this switch. No one else will activate it. So, this is the way we can control it. But, there is a problem here. So, I will end here. In the next lecture, before watching the next lecture, think about what is the problem and what will be the solution. If you can find out the solution of this problem, then you can watch the lecture so that you can find out whether you thought the same or something else. In the next lecture, we will find out the solution of this problem.