course is on digital circuits and digital systems. We have this, signals. A signal is
a variation in a physical parameter, temperature variation is a signal, speech as I speak now
it’s a signal, video is a signal, light intensity variation. Now any of these signals
that you get need to be may be processed to be available to the other end may be stored
so you do lot of processing of signals in real life. For example, if you take a microphone
the speech signal that you give into the microphone if necessary it needs to be amplified and
then given out as a signal out of the speaker, the sound signal out of the speaker. So it
is a typical signal processing scenario.
We are in the electrical engineering domain we talk about only electrical signals that
means variation of an electrical quantity a voltage or a current as a function of time.
A signal is defined as a variation of electrical quantity usually a voltage or a current with
time. Of course you can also a signal which does not change with time then it is not called
a signal any more it is the DC value we say. For example, if you know that the value is
not going to change there is no need for processing so you know the value so you can use the value
wherever you want to use it.
Now, once you have this variation any signal that naturally occurs the speech or temperature
variation or as I said the illumination changes in the television or a seismic earthquake
activity any signal first you need to convert it into electrical variations some other are
mechanical so other physical parameters so there is a transducer a sort of a device this
device which converts non electrical quantity into an electrical quantity electrical signal
known as the transducer. So the output of the transducers in electrical signal is where
we define the signal as the variation of the parameter of interests the voltage or current
Normally a signal can take any value of course within given limits and different instance
of time a signal varies continuously. For example you have a time variation of signal
voltage level of a signal as a function of time, if I plot like this then any number
of values this signal can take as a function of time
But of course there is always a limit, what is the minimum, let us call this minimum value
as 0 and maximum value as Vmax. With two different values we define and say that signal always
varies within this range, this is the range of the signal. And at any instant of time
it can take any value and what is the instant of time is also not defined, I can make a
measurement here and immediately at very next instant of time or I can do a measurement
here and measure much later here nothing is remaining here. This variation of signal which
can take any value between these two limits and such a signal is called analog signal.
Analog signal or analog quantity can take any value at any instant of time within of
course the limit defined within the range specified.
And on the other one I want to process the signal only at discrete instance of time.
Suppose I want to monitor the temperature of a system every minute or every hour or
every thirty minutes or whatever you discretize the time at which you look at the value of
the signal the signal will vary continuously all the time and you are looking only at the
discrete instance of time at a definite instance of time only there you are looking at and
such a signal suppose I put this value I will have equal intervals of time so call this
t0 the starting point then t1 t2 need not be equal but just to explain it little easier
I make it at equal intervals of time so I will monitor the value of the signal v(t)
at instance of time t0 t1 t2 t3 t4 as long as I want or as long as I am interested in
the parameter so such a signal is called as the discrete time signal. The signal still
An analog signal is a signal which takes any value between the two defined limits as a
function of time. But even though the signal varies I am only interested in looking at
specific intervals of time and such a signal is a subset of the analog signal that is called
a discrete time signal. The problem in these two cases whether you want to continuously
monitor what is continuous finally it has to be discrete. Even it is a one micro second
then what happens between one microseconds even one nanosecond can change in between
Finally we can only observe. Physical parameter will vary with input and output but if you
become an observer the observation can only be discrete.But whether it is a discrete time
signal or analog time signal the variation of the signals between these two limits is
a continuous variation there is no defined points by which it can vary. What I am saying
is supposing my initial value is 0V and Vmax is 5V as an example, as an example I make
this 5V I am only allowing this signal to change from 0 to 5V and within this 0 to 5V
it can take any value.
You may have difficulty in representing because you have limitations in the digits you are
having in your calculator or I cannot represent any number beyond a particular number of digits
to be meaningful. But theoretically it can have number of levels between 0V and 5V. Now
when you are trying to transmit a signal because after the entire signal itself as no meaning
unless you use it somewhere.
As a change in the speech, when I speak my speech is picked up in the microphone and
it gets converted into electrical signals and the electrical signal is amplified by
the amplifier and then is put out on the speaker which brings it out as a speech signal. So
there is a processing involved in any signal and if there is no processing then we are
not interested in any signal. We are not interested in looking at a signal just for the variation
sake. We don’t want to stare at a signal just because it’s nice to see, it keeps
changing it’s nice to watch so I am sitting and watching it, it is like a wave in the
ocean. When you go to the beach and sit there and watch the waves I like to do that myself
because that’s only for fun, for relaxation.
But when you have a signal you have to use that signal somewhere. You transmit it or
you store it for later use, one of the two things. I pick up the signal and process it
and give it as an output to the another system another transducer which will convert this
signal into the physical parameter like a sound or a light or whatever or I may even
store it for later use.
Suppose I want to know yesterday’s temperature variation over today’s temperature at 11
O’clock yesterday what was the temperature and at 11 O’ clock today I want to know
what is the temperature and at 11 O’clock take the temperature reading store it, today
I take the 11 O’clock temperature and say that today is hotter than yesterday.
So either you store or transmit it when I do that how accurately can I represent my
variations within these limits of 0V and 5V as I said I can take infinite number of values
I may not be limited by the channel, how accurately can I send the signal, I can directly send
it or the output I can receive which will be an analog signal. But if you want to store
it and reproduce it I would like to be limited by the number of digits I want to use. That
way I can safely say this is within that and within that limit I will define various levels
the signals can take and I will say the signal is in this level tomorrow in this level sot
there is a change of so many levels.
So if I further discretize it I discretize the time to start with. originally I had a
signal with continuous time and continuous amplitude variation then I let the amplitude
continuously vary but discretize the time, I am going to introduce one more discretization
in the amplitude I will say I will only let the signal take a specific amount of level
specific number of discrete levels so 0 to 5V even though signals allow to vary I have
no control over the input signal, the temperature variation and when I record it I only record
it as discrete levels or when I process it I only process those discrete levels, when
I transmit it I only transmit those discrete levels.
Of course how accurately I want the reproduction depend upon how many levels I want to have,
I have only two levels, it is 0 or 1, 0V or 5V is the signal present or not present that
is too crude or I can have four levels 0 to 1.25, 1.25 to 2.5, 2.5 to 3.75 and 3.75 to
5. I can say if signal is less than 1.25 then it is level 1, between 1.25 to 2.5 I will
say it is level 2, 2.5 to 3.75 I will say level 3 signal and 3.75 to 5 I will say level
4 signal then you know that the signal is in this range. Therefore more and more levels
are introduced and I can introduce more and more accuracy in transmission and reproduction
but still it is a discrete level. So when I discretize the amplitude in addition to
discretize the time I get what is known as digital signal. That means I will only allow
this variations let us called this level 1 or this I write as 0, I will say L0, it will
be level I, L2, L3, L4 etc.
Depending on how narrow or broad these ranges are the total number of steps will be decided.
The total number of steps to be decided depending on the level of each of these steps I am going
to take. Now I will say suppose I want to represent
the signal value at t1 it is between L2 and L3. I cannot say it is between L2 and L3 it
is not possible to store between L2 and L3 or it is not possible to transmit between
L2 and L3 I have to either transmit between L2 and L3, I have to make a prior understanding
I will always round it of to the nearest lower level or nearest upper level.
So for our example in this case let us always round it of to the nearest lower level I will
say at t0 the signal is L2, at t1 also the signal is L2, at t2 the signal is L3 because
here it has become between L3 and L4 at t2, at t3 it is L4 at t4 it may be L5 and so forth.
Hence each of these levels can be stored or represented by a smaller number of digits
than originally it had intended to be. Suppose I have infinite number of levels I need infinite
number of digits to represent it. Now each of these levels is going to have discrete
levels so I will have fewer digits to represent, fewer for storing and fewer levels to transmit
in the case of transmission.
Now let us say there are only a total of eight steps, between 0 and 5V I divide this range
into only eight steps, I don’t expect much variation in temperature or I am not interested
to find a variation, or I am not interested to find whether it is too hot today or too
cool today it is all like if know where the temperature is in this range of 0 to 5V in
eight levels you tell me and if I tell you that then I will use eight levels so these
eight levels can be represented by eight different values so it is easy to store eight different
values and transmit eight different values rather than having to store infinite, supposing
the signal can be anywhere from 0 to 5V if is 4.7392481 I should have so many digits
to represent it or so many digits to transmit it, I am now removing myself from it, the
accuracy that much is not required. On the other had I have the flexibility of increasing
the accuracy by increasing the number of levels.
If I am willing to store more levels and transmit more levels we improve our accuracy. If you
are not interested in storing more levels and transmitting more levels then your application
can now decide the accuracy that you want. So there is flexibility in this digital domain
which is not there in the analog domain. In analog domain if you make a measurement, suppose
if you go to a physics lab make a measurement of current or voltage the representation is
analog the needle moves, it stays somewhere between 3.2 and 3.3 but you will only interpret
it is 3.2 or 3.3 or say 3.25 or 3.275 like that you will make a guess. But really if
you want to be very accurate I should be in a very large meter with minor sub-divisions
of each of those and then keep on doing it till you can get accuracy.
There is an accuracy built in analog also because of our observation power and because
of the limitations we are using for measurement, now I am legalizing it that’s all I am making
it official. So I am now saying I am going to tell you these are the levels permitted
always represent your signal within these limits. But if you give an analog meter I
approximate it, here I approximate it in a systematic way so now this is the digital
domain we will be talking about.
Now why do we go for digital because even though there is inaccuracy built in analog
also if you want to improve the accuracy of analog what will you do you will do a more
precise meter with a large range and each range subdivided into many sub regions so
that you will not make a mistake. Supposing you know the current always have to be between
2.5 and 2.7 I will make a reading of 2.5 to 2.7 so large and between that I will divide
into smaller and smaller sub-divisions. This possibility improves the accuracy of the meter
by any amount by putting more and more of precise instrumentation. By making a precise
instrument for measuring current or voltage or any other quantity you are trying to measure
I can always improve the measurements of analog signals. Likewise I can always improve the
accuracy of my digital instruments also by having more and more levels because I need
to store more and more levels or to transmit more and more levels.
So accuracy can be decided based on the application required. Then what is the advantage of going
digital. Analog also has the potential inaccuracy which can be improved depending on the need
by extra hardware, I will call it hardware or extra precise instruments. What I mean
by hardware put more money in other words. If you put more money you will get better
system is it not? Anything if you put more money you may get a better system, more money
you get a better car right? That is what it is.
In digital also I have a potential of improving the accuracy by putting more and more levels
which means more and more levels means more and more hardware then I should have some
way of representing more digits more levels, earlier I had fewer levels now I have more
levels so now I should have some other hardware to represent this so here also it is going
to cost a little more in terms of instrument implementation.
But now why analog why digital? So this is the difference between the analog signal,
discrete time signal and digital signal so in this particular course we will be dealing
with digital only, both in time and levels it will be digital. We are not talking about
analog signals that is analog electronics POE Principles of Electronics, you will learn
later on and discrete time you will learn some other time for some other specific applications.
This course will deal with only digital signals and digital processing of signals, digital
representation of signals; digitally you have to store it etc so this course is on digital
circuits and digital systems.
Now, one may say that signals are basically analog in nature when it is generated. When
it is generated most of the signals are analog, temperature variation is there, you can’t
say that temperature always jumps between one degree intervals can you say that? Today’s
temperature you want to measure can you say that my temperature will only jump from 31
to 32 in between it should not jump, can you force it? No, you need not take cognizance
of the fact 31.2, you will say either 31 or 32 but then see temperature will change, analog,
there will be infinite levels, it will only take 31.2745 also it can change you don’t
Likewise all signals are analog similarly when you put the thing back and after processing
or storing, transmitting and get this back on the other transducer reverse transducer
in this case, in the case of microphone the reverse transducer is the loud speaker, the
signal makes the sound possible the loud speaker the electrical signal is converted into sound,
the light is picked up as an electrical signal it is processed and in your picture tube at
home television receiver the electrical signal is converted back into light where you see
the shadows of all these movements which you are addicted to, all the time watching TV.
So it is again a conversion of analog to digital, digital to analog and back so why do we have
to go through the digital path? Why can’t we take analog signals? Anyway inaccuracy
is there, in digital also the accuracy can be defined by you, in analog also there is
a provision to improve accuracy by spending more and more precise hardware and more and
more money, in digital also I can do more and more hardware and then get better accuracy
so when that is the case why suddenly make all of them learn this course digital? One
thing is I am going to get salary out of this course teaching you that is the minor reason
but the real reason is digital signals are easy to store and manipulate without much
error, I will give you an example.
Supposing I am measuring an analog value I am storing an analog value, how do you store
an analog voltage? How do you store voltage? Capacitor, you store the value in a capacitor.
Supposing I charge my capacitor to 1.27V today and tomorrow somebody else comes and measures
it then it is equal to storing and retrieving it later or storing and transmitting it, you
stored 1.27V and tomorrow somebody comes and measures 1.25V does that person know that
you have stored 1.27 volts if he knows then there is no need for storing you can also
tell him then there is no need for capacitor, if you are going to see that fellow tell him
it is 1.27 he doesn’t have to come and measure. So when you leave a voltage of 1.27 volts
on a capacitor and measure it again you don’t know how much is the last.
For analog value because 1.27 is only our limitation, as I said it can be 1.27 to and
in that case it can be measured as 1.27 too whatever value you put you should be able
measure it accurately but there is always a leakage or I am transmitting analog signal
let us say 1.72 instead of storing in a capacitor I am trying to send it across a wire to the
other end as a signal so you try to send 1.72V the receiving end it is measured as 1.75V
this person has no idea that you sent 1.72V and if he knows that you have sent 1.72V then
there is no need for a transmission. So the other end receives it as 1.75 volts he was
not sure about what you have sent that was one point seven two volts. There is a 0.03V
noise which has been added in the transmission part which itself is 1.75V but he doesn’t
know exactly how much is the noise added. Now there is uncertainty about the values
of storage and the transmitted signal in an analog domain.
Take a digital example; I have only eight levels as I said or a minimum number of levels
whatever is the level but I will take eight as an example. Between 0 and 5V I have eight
levels so when you divide 5V by 8 how much is each step? It is 0.625. So if the voltage
level that I want to transmit is between 0 and 0.625 I am going to send it as a 0 level
that is what I told you, I am going to round if off to the lowest level. If it is between
0.625 and one point two five if it is 0.625 and 1.25 you know it is L1 level one.
Supposing I send 0.75 let us say there is a noise added, at the same .03 a noise was
added same channel I am sending so the noise is added in it so 0.75 is going to be received
as 0.78 but it will still be recorded as L1. The effect of noise on a digital transmission
is much lower compared to the effect of noise on the analog transmission. Since I only know
that predefined levels as the possible levels I know it cannot be 0.75 it cannot be 0.78
this guy must have send 0.625. I don’t care whether 0.75 became point seven eight because
anyway you send only 0.625 which is level 0.
Unless there is a marginal thing where you are trying to send 1.25V you send 1.24V which
is referred to as L1 and 0.2 got added so 1.24 plus 0.2 will be I will not even say
0.2 so .01 got added so 1.24 becomes 1.25 then you are not sure whether what you sent
was L1 or L2 but occasionally these type of extremities are there. I am not saying it
as a perfect transmission I am saying it is better than analog in noise performance. That
is one of the reasons why you want to go for analog. It can store and reproduce values
not more accurately but I will say more reliably than, why did I not say accurately? Accuracy
depends on number of levels I use. If I am going to truncate my 0.825 as 0.625 is not
accurate by any stretch of imagination but I chose to have only eight levels. If I wanted
I could have had 16 levels, also if I had wanted I would have had 256 levels, if I wanted
I can have 1024 levels so that case becomes more and more accurate. Accuracy depends on
the number of levels but more reliably I can store and reproduce and more reliably I can
transmit and receive, that is one reason. Do you think it is a valid/good reason to
for digital? No? You are not convinced. I think it is a good reason.
Now second reason I will say is I will go back to accuracy a little bit more. I said
accuracy can be improved by analog or digital case. In digital case it is having more number
of levels and in analog it is by giving an instrument which is more accurate which can
handle these lower order values better by increasing the sensitivity of the equipment.
For example, a meter, how does it work? A meter works by the current carrying coil which
just makes a deflection of the pointer and where it stops so if you want to make more
accurate measurement I should have more sensitive coils but now the difference between having
more levels and more sensitive analog is very different.
To improve the accuracy it is easier in digital because all I have to do is to increase the
number of levels. So reproduction of levels is the same effort. Hardware wise it is more
but then the similar hardware I have more of it. So if I have similar hardware more
of it I can improve the accuracy of a digital system. In analog system to get more accurate
I need to struggle more I need to slog more. Analog improvement accuracy is more difficult
than digital improved accuracy. Digital improved accuracy means more levels which are identical
to the earlier levels. Instead of having eight of those levels whatever it is I will have
sixteen of those whereas for analog I cannot say.
For example, if I want to make a measurement of the distance from here to here if I ask
you to measure and give me the feet you will very easily take your foot ruler and measure
and say seven feet, eight feet and if I ask you to do in inches then you will be little
more careful you need a scale with an inch, rule of an inch calibration in it and then
have to be very careful and then finally if I say give me the nearest millimeter then
I need an instrument with a millimeter calibration and then I have to be very careful in my measurement.
So, by measuring more and more accurately in analog systems is difficult than having
more and more levels and improving the accuracy or precision of a digital system, that is
another reason I have given for a digital. So the cost of more accurate system is proportional
to more accuracy in the case of digital whereas it increases the exponentially in the case
of analog. In analog the increase in cost for most accurate systems is not proportional
to the accuracy improvement but it is much more than that.
For digital I spend more money I get a similar one. If a I am happy with four levels be happy,
if you want eight levels give me double the cost I will give you, in analog I can’t
say that so it is more difficult to make more meaningful measurements more accurate measurements
in analog compared to digital or storage. When I say measurement it means storage and
transmission everything. The quantity we may signal after all what did I say the signal
has to be represented, stored, measured, transmitted, everything is part of signal that is called
signal handling or signal processing. The signal has to be processed, you can call it
handling of the signal doesn’t matter to me. So these are the reasons why we go for
digital. So now the effort is to convert everything that you see in the world and why can’t
you do everything in digital? It is not possible.
So I told you why digital, why do we need analog? If you say so much about digital being
so good can you not do away with analog altogether and have only a digital world and not have
the principle of electronics course in your next semester? It is a good tempting thought
but unfortunately not because all real life signals are analog signals. Be it a temperature
variation of a body or a temperature variation of a parameter or anything or a speech or
a light or heart rate or whatever you think of, have you seen the ECG waveforms in monitors,
in hospitals, in movies? Suddenly the heart rate will come and then follows that that
is how they represent a person dying in a movie is it not?
So all are analog signals unfortunately or fortunately if you look at the analog people
they will say otherwise they won’t have jobs. So analog signals are there and our
job is to convert these analog signals to digital signals and because we live with digital
people but today technology has improved so much it is easier to do digital as I said
it is easier to do digital cost of the digital becoming lower and lower so we want to do
more and more of digital so what we do is we cannot do away with analog I told you,
first we pick up the signal analog by a transducer as I said, sometimes the signal is so weak
that you need to amplify it before you convert into digital you need to amplify it. Supposing
you don’t do an amplification sometimes the signal gets lost, the signal is lost completely,
you get very weak signals and if the signal is not very weak you can directly convert
Therefore take an analog signal convert it to digital preprocess if necessary that is
if signal is very weak, convert to digital, by process I will put anything I am not going
to put separately store measure and all that I combine all of them, manipulate do whatever
you want with that signal that is called processing, just storing and reproducing is also processing
and then convert it back to analog this is the flow of any processing today and because
the technology advances because the digital domain being so dominant today in electronics
they are trying to push as much as possible digital domain and have as little as possible
So in any system today you design ninety to ninety five percent of the activities are
digital but that five ten percent of the analog is not real, without a proper signal whatever
processing you try to do that is not going to help you. I am not trying to say analog
is not important, I am not trying to say don’t go to analog but more effort is put on digital
more amount of work is done in digital domain than analog domain. But design efforts are
very difficult in analog as I said. To improve the accuracy in analog is not easy but digital
is easy. So effort wise it may be even equal or slightly different but then I am not saying
in reality in that sense please, do not misunderstand me, do not misquote me to analog professors
and pick up a fight for me with analog professors who are my colleagues here, I am not saying
that but digital as lot of these applications today and what we will be seeing is only this,
we are going to do this process convert to digital, convert to analog and that we will
learn later on in future courses but in this particular course what is this signal, how
are these signals represented in digital, how are we going to use it in processing,
what are the various things we can do, what are the various things we can do with this
signal, this is the basic building blocks so what we will basically study in this course
are building blocks of digital circuits and systems. There are several other things but
we will not go into the details.
We will have to do from the analysis point of view we have to analyze the behavior of
them, how does it work, what is a building block, how do you define the input output
relationship of this, how do you analyze it, how do you use it, analysis, use and design,
how do you design it to build one? That is the crux of the subject matter of this course.
We will go into the details of the subject matter this is further divided into combinations
circuits and sequential circuits and all that we will see them as we go along.
So basically we will look at the basic building blocks of the digital systems and digital
circuits find out their behavior how they are built and how to use them in known applications
and in a reverse mode given a requirement in a digital system how do you go about designing
the requirements or what are the building blocks you need and how to connect them in
properly and so on, that is why we call it the design phase. Design is given the specifications
of the circuit how are you going to choose the proper building blocks, how are you going
to connect them together, how are you going to make it work to give you the satisfactory
There are two types of circuits basically; one is called combinational and the other
is sequential, both come under the same digital category. I will define the difference between
these two a little later on. So, in a nut shell you want to know the course content
of this course we will be doing the analysis use and design of combinational sequential
building blocks which are required for digital circuits and systems, one sentence course
formulation and what are the books we will be using? A very good book is called “Digital
Design” by Moris Mano M. M Mano he is called as Moris M. Mano this print is all book I
think, it has come in cheap edition it is available, I think it is available in our
This Moris Mano has come through several iterations, it has been there for a while for the last
twenty years this person has been writing books and updating and improving the contents,
this one is the latest version called as the third edition, digital design edition 3. Then
we have Roth Junior C. H. Roth “Fundamentals of
Logic Design” by Jaico Publishers, I don’t know what it is Jaico Publishers 1998, there
are two typical but there are so many books.
Any book which as title like digital design, logic design, digital and logic design digital
circuits, good enough because these are all very basic stuff we are talking about, the
basics, the first introductory material and digital there are scores of books at least
about 15 to 20 good books you can see in any library and I will not be following one book
strictly, I would like to teach you everything you need to know in your first level course
but does not mean that we will be following the book that cover to cover it is not necessary
because this is such an interesting course we have been teaching this course for a while
so some books doesn’t cover one topic very well, some book does not cover a topic at
all properly so in that case I will go on, I don’t even have to follow books because
I am teaching this course so many times so I will just sort of give an essence of my
experience of teaching this course over years, might as well has been a good practice I have
been doing it for a while without any much complaints. So that’s what we will do but
you need to have a book so that you need to follow the material and do more studies, sometimes
we are not spending enough time in the classroom we want to do further studies, sometimes something
is not very clearly explained in the class you want to go back and refer to a book so
please have a book, I am not saying you should not have a book but do not expect me to follow
a book from page to page and it always nice to have a basic digital because book because
this is a first course lot of other things are done.
As I said today digital world is technologically a very advanced world so lots of opportunities
are there for you to do digital, there may be an advanced course in digital that you
may do, you may be doing some mini project, you may be doing even a major project in digital
area so it is always nice to have a reference book with you instead of always having to
borrow or copy somebody else’s book and all that.
So if you are thinking of buying a book you can buy one of these two books, there are
so many others also. If you are doubtful about a particular book and if you want to know
if it is good or not you can always ask me, you can browse through and that will tell
you. So these are the various things we need to know and as we go on we develop a material
and for homework I may have to prescribe some of these books so that may be a good idea
that way to have, at least there must be enough for books available so that you know what
problems are there for the class.
This is where we will stop today and in the next lectures we will start with the detailed
subject matter as I said levels and all that, we will be more specific how to present levels,
what do you mean by level and what are digital signals and how do you represent digital signals
and then we will start with the simple gates and then go on. It is a good idea to have
a book and follow the book read the book sometimes it is better to read ahead of the class if
possible so that way you can understand this topic better. I will prescribe homework from
the book so that you can start also working out problems, okay we will stop here today.