 I think we must have time for the last story also whole idea is not to go this is the new thing I wanted to show you the new thing is from inverter to programmer for logic I told you that in one and half hour I must take you through this journey of quickly understanding without detail just like you understand a movie you know we do not understand detail understand a movie. So, I saw the sixth sense by some what night night Shyamalan whatever his name is and in the in the end I did not know that the fellow was already dead all my family knew I did not understand. So, I did not have the sixth sense to understand what happened in the movie. So, he is ok I also like the movie. So, I did not know who was the murderer I still like the book it is like this even if we do not understand everything the story is compelling how it all went from a simple inverter to a VLSI in digital logic with MOS. So, this is the new thing I think Prof. Dinesh Sharma has given you a small dose of MOS transistors for your information he and I used to work every day basis for 20 years together. So, he came to IIT much earlier than I came much later. So, what was the digital logic in VLSI how did it get there? So, 1959 to 60 first indirect circuit was made in 1960 by Kilby of Texas Instruments and Noyes who made a linear IC for fair child semiconductor simultaneously, but separately and they both got the patent for this, but only Kilby got the Nobel Prize in 2000 and Noyes did not get and the simple reason is well known in TIFR. It is not only you have to do good work great work, but you have to outlast your competition outlast meaning you have to be alive and the Nobel Prize is given you have to be alive it is not given posthumously. So, this fellow could not make it this old man was still alive when they give a Nobel Prize for making integrated circuit and putting the entire population of earth in a electronic sera bring PC on your tabletop when we are students we never even imagine thing we require a whole building will ultimately be available we could not imagine Texas Instruments therefore, produce the integrated circuit which are digital and fair child and later many other people actually made the U.S. 701 of operational amplifier and many other things because of that parallel path the second part of the story is though field effect transistor was proposed prior to Nobel Prize winning point contact transistor by Bell Labs and Shockley was one of them and Shockley had actually given the full pinch of current equation before they invented this transistor in 1947. So, 9 in 47 is a landmark here in 1997 they celebrated 50 years of it the good things happen in 1947 I was also born in it. So, I am following this progress of all integration from transistor onwards I will tell you little anecdotes from time to time. So, 1968 well beyond 1960 the first TTL came up in 1968 the first successful MOS field effect was done and poor fellow has never got a Nobel Prize who made that, but it is everywhere the MOS transistor has won the heart of all people the greatest thing is self-isolation and MOS transistor acting as switches in relay that is why I think the next few slides will tell you that the transistor characteristic is a figment of imagination when you have got billions of transistors nobody looks at the transistor characteristics, but we teach them nevertheless because they are good for bipolar transistor they are not required for a MOS transistor. So, MOS inverter symbol is the same if I got a high input becomes low low input becomes high. So, we have got this 0 0 like that 0 1 0 1 same symbol the important property which Texas instrument did was to assume further is not enough they said if we put two inverters in tandem then they must do exactly the same that means the output of one should act as a corresponding input to the other one by definition right it is a chain because if it is a inverter, but if it cannot invert by its own copy then it is not a good inverter. So, this is like cocoa game only one player cannot be good everybody has to be good otherwise you cannot win the competition. So, this is the condition when something is high this is low this takes it as a low and then gives high. So, that is the condition it must follow instruction. So, whatever as the input specifications of a gate must accept the output specification of the same gate because another gate of the same kind is going to connect to it. So, that is the important thing. So, what is an inverter? This is an inverter simply. So, the color is there one black color one blue color if I give input a what happens is this acts like a switch that switch turns on and it that one for now we do not worry how, but that remains off. So, give a high that switch is off this switch is on and this switch connects it it becomes ground. So, it becomes low exactly opposite will happen when this a is low this switch goes off that switch comes on then it connects to V D D becomes high. So, we need this important property of these two switches that when this is high this gets on, but that goes off and vice versa that is called complementary this is called complementary that is the two transistor must be complementary of each other as far as the switch operation goes. If this is high this switch is on this has to be off by definition and vice versa. So, now I have again shown the same thing once which is on that is off once which is on that is off. Therefore, the reason why a CMOS logic works rail to rail 0 and V D D TTL does not work like that TTL you apply 5 volts it can give only 3.6 volts maximum. And if you apply high voltage does not become 0 it is less than 0.4 there is no 0 and 5 volt there, but here since I am now taking analogy of a switch there is a 0 and V D D that is the reason. So, please forget all transistor characteristics of MOS simply forget, but today digital logic just forget all characteristics is a good switch operated as a switch. Then we will understand millions of them billions of them more easily no burdening of transistor characteristics which in great detail professor must have derived right all those square and all this. So, how do you convert this inverter to a NAND gate. So, what we have to do is instead of one input I need two inputs. So, I now put instead of this one transistor I put two transistors in the lower half if a is high and b is high both this switches are on and by definition these two transistors above should be off and exactly opposite should happen. So, now there is a dual if you have got things in series in the lower half of the circuit things should be parallel in the upper half of the circuit because only one of them is supposed to be on either the upper half or lower half. Now, you can verify why this is parallel this is series. So, I leave it to you as a exercise, but this is the way it is the algorithm is simple. If the lower half of the circuitry has got anything in series and parallel when you go to the upper half of P MOS transistor then it becomes exactly opposite. It is just like D Morgan's theorem no we do exactly that. So, now is a lower half upper half symbol remain same truth table remain same now the MOS transistor is acting as switches. So, this is a switch logic no resist no voltage is no nothing in the switch logic we are quite happy with this kind of notation everything is connected and then symbol is like that. Now, we want many input suppose I got a memory of 1 GB and then it requires 22 input for selecting the row and another 22 input for selecting the column. So, what will I do I put 22 of these inputs happily a to z allows up to 26 right how many characters are there no, but we are not keeping English here. So, first standard does not matter I can easily speak about a to x as 22 or 20. So, I can have a to x here now I need 20 of these in series. Now, the question will come whether a switch is an ideal switch or it has got a resistance if it has got a resistance resistance will keep on adding and become huge and then it will not work as a good switch. So, it becomes a bad switch therefore, it is never used like this. So, this individual one is any one is shorted is good now more than many shorted is bonus, but this is not acceptable. So, what we do is invent innovate. So, there are two innovations, but just put a simple resistor the resistor let us say is 10 kilo ohm and this switch is 100 ohm or 10 ohm then 10 ohm versus 10 kilo ohm. So, we will get 100 of that voltage term. So, V d d upon 100 will become my low voltage will not be 0 when one is connected it will be 100 of V d d, but when all of these are off this resistor will bring the voltage there full voltage. So, V d d is ok, but the lower voltage is no more 0 and therefore, we have to take that into account that it should not malfunction the other sorry the other one is a current source. The current source is put because invariably all these many devices have got a parasitic capacitance and we got to charge that capacitance within picosecond nanosecond depending on the speed of your circuit. And therefore, nowadays everything is taken as a current source. So, MOS transistor when it is in saturation is like a current source MOS transistor when it is in the linear region is like a switch these are the only two things you got to remember in the MOS transistor logic. In the saturation mode it is like a constant current source in the near the origin it is a small resistor like a switch. And therefore, now I can get anything any number of a nor of any number of things is good enough. So, logic design using nor. So, now we make a statement that any sum of product you give me any function with a sum of products I can always implement it using nor and that can be proved by D Morgan. So, I am not going to prove that but suppose this is the exclusive OR function a bar b plus a b bar. So, we do a double bar so, without changing the function the inside one we simplify and then we get this just to prove that any sum of products can be converted to functions of nor. So, I have now got this one nor and this becomes. So, if this is called capital D and this is called capital E then D plus e bar that is another nor. So, we get three nor to do this. So, I have proved this is called proved by induction if something was for one something was for two then it will work for n. So, I have already proved that any sum of product for two I get this. So, you can now verify any number of terms I have I will still get this. So, there is no proof required this is by induction that this is always true that any sum of product function can be implemented by nor. So, now we grow we grow big. So, if you have got functions of three variables till it is true any sum of product of three variables also it is true any sum of product of four variables other any sum of product of twenty variables also it is true. So, that means all I need to do is make nor, but how many nor circuits will I do how many nor circuits will I make. For every row I have got this circuits for every row and there will be million rows and million columns and I need millions of this nor circuits. Therefore, I require billions of transistors even to address the individual row and address the individual column in a memory I require this thousands and thousands of gates, but if I have got a logic like this seven segment display as an example I write this 0 this my seven segment the 0 will be 0 0 0 0. So, as an example one is 0 0 0 1 this is a binary equivalent of that. So, a bar b bar c bar d like that if you write if I take any particular function segment 1 occurs in 0 1 4 5 6 8 9 you know the segment 1 is used in this function segment 7 is used in some other function occurs in 0 2 3 5. Please find an error no problem students are interested to find any error any time because I do not read books and copy from the book all my notes books are shut I write from my memory that is the best way then I also make some mistakes over the years the student point of mistakes and I correct some of them I leave some of them every year the students are supposed to find that mistake with madam. Otherwise the mind is not alert every time professor there is something is always right then you do not have to listen just read the notes that is what you will think that is what happens and then I announce before the exam that if there is any error otherwise in my notes then if you put it in the exam you will get 0 mark because that is no excuse you cannot say such your notes was having a wrong answer you are supposed to correct it I tell that in the class, but never correct the notes. So, that works very well. So, now we have this say y 1 or y 7. So, now what is this sum of 7 products with 4 variables the 7 products can be called p 1 to p 7 how many products are there anyway with 4 variables the 16 products p 1 to p 16 you can call it m 0 to m 15 now whatever and then there is another implementation and this is called PLA. So, anyway do not worry about exact location of this the advantage of MO is another one that they are self isolated they work only a switch all those you are fine if you draw anything like this circuit you know the NOR circuit 1 transistor 1 transistor 1 transistor like that then layout is exactly the same the way you draw it. Therefore, if this is the NOR gate with that current source here the NOR gate is going to work with a b c d 4 transistors the gates will be connected to appropriate 1 and the output will go here p 0 to how many up to p 16 that is p 0 to p 15 maximum 15 product, but in my particular circuit I want only 7 of those and then I will do this 7 of these and without going into detail I want to now implement the say that is the NOR the upper 1 is the NOR and I want to implement NOR of that NOR of this p 0 to p 15 there are 7 segments I must get an output for each one of them. So, now I have got a set of I have got a set of equation Boolean equation y 1 some p 0 to p 7 or something and y 2 etcetera to y m. So, there is a subset here. So, there is a subset of all the possible combinations right, but we may not have 15 because we have got only b c d the 7 segmented displays only for the b c d. So, we will have only 9. So, does not matter. So, once we have this called simultaneous equations of Boolean equations and therefore, my inputs of 4 my outputs are 7. So, the OR is made for 7 such things. So, now you see here some of them are not even connected here if only say p 0 p 1 p 5 is not there that p 5 does not get connected this gate remains open and therefore, it is inactive that does not act as a switch. So, exactly whatever is required is connected and therefore, you now get the functions finally, output as y 1 to y 7. So, I have got a perfect implementation of the set of Boolean equations how many assumptions I have now said there is a sum of products I can always implement by NOR. So, one set of NOR is inside in one bar. So, it happens that this creates that first p 0 to p 7 that is called the AND part and this creates the NOR part. So, two together implement exactly that and I have got exactly the function y 1 to y 7. Now, what is the programming all these cells are here the transistors if p 4 is not there in y 1 that p 4 transistor is not connected. That means, I should connect only those which are required and therefore, this is called the AND or programming and this is called the programming these ones are not connected only these are programmed. So, the AND regions and OR regions are programmed by showing a dot there whichever terms are required we show a dot that we require that and this called therefore, a programmable logic array what does it do it can program any set of equations this m number can be anything m can be even bigger than 100. So, there are many combinations of this digits that we can use. So, there are 7 outputs and there are 4 inputs and then we can have this particular program. So, this is called a programmable logic array. Now, the generic thing is it is called programmable logic devices allows a full programming of all 0 to 15 terms or it allows only a partial one it depends on which one is full and which one is partial. But, in general this is called PLD and they are made permanently it is made by manufacture the programming is done by you know flowing a fuse there or you know making that connection by breaking down a insulation and that is done by programming there is a machine for writing this thing in and this become programmed. Now, they can be reprogrammed if it is a electrically reasonable operation. So, E program so, not the prom, but E prom is a programmable logic and then it cannot be undone. So, it is a permanent then they were earlier this ultraviolet thing which can again reprogram, but now we have got electrically. So, we can continuously write and we can continuously modify it should you need that modification. So, the today's craze is what is called reconfigurable computing or system. So, continuously it can be reconfigured on a command from elsewhere I can reconfigure this by electrical means. So, this is the summary I have given. So, program the AND region program the AND region for the input variable n variable outputs are p products out of the total possible 2 raise to n products I can only select p products and then the output is programmed for m outputs depending on whatever the combination. So, they are generic programmable logic devices field programmable E proms and the most famous and most popular is the field programmable gate array. It all began with 10000 gates now it is I do not know anybody latest number what is the maximum number of gates last I heard of was 100 k. So, it must be definitely a million now that many gates are available for you to do anything you want to what is done by this digital logic including the flip-flops. So, I have got this 3 application 2 of these are my own applications and I will tell you why my applications are important. So, there is a stepper motor control once I wanted to actually control the temperature of a furnace and I had to actually use a stepper motor to move the set knob the temperature setting knob in a programmed way earlier I used to sit there myself and the programming requires 20 hours. So, then I have to make all my friends sit there for 4 hours each after 2 days I had no friends left all become enemies after he is there he is going to make me sit there for 4 hours. So, finally, I was myself not my own friend how to do it you know day in and day out. So, I said I must make a electronic gadget. So, I was not very fond of electronics in particular, but I had to make this gadget. So, I made this gadget I will only touch the essentials of this as far as the this is the diagram I like finally, I had to make a sequential machine. So, depending on which table it is I must give a pulse to one of these 4 windings to go in the right direction. So, I can select the direction and I can select the speed at which it moves and therefore, I have to make what is called a state diagram. So, if it is in the a b c d state and I get a direction pulse then I must go into this I get the direction plus 0 I go into another state. So, depending on direction I must take the next object this is a very common thing. So, somebody will have already done it or you will have done it yourself. So, you have to pick up an application which is in good English and start implementing it by making this the diagram state diagram. So, you have to find how many states and then you make this requires to be transferred to electronics. So, electronics require these 4 states in the circular the numbers written across that are 2 digits. So, to implement a 4 state machine I require 2 flip flops say E and F. And therefore, with 2 flip flops we got this done and then it was able to rotate plus minus and then it will do this job. So, this was the full diagram this is what I made. So, there was a clock. So, 1 kilowatt whatever then I kept on dividing till I got 1 second then this become every 2 seconds it become every 4 seconds every 8 seconds every 16 seconds like that all the way to hours and then by selecting one of these every 5 minutes 1 hour 2 hours I was able to give fewer and fewer pulses. So, as it become cooler and cooler I go to here where pulse change every minute and there are 200 pulses required to change it by 1 rotation and 1 rotation was 20 degree centigrade. So, all was calculated and I can select progressively the slowest one as we become cooler I wanted a exponentially going down cooling rate. And therefore, all this was done then there was a splitter logic 2 flip flops stepper motor received and the stepper motor was actually monitored by some optical scanner. Optical scanner is required because you cannot depend totally on a open control this is called open ended control we will not know whether it is doing it or not. Because what I wanted to do was put it on and go to sleep put it on and come back tomorrow put it on on Friday evening 10 o clock and come back on Monday morning and they should have done that job. So, and I have to know that it has done the job. So, it has to be logged in. So, this is the nature of any application that you need. So, what is the moral of this story? I will do any electronics if I am forced to do it. Necessity is the mother of learning if there is no necessity I will not learn. I will I will read a case study from my book and keep on repeating in the class. So, there is another one the actual numbers what rate I wanted at what temperature and all this is the way an application has to be done. Then this is a an example just for the heck of it. So, there is a lift and I want to count the number of people going in. So, I must put two sensors one laser which is shown red and one laser which is shown green, but both are infrared lasers or infrared LED and detector. So, how do you detect a person going in? It must first operate x 1 and then x 2. So, if this is the sequence of x 1 and x 2 then the person has gone in. So, as soon as it is x 1 it goes to a state diagram circle which has x 1 has been detected, but if it again operates x 1 then it comes out it comes back to original state nobody in the lift. Then again it goes like that if it operates x 2 then I put a counter up. So, this is up down counter which is programmed. So, every time x 1 and x 2 are operating in that order my counter goes up 1 person in 10 persons in after 8 person it will give a alarm that is the capital yes please. No these are all hypothetical problems for students. So, we do not do any such thing this is not a real case this is just for understanding. So, we have this case that the person comes out then he operates x 2 first and x 1 next and then it should count down. So, this was an exercise to students just to make a up down counter I think you have got a exercise tomorrow. Then you will why are we doing this experiment up down counter the same counter why sometimes accounting up sometimes counting down professor wants us to trouble you that is the that is the for this where it is required that is the way it is this is the state diagram. As soon as we get x 2 then it says all I am likely to have a person going out etcetera. But I am here nobody is inside and then it starts all over and then keeps going up and down. So, this is the diagram and then we require 5 states therefore, I require 3 that is the way it is counter 2 raise to n n being the number of flip flops. So, the number of states in the diagram are 8 then I require 3 flip flops anything more than that I require the next. So, flip flop number does not increase that fast number of states go as 2 raise to n then you do this is that logical implementation the flip flops and this counter and all this is the output of the flip flop 1 output of flip flop 2. If that none is not a condition then we can even do with the 2 flip flop because none is very easy as you wake up it can wake up with the 0 you do not have to have that as a state and therefore, 2 flip flops will do it. So, this is the way an application has to be created to get the student interested otherwise you can give a standard formula or problem that do this up and down counter. So, I think I had done what was needed the journey to go from logic inverter to a VLSR logic the simple truth is all we have to think of a MOS transistor is a switch in the and the logic has to work with the switches as a concept only way when we want 20 inputs and so on we found that the linear connection of 20 odd transistor is not desirable then we connect a current source because the MOS transistor in saturation is acting as a current source. So, now with these 2 ideas now we are able to do all programmable logic what is the difference between PLD and sequential machine PLD is operating on the state of input as of that time it does not depend on what is previously done whatever is at that time combinational logic will only given output, but in real applications we have to know what was the history also like how many people were already inside the lift that we have to know. So, like that history we have to know the history and therefore, memory units are required and the flip flops are those units if you now make sequential circuit you can now make the application. So, FPGA has this capability of you know connecting themselves as flip flops connecting themselves as combinational logic connecting themselves as adders, subtractor, multipliers, soul arithmetic logic etcetera etcetera. So, whatever are the building blocks of a microprocessor or any real application the FPGA has got the reasons in which these are pre-programmed and available for users to use and therefore, it becomes very easy to program an application on FPGA. So, now for the last one there are of course, students who are coming after experience of 4, 5 years and doing PhD here and. So, there is a story about a particular professor very, very sincere fellow very silent very, very likeable, but his colleagues were not very happy the colleagues asked him once how come you define the problem for the student then you solve it finally, you want write his thesis I mean what is this do not you get irritated that you have to define the problem solve the problem and also write the thesis, PhD thesis he said it is ok. No, no, no, but you must be irritated sometime he said yes when they come and ask for the progress. So, that is the worst part of any professor's mind that you get a student for him he has to do all three and on top of it we will keep coming time to time and ask what is the progress. So, I think short of that it is a pleasure to be talking to you and I guess I have taken you to the journey from an inverter to a VLSI as I said it is not my objective to teach you more experience, but I think in every field or every topic you go to analog like that first concept to the students should be that overview that how everything gets connected you can tell in the beginning and then in the end. So, there is another one which is a cliche for you that you tell them what you are going to tell them by overview like this then you tell them in detail and in the end you tell them what you are told them the third time they will understand. So, you must not ever actually in the end hurry up and say I have to cover more topics I have to cover more topics you know in a hurry you finish chunks of thing in the end your job is to uncover the topic not cover the topic for the student you have to uncover the topic. So, that may you have to set a pace which leaves you five lectures in the end without anything to be done and what is that five lectures for is to give them that final one that what I have told you I am telling you again. So, third time you are lucky they will understand because as I said they are like a baby start standing up walking running only when you start running they perfect the previous stages and therefore, in the end you have to tell them again what you are told them and for that you must not leave anything to chance you must cover all your topics four lectures before the end. So, that you can uncover lot of learning and that is the purpose, but unfortunately the syllabi syllabi of university is so cramped with knowledge two courses being squeezed into one and so on, but I I still attempt I think even a student I assume that you can appreciate even a student in such overview lecture will understand something you may not actually do everything, but then that is why the tutorial is absolutely the must without tutorial a course is going to be flat you tell them they forget the tutorial is the one where they actually remember and a project a real project with the purpose it may be a a hypothetical project like counting people in a lift, but a project that hypothetical also will tell them why they have to count up and down. So, like that every laboratory exercise must have a English story why they are doing it I think we do not have that here we should an example of why somebody wants to count something up and down that story has to be there why you have to take the characteristics of a transistor that story has to be there you have to say that this characteristic is important for this reason. So, in m o s what is the important thing the straight line portion and the saturation portion nothing else is important that you have to tell them any questions why they I conduct many courses one day, two day, three day, five day for industries the most important thing is to finish on time with time for questions when do we not finish on time and leave no time for questions when we are afraid that we cannot answer any question then you must take more time. So, that the audience is so tired and wanting to have cup of tea so badly they will not ask any question. So, I think we have few minutes still left 11 o clock question. So, I have those six lectures I told you one on inverted to VLSI logic other one is RLC analysis to VLSI analysis and then LED to lasers and two of my other favorite topics is what is the innovation for students and what is design of experiment for experimenters the last one for all you people I will write I have not written yet one and half hour overview of how you can get results which are publishable and will get lot of citation. How to plan research it will get you very good papers which get cited. Sir my question is related to VLSI it is about pass transistors we say that we should not connect more than four pass transistors in series. Yes. Can you throw some light upon that sir. So, the same good reason we had this 20 or 30 transistors and their resistors will add so we should not. Why exactly four I mean we are not five transistors. This all depends on detail specifications and my answer will flabbergast you to no end this is my knowledge I had in 1984 after that I am not doing VLSI. But VLSI has not moved too much 25 years. What I am saying is a principle basic principles remain same the specification why four because now we are going from five volts to three volts to two volts and now future VLSI will work at one volt then they will reduce that limit to two where depends on what voltage you have access to what is the noise margin you have got to define a zero and one as the voltages are going down the number of series transistors will go down. In my time we used to say not more than eight with five volt applied but now that number has to go down otherwise you will encroach on the noise margin. So, zero will not be recognized as zero it will become one etcetera but concept is same that too much of resistance will come and voltage drop will appear any other question but I am not a VLSI man I left it in 1984 but it is ok the general knowledge remains same that is a good part of it. So, after all what does the professor teach whatever the syllabus is one of our old professor if you say professor teaches what he knows finally he does not teach as per the syllabus he only teaches what he knows. So, I think as a basic funder happily first year to second year courses there is no problem at all not only it is good if you teach them what you know it is appropriate that you only teach them what you know when you teach them in third and fourth year you have to read more recent work and then I prepare yourself with information see the fourth year courses are more informative less knowledge and less wisdom this is the way it goes data information knowledge and wisdom as you go to the fourth year it becomes only information but they need the information. So, how are they doing the current mobile networking and all that this is the information. So, what is 2G what is difference between 2G and 3G spectrum that is the information sorry I do not know but people who teach will have to know they will have to learn. So, with that I think we will end. Thank you very much.