Already, we have learnt how to design the combinational circuit design or simple

combinational circuits, complex combinational circuits. How we can synthesize the

combinational circuits from, given Boolean equations or given a problem? How we can

design a combinational circuit? Today, we will start discussion on sequential circuit

design particularly the Synchronous Sequential Circuit Design. Now, first we consider

the design of sequential modules, what do you mean by sequential logic circuits.

Now, in combinational circuits, we have seen that the combination output of the circuit

depends only on the inputs of the particular circuit. Now, the sequential circuits depend

not only on the present inputs. But also on the past history of inputs and time, means

that the present output depends the present input.

As well as, the previous state and that state is a time of or is a function of the inputs

and time, so that is why it is written that past

history of inputs and time. Now, a memory element is attached with the combinational

circuit, which allows the output to be fed back as input, mainly that how the sequential

blocks are developed.

Now, see the normally this is the design of a simple sequential modules, one

combinational circuit is there and inputs all ready we have seen that, these are the

present inputs. Now, for combinational circuit these

outputs are the only the function of present input, but here one memory element is attached.

And that it is the sum of the outputs are attached with the memory and it is then fed

back to the combinational circuit. So, these thing, these combinational circuit

attached with a memory elements which feedbacks some of the outputs is a sequential

module. So, this is the basic module of a sequential circuit, now what do you mean by

synchronous and asynchronous circuits.

Now, the with the memory elements we will attach a clock, so whatever was there in the

sequential circuits the present input is there the outputs are there, some of the outputs

attached with the memory element and they are fed back to the memory. Now, we are

another input, this is a clock input that is given to the memory, so what it will be

doing.

See the clock pulse is used to regulate the feedback, when the clock pulse becomes high

the inputs are enabled. So, if we see the picture, so when this clock pulse say here

we are giving say one clock pulse, so when this clock

pulse is high means this is high, then only

this inputs are this memory inputs are enabled to the combinational circuit, so this is the

circuitry description the sequential module description. So, mainly there are another

control input and that is the clock pulse is attached with the memory element.

Now, this circuits with feedback, so memory elements can be created by simple gates

this is the inverter NOR gate and NAND gate. And mainly this is the basis for

commercial static RAM designs, means the one bit memory element. And cross coupled

NOR gates NAND gates that are also used that means, inverter NOR gate NAND gate

mainly, they are the they are used to design one bit memory.

First we see the simplest design, see we consider here 1 inverter we if we draw say first 1

inverter is there we apply 1 1, so what will be the output, output will be 0. Now, another

inverter is cascaded with this, so it will be the output will be 1, now if it is feedback.

So, here I am giving 1 and that 1 and getting

here and see here the concept is, as if the delay

of two inverters up to this time this. The some of these delays up to this time this

1 is stored in this circuit, my input is 1 input

is 1 my output is 1 and as if this is the time and

stored this one the time during which the 1 is stored. So, this simple concept is being

used. Now, before we read the in details the design of flip flops or this memory elements

using NOR and NAND circuit first we define a flip flop and the latches.

So, mainly the latches and the flip flop they are the basic sequential logic elements, now

the latches and flip flops mainly, the latches and flip flops they are the most important

type of sequential circuit. So, flip flops are used as building blocks to construct larger

sequential circuits and flip flop operates in one of two modes, one is called the direct

mode and another is the clocked mode. Now, first we see the definition of this direct

mode flip flops and the clocked mode flip flops.

Now, direct mode flip flops that respond directly to the applied inputs means the output

changes as the whenever, the input changes. And the example is the we will see later that

SR flip flop examples are SR flip flop and gated the D flip flop, now the clocked mode

flip flops respond when a clock transition occurs that means, there must be 1 clock input

in the circuit. Already we have seen that in the sequential module, 1 clock input we

can give to the memory elements. So, when a clock

transition occurs from one voltage level to another that time only the output responses.

So, the output respond when the clock changes, now the examples are the T flip flop

or sometimes we called the toggle flip flop it is normally called T flip flop, when JK

and clocked D flip flop. Now, one by one we will see the different type of flip flops.

Now, first we see the latches because that is one basic elements, so we consider all

ready I mentioned that the way I have one bit memory

we have designed using inverter, say two cascaded inverter see here two cascaded

inverter and the output is feedback. If I give

1 intermediate 0 then it will be a 1, now I am taking 2 NOR gates, so this is 1 NOR

gate this is 1 NOR gate. There are 2 inputs one

is called the R means the reset, another is set

S. So, normally these are the 2 inputs R and S, the reset and set reset means R set is

S, so this is the 2 inputs.

Now, the circuit made that output of the first NOR gate, that is being fed back as the

input of the NOR gate where S is another input. Similarly, the output of the S that is

being fed back to the NOR gate where R is another input. So, thus this is the circuit

that means, two NOR gates we have taken R is 1

input S is input of the two NOR gates and the other inputs are actually the output of

S and R or output of the two NOR gates. So, the symbol normally used is that one rectangular

box the 2 inputs are R and S 2 outputs are Q and Q bar Q bar that means,

Q bar is the complement of Q. So, the 2 outputs is are the complements and the these

are the symbols.

Now, we see the function table, see that these are my inputs of the circuits these are the

inputs, one of the output Q this is my one of the output circuit I thing. We remember

that two NOR gates are there one R inputs, one

S input and the output of this is fed similarly, the output of this is fed this is Q this Q

bar. Now, this is the function table that when the

inputs are 0 0 then it is denoted as Q i output is Q i plus 1. Means we can write that this

is the present state, say this is my as all ready we have mentioned that the present

output. Or better I write that present output is a

function of the present input and the, so this is

my present output and the previous state. So, this is my present output and this Q i

we denote, that sum of the previous state that

previous state. So, from where we have started after that if we give the R S inputs at 0

0 then the it will be the previous state. So,

if it is 0 1 now, if I give 0 1 then output is 1 if it

is 1 0 it is 0 0 and if it is 1 1, then question mark means this is undetectable this is

undetectable. So, now each of the input cases we see each of cases that how the function

table forms by this circuit.

See first we assume that the first case that R equal to 0 and S equal to 0, so input is

fed, so R is 0 and S is 0 this is my circuit. Now,

if the earlier Q value was 1 and then that if R

equal to 0 what will happen? See earlier Q value was 1. So, 1 must come here, but this

is 0, so what will be the outputs say if we mark

the first NOR gate as the N 1 or the top NOR gate is the N 1. But we will now get as

the N 2 then what will be the function of the

or what will be the input of N 2. So, if we consider N 2 the inputs are inputs

are 1 0 then the output will be, because it is a

NOR, so output will be 0, so that means, here 1 0 will come. So, for N 1 for N 1 the

inputs are 0 0 output is 1, so that is why it is written as 1. Now, what will happen

it Q equal to 0 say that means, if we assume that

Q value was a 0 if we assume that Q value was a 0.

Now, if my Q value again if we draw the circuit say this is my NOR gate this is my R

input, another S input it is fed back this is also feedback. Now, we have assumed that

this Q equal to actually Q i means the previous

state that equal 0. So, far, so far N 2 the inputs are 0 0 0 0 output is 1, so what will

happen for N 1 this 1 will go here. So the inputs for 1 the inputs are 0 1, because the

output of N 2 is 1 and that is being fed back to

the 1 of the input of N 1 NOR gate and the output will be 0.

So, what we have seen when the previous output of the circuit, so previous output of the

circuits say Q i that was 1 my the present output Q or we can write Q i plus 1. If previous

we can denote Q i then the new current 1 is Q i plus 1 that will be 1. If it is Q i equal

to 0 just now, what have seen then the present

output you can denote Q i plus 1 and that is 0,

so that is equal to equal to Q i and this is equal to Q i.

So, what we can tell that this is the we this case we are discussing

that if R S inputs are 0 0, then this is the previous that we can tell

the previous state or we can tell that this is

hold. That means whatever signal level was there in the output it continues that mean

it holds that value it holds the signal value,

so R S 0 0 it is hold state.

Now, if it is a 0 1 similarly, if we see that if it is a 0 1 or 0 0, if it is 1 0 means

the reset goes active. So, what will happen if R equal

to 1 and S equal to 0 then in the similar way,

we are getting that Q equal to 0 and the complement of Q, Q 1 is 1. Since both inputs are

0 the output is forced to 1 the earlier situation all ready we have seen. Now, the output Q

bar is fed back to the gate and both inputs being 1 to the output Q stays at 0. That means,

if it is 1 then if it is 1 then R equal to 1 and the other input is also 1 that means,

for N 1 what we can we tell N 1 the inputs are 1 1.So,

the output Q is equal to 0, so that we are telling reset as the output is 0.

Now, again if we give R equal to 0 S equal to 0 then this reset goes inactive that means,

Q changed from 1 to 0. And the signals on R will have no effect, now set the latch.

Now, setting S to 1 then 0 now, if we see that setting S to 1 that means, then 0 that

means, 0 1 that activating S will set Q to a 1 stable state. When R and S are activated

simultaneously both outputs will go to a 0, when R and S now, go is active 0 both inputs

at both gates are 0 and both gate outputs are 1. Now, these I fed back to the input

drives the outputs to 0 again, so both inputs are

0 and, so on and it will continue, so what will

happen.

So, if we consider if we see that again if we draw the circuit say the NOR gate, now

say both inputs are these are 1, now if R 0 and

equal to S equal to now, then what will happen. That here also is it has 1 has come,

so this will become 1 1, because NOR gate, so it will become 1 and this will become 0,

so and it will continue that thing. So, when R

and S now go inactive 0 both inputs, when R and S now go inactive 0 both inputs at both

gates are 0 and both gates output are 1 just now we have seen.

Now, these one fed back to the inputs drives the outputs to 0 again, because once the

output of the NOR gate one of the NOR becomes 1. Then it will force to the other NOR

gate output be 0 provided the other input is 0 just now we have seen that thing. So,

again both inputs are 0 and so on and it continues.

So, what we see that again if we consider that means, say again if we draw two NOR

gate, see this is my R input and this is my S input now if it is 0. So, we are considering

some previous state and previous state just now we have seen, if it is are R equal to

0 S equal to 0 then this becomes 1. So, previous

state is 1 my Q i was 1. Now, when this becomes 1 this is 0 plus 1, this becomes 0

this is 1 and then this is again this will go 0, so

this becomes 1. Now, if the R input and if this becomes 1

then what will happen, see that these output forces actually, this is the reason because

my the other input is 0. So, this is the reason that it forces the output of this N 2 NOR

gate to be 0. Similarly, if this output is 1 then it

will force the N 1 NOR gate output to be 0, if the R input is 0 and it will continue,

((Refer Time: 31:18)) so that is mentioned here. So, this is 1 fed back to the inputs

drives the outputs to 0 again both inputs are 0 and

so on and it continues.

Now, these oscillations…So this will be a oscillation continues indefinitely for a

perfect circuit. But as the delays are not consistent,

because the even they are 2 NOR gates, but the delays are not sometimes there will be

a change in the time some processing time of

that gate that we have calling the delay. So, delays are not consistent in both the

gates, so the circuit will collapse into one stable

state or another and this collapse is unpredictable, because we do not know that which 1 will happen

0 or 1. So, what we can summarize that this 0 0 this

means this all ready we have seen this is a

hold state. So, 0 1 this is 1 means this is my set and 1 0 all ready we have seen this

is my reset and actually, 1 1 this is unpredictable

or we call undetectable whatever, so undetectable, so mainly these are the four

situations of the RS latch.

Now, the same operation we can get using NAND gate also, see now we are taking some

the similar type of structure, the taking that again one NAND gate R input is there.

Then this is with inverted inputs means, my R is

actually R complement otherwise the same circuitry I am taking, this is NAND, S output

again this is Q and Q bar. Always that inputs are inverted means R is R is complement

S is S complement and that similar type of symbols. We can use only see here this

bubble means here this bubble means it is inverted inputs.

Now, this symbol is same that R bar and S bar, again we are taking a rectangular shaped

box and Q and Q bar are the again this bubble is the inverted means that this is also

inverted, so this is actually inverted output. Now, the R S here the will be the same that

this is my inputs, so it will be as it is inverted, so actually R bar S bar 0 0 R S

0 0 means this is actually, the situation of 1 1 of

our NOR case and 1 1 means this is unpredictable. Similarly, it is 0 1 means actually 1 0 and

that is my reset case it is 1 0 means 0 1, so

actually this is my set case and 1 1 means this is my 0 0, so this is my the hold case.

So, actually only we are getting that as if the

inverted inputs, so the cross coupled NAND gate or the cross coupled NOR gate both forms

the same type of latch circuitry.

Now, we take the clocked SR latch, because all ready we have seen the sequential

module when the basic sequential module we have discussed.

What we have seen, that actually this is a combinational circuits say combinational

circuits C L, combination logic. Some inputs are there outputs are taken some memory

elements, this is the memory elements whose design we are discussing know. And it is

fed back, one clock is the another input of the memory elements. And when the clock

becomes, so this is one clock pulse when the clock becomes high then only the inputs are

enabled, so these are these are enabled, so mainly we are discussing this one.

Now, adding a control or clock input to the latch inputs the latch can be disabled or

enabled. So, now we are seeing the same NAND gate or say one AND gate as if this is a

gated thing. First we see the clocked SR latch, so this is one R is fed to one AND gate

and 1 clock is, so this is my clock input and that is the input of both the gates. The

output of these gated input is fed to the NOR gate

of the R S latch output is Q bar. And similarly, we have taken… See that means,

here when the clock is on or the clock is high

then only the R input is enabled or because as it is the AND gate. So, what we know that

say it is R and this is my clock. So, when clock is 1 then only I will get R

here, because my AND truth table is 0 0 0 0 1

0 1 0 0 1 1 1. So, if we see these two situation as if this is the R input and this is my

clock input. So, when the clock is 1 when these two clocks are 1 or this in this case

that means, the if we if we draw.

Say as this is a nothing, but AND, so R and the clock these are the 2 inputs, so the gated

output we can tell that is 0 0 0 only 1. Now, we consider only

this situation and this situation when the clock is high, then this

is 0 this is also 0 means R this is 1 this is 1 that

is means R. So, actually when the clock is high then the clock is high, then output equal

to R, output means my gated output, so that is why it is called a gated.

Now, similar thing will happen for the S inputs also that means, that here also that S will

configure, so this will be the situation. Now, when C equal to 0, R and S inputs cannot

reach the latch just now we have seen because it is a AND gate. So, if C equal to 0 then

both inputs are these are 0, because AND gate if any 1 of the inputs is 0 the output will

be 0, so if clock is my clock is 0 if to my clock is 0 then it will be 0.

So, now I know if R equal to 0 S equal to 0 this is my hold case, means hold its previous

value all ready we have seen. So, when it holds its stored value this is the hold its

stored value so that means, when my clock is 0, now

see we are trying to define the memory or function the function of the circuit as a

memory with respect to the clock. That means, when my clock is 0 then whatever, value was

there in the previous case that is being hold.

So, this is the clock equal to 0 means R input and S input both are 0 and all ready we

have seen, for the RS latch that this is R equal to 0, S equal to 0 means the Q value

is the actually the previous case the Q i we have

denoted. So, this is my this is my Q i the previous case hold. Now, when C equal to 1

that means, our clock is now, my clock is high, so if we see my clock is 1.

So, what we have seen actually here not 0, R and S will come into come as input,

because we all ready we have seen if clock is 1 then this is my whatever value we have

given in R and S. Then if clock is 1 then whatever R value and S value means this

becomes actually, when clock is 1 this is behave as a whole circuit will behave as R

S latch, so it is the functions as before.

So, now if we represent the functional logic of the clocked SR latch, then it becomes first

this is my symbol of the clocked. So, there are 3 inputs now, 1 is R input, 1 is S input

and 1 is my clock C means the clock, then again

that one rectangular box and outputs are as usual Q and Q bar. Now, if we draw the truth

table then these are my inputs and 1 output we are showing other is the complement. So,

if R is if clock is 0 see this is the situation when clock is 0.

So, whatever clock is 0, whatever value in the R S we give that will not reach in the

R S output or will contain that R S latch input

of the R S latch, so it will be it will be the hold

case means the previous state. Now, if the clock is high, so for these four cases see

the clock is clock is high. And if the clock is

high or clock is 1 then whatever, R S value we

give that will reach as the input to the R S latch. So, it will behave as the it will

behave as a simple R S latch only clocked because only

it will be enabled when clock is high. So, it will be the same situation hold set

reset and unused or undetectable or unpredictable or already we mentioned. So,

this is my simple RS latch only this is a clocked RS latch better I write to that RS

latch clocked. So, only we are getting one extra

cases actually four extra cases, that when clock is 0 that whatever R S value we gives

0 0

0 1 1 0 1 1. Then it will be all the cases it will be the hold case means whatever, previous

value was there that will be hold in the output.

Now, clocked D latch see the simplest clocked latch of practical importance is the

clocked D latch. So, it is again defined like first we see the circuit, so as if say this

is my it is defined now, a D input it is 1 of the

input of the AND gate say this is S NOR gate. Now, this D input is fed through a inverter,

now what is the practical meaning of this thing

see that as if this is my another input of the R S latch. So, both active 1 inputs and

R and S cannot occur, that means see this is if we consider this circuit this is nothing,

but the clocked R S latch, this is the clocked

R S latch. Now, the inputs are manipulated. Now, this

S and R input these are symmetrical, so as if… 1 D input we are now telling this is

a 1 input that is fed, and these D input being inverted is taken as the R. So, what will

happen when D is 1 that means, my S is 1 and S

is 1 as it is inverted. So, R is 0, so this is 1 case 1 case. When D is 0 when D is 0

then S is 1 and S is 0 and R is 1 this is my second

case, see that means, never it will happen, because 1 input is inverted of the other input.

So, both will be active 1 that that type of situation will never happen, so this is R

and S cannot occur. So, when D is 1 what will happen

when D is 1 the situation is when D is 1. Actually, this is the S equal to 1 and R equal

to 0 and we know that 0 1 that means, R S if

we consider, RS latch clocked RS latch this is 0 1 means this is 1 that is my set case

output R this is set case. So, D is 1 when D is 1 my output Q is 1, so now we will

consider as if, so D latch as if I have only 1 input now if we draw that thing.

Say as if I have if we if this becomes the symbol as if I have the only D input clock

is there obviously, because the it is clocked

latch. And similarly Q and Q bar this is my flip

flop D flip flop or better latch. Also we can tell, better we write I will write now,

I write clocked latch, so thing is when D equal to

1 this is the Q equal to 1.

So, it removes a undefined the behavior of the S R latch, because S R latch when S equal

to 1 R equal to 1 that was the only confusing situation that S equal to 1, R equal to 1

the output cannot be defined or we have mentioned

that is unpredictable or undetectable. Now, we have removed that cases by inverting

1 input of the others that means if 1 input is 1 the other input never be 1 it becomes

0. So, it removes the undefined behavior and that is the beauty of the D latch, so this

undefined behavior of the S R latch and this is

used as a basic memory element for the short term storage.

So, symbols are often leveled data and unable clock D and C, so now as it is the function

of only 1 input. So as if we are we are considering that my D means this is my D input,

so this D means, my data input that data which I want to store in the memory. And this

is being inverted this is my clock again that

same symbol I can tell Q and Q bar and, so this

is D and clock all ready I have shown this symbols and this is my Q Q bar.

So, the function table will be that if these are my inputs will be only one data input

D and this is my clock and this is the output. So,

if clock is 0 all ready we have seen if clock is

0 the input cannot be reached. So, whatever D value is there 0 or 1, whatever D value

is there 0 or 1 that it should to be a hold case,

because my R S inputs will be 0 0, because if

clock is 0 all ready we have seen that it is 0 0, so it is a hold case.

Now, if clock is 1 then whatever D value is there that will be my input of the S input.

So, D is 0 means S is 0, S is 0 means R is 1,

so R S is 1 0 and that is my reset, so that is why

when D equal to 0 this is a reset. If D equal to 1 D equal to 1 means my S equal to 1 and

S equal 1 means my R equal to 0, so 0 1 means R S input 0 1 means this is a set case. So,

this is set that means, when D equal to 1 this is a set.

So, what we can tell that D equal to 1 means Q equal to 1, D equal to 0, Q equal to 0.

So, see the functions… also function becomes

very simple that means, if D equal to 1 output Q equal to 1, if D equal to 0 Q equal to 0.

So, this is treated as the basic memory element. And that is why this is the most

important sequential element, that it taken as

the basic building block for the higher memory design or that high dimension memory

design. So, next day we will be discussing the other

flip flops and latches and the differences between the latch and flip flop and then how

it is being used for the high dimension memories etcetera. So, mainly today’s class

we summarize that we have what to do we

mean by the latch or the flip flop and how it is being used to store one bit that we

have told. So, will end the class here.

Thank you.

We have learned how to Design a Sequential Modules or actually what do we mean by

sequential circuits. And how we can store one bit memory or how the sequential modules

are used as the memory, Then we have seen the construction or the design of the S R

latch the clocked latch the D flip flop etcetera.

Now, today we will continue the discussion on the sequential modules, the other

different type of sequential modules that are being used in real life circuits. But,

before that we will see, that what do you mean by

the propagation delay setup time hold time and actually how this times are effecting

the actual value.