W12-02 Go through the Gates #Logicgates #Electronics #SemiconductorPhysics

So, we once again started learning the basic addition and two numbers I gave an example

how to add two numbers. And essentially what we need in that exercise is the basic fundamental

thing I must know is the sum of two digits. So, here we have this sum that we did

last time and we saw that how I should know 1 plus 5 or 6 plus 3 or 0 plus 7 plus

8 and then there is a carry there is a sum carry and sum. So, essentially if you think

it is as a device what we are giving is we are giving two numbers a and b and we are

taking two outputs sum and carry. So, in all of these these kind of equations that

is written these are the two input numbers these are the two input numbers and these are

the two outputs one output you can call carry and another output you can call sum.

Same thing happens in the binary number edition also. The benefit is that we have only

two digits two symbols and therefore, the things are less in number simpler. So, let

me do a addition of two numbers written in binary system. So, let us take two numbers

in binary system. So, I have two numbers let us say 1 0 0 1 1 1 0 1 like that and then

the next number could be 1 here 0 here 0 here 1 here 0 here 1 here 1 here 1 here 1 here like

that and we have to add. So, what do I need 1 plus 0. So, I should know that 1 plus 0 is 1 and

if I write 1 I also write 0 here. So, this is carry digit and this is that sum digit. So, 1 plus

1 gives me sum that I write here and carry I write here. Then 0 plus 0. So, I should know that

0 plus 0 is 0. So, sum is 0 and carry is 0 and that sum is to be added in this. So, 0 plus 1. So,

0 plus 1 is also 0 1. So, sum is 1 and carry is 0. So, 0 plus 1 will be 1 and 1 plus 0 will be 1.

So, this will be 1 here. Then comes 1 plus 1. Now, what is 1 plus 1? So, 1 plus 1. So, the number

next to 1 in our counting we have one digit numbers exhausted then 2 digit number exhausted

then 3 digit number and so on. So, if I add 1 to this 1 I get the next number consecutive number

which is 1 and 0. So, that 0 is the sum and 1 is the carry. So, I put the sum here

and carry here and then 1 plus 1 is again 1 0 and 0 is the sum and 1 is the carry. So, this 1 plus

1 is 0. So, I have to remember that sum is 0 and that sum is to be added here 0 plus 0 and that is

0 and that carry still remains that carry goes here and then 1 plus 0 is 1 and that 1 plus 1 is

1 0. So, these 0 goes here 1 goes here 1 plus 0 is 1 1 plus 1 is 0 here and 1 here and now,

I have 1 plus 1 and plus 1. So, 1 plus 1 and plus 1. So, 1 plus 1 is 1 0.

This 1 and this 0. The sum is to be added here and carry I have to remember. So, that sum is added here

and then that gives me 1 here and that carry goes here there is nothing here 0 0. So, that is 1.

That is how we sum the numbers. Similar procedure as we did in decimals.

So, the basic things I must know for this addition is addition of these two digits. So,

if I write it as a device then my inputs are here A and B, let us call it A and B and I have

two outputs which I can call C and D, C and B and then this is this is some kind of a circuit

digital circuit and then the circuit should be such that if I write A here B here and S here

and or let me let me see here and S here. So, if this is 0 0, if this is 0 0 I should get

0 0 0 carry and 0 sum which should be 0 and 0. If it is 0 1 then I should get sum as 1 and carry

as 0. If this is 1 and this is 0 1 second I should get the same thing and if this is 1 and this is 1

and carry should be 1 and sum should be 0. This is the input output that is our requirement.

My circuits should do this, this circuit should do this. If I take this A as 1 and B as 1 I must

get the output C carry as 1 and output D as 0 and similarly for E all combinations. Since there

are only two inputs so I have four combinations. So, when you exhaust all the combinations of

input and tell what should be the output corresponding to these inputs that table is known as

truth table. This is known as truth table and our circuit will take these inputs that means

voltages will provide low and high. We have to pre-defined normally say 0 to 0.8 volt or 0

to 1 volt is low. So, anything if I apply 0 volt here 0.5 volt here that is low and that will

be treated as 0 and anything if I apply here which is pre-defined more than two volts that I can

define how much is that. So, if it is high if it is that high voltage more than two volts

then that is 1 and similarly for B. So, this is the kind of circuit which we call digital circuit

which takes only digital inputs it takes voltages it takes only voltages but those voltages I see

it as digital either low or high I do not distinguish between 1.7 and 1.8. So, for us it is

digital 0 or 1 this is the kind of circuit. Now, how to design such circuits how to design such

circuits in which the input is given as voltages and depending on what whether it is high or

it is low desired output is achieved. This is by the way this is the truth table this kind of

combination this is also known as half adder 1 half adder because here you had seen I had

this 1 plus 1 plus 1. So, I had to do some mental calculation 1 plus 1 will give me one

carry and then 0 sum and then I have to remember that the carry is still there and some is to

be added in the sum and so on. So, if we can put three numbers together as input and then

ask what is the final sum and what the final carry. So, that means I will have circuit in which

three inputs will go a b and c a b and say like here 1 1 1 here 1 0 1 1 0 1 1 1 0. So,

there are three inputs and then I need the final sum and final carry I do not want to remember

in between what happened and then carry in my mind also. So, if I have this kind of circuit

designed and then I say that I need the final carry and the final sum you can make your truth

table you can make this kind of table this time you have let me not call it c c is for carry

let me call it d or x y z let me call it x y z no confusion x y and z. So, you can make a table

x y and z and then carry and the sum and then you can put numbers here here here what should

be the carry what should be the sum how many rows will be there how many rows will be there

there are three inputs each input can be 0 or 1. So, there are those combinations are to be written

all those combinations are to be exhausted 0 0 1 0 0 0 every everywhere you have to

make so 8 8 rows and for each row you know how much is c and how much is s and that kind of

truth table that kind of circuit which can do this that is known as full adder.

So, any digital circuit which takes digital input and gives digital output that is digital

it takes digital input means it still it is an amplifier it is a transistor or it is some

some electronic circuit combination of diodes, transistors or resistances it is a circuit

electronic circuit and electronic circuit only takes voltages and currents and it gives

output as voltages or currents but then the design is such that if the voltage is in this range

any if I call it 0 and if the voltage is in that range I call it 1 and similarly for output

and for input then I should get this truth table implemented. So, that is the digital circuit it takes

digital inputs and it gives digital outputs could be one output could be more output could be one

input could be two input could be three input and so on. Now, to design such a circuit the basic

block basic blocks with which you design complicated circuits are called logic gates.

So, logic gates these are themselves digital circuits and there are several of them I will

describe and these are taken as the basic blocks. So, you have one single unit one integrated

circuit you go in market and say this logic gate and you get that. So, the whole circuit is inside

and then use those gates and combine them in appropriate fashion to design the circuit which

keeps you desired outputs at desired inputs right. So, some of them which are very basic and

which I will describe the first one is let us talk of this not gate this is called not gate

and what is this it is very simple it takes one input and it gives one output. So, this is not gate

and not gate takes one input just one input and then it gives one output.

A let us call it A and let us call it Y. So, if A is one truth table is very simple if A is one

then Y is 0 and if A is 0 then Y is 1 finish this is the truth table for not gate. So, if this is one

this should be 0 if this is 0 this should be 1 that kind of circuit is known as not gate and

you must remember we have already discussed this kind of circuit and it is nothing but a transistor

at transistor in switch mode okay a transistor in switch mode. So, if you have a transistor

if you take N P and transistor as we had been doing it you have that load resistance or collector

resistance and then you put your biasing here you put some resistances some capacitance is

all those things I am not showing and then here is that input right. So, you can put a resistance

here you can put a resistance here and then this is the input point. So, essentially this is it

is like this and that is this is that point A and you can take your output from here this is the point Y.

Okay. So, if you operate it as a switch that means this voltage is given high

suppose you give 5 volt here and then this base emitter junction is forward bias and it goes and this

is a sufficient to drive the transistor in saturation mode okay you have a cutoff mode you have

saturation mode in between you have that active mode linear region right. So, B in saturation mode

or in cutoff mode so if the voltage is given here if sufficient voltage is given here so that you

have driven the transistor in saturation mode then the maximum possible current can go in that

configuration and then you have a current from here and once you have current from here then you

have drop your potential drop here okay and therefore this potential is low right in collector

current goes like this this is NP and remember so it goes like this and so this is high voltage

but then you have drop here and this becomes low voltage. So, if you put high here if A is high

B Y is low okay you apply a voltage high voltage high voltage means not 1000 volt high voltage means

I in our case is just 3 volts 4 volts 5 volts which drives this into saturation mode.

So, that there is a current from here there is a potential drop and this becomes quite low

and if you give this low if you give this low you you do not put a battery you give 0 voltage here

then no current goes it in cutoff region and since no current goes anywhere no current goes here

so the potential here and potential here it is same and this potential is high so this potential

also becomes high so this transistor single transistor itself is is not gate so you give one

input you get one output if the input is one output is 0 and if input is 0 output is 1 and there is

symbol for it okay symbol for not gate and that symbol is you put a triangle and put a line here

put a small circle here and then a line here and this is the input this side is the input side

and this side is the output side so this circle actually denotes not operation so this is a symbol for

not gate so this one symbol is 1 then next is let us take and gate so next one let us take

and gate it is called and gate this and tells that if you are all inputs are high if you are

two inputs the first input should be high and second input should also be high say both the inputs are

high then the output is high and if any one of them goes to low or both of them go to low

then the output is low that is why the name and so that means if I draw the truth table

if it is two input and one output the basic and gate will have this you can have more inputs

but the basic and gate will have two inputs and one output so if this is 0 this is 0 this is also 0

right and then if this is 0 this is 1 still this is 0 because a and b both should be high to

give you this high value of y so 1 and 0 that should be 0 and 1 and 1 that is equal to 1 so if

you have a circuit of this kind that circuit will be called and circuit both of them should be

high then only the output is high otherwise it is not so it is not our binary addition one plus

one is one here so that and it should not be taken as a addition or this two and three makes

five it is not like that now this kind of thing you can think without any semiconductor or anything

like a switch so you can have a two switches it is just to conceive the idea what is add you can

have two switches and this can be treated as input and then you have a lamp out here

so this is your output this is a lamp and this is our output and then you have appropriate

battery or power source okay so you can treat this as a this as b and this is y lamp on

y is equal to 1 and lamp off y is equal to 0 that is the output and input switch S1 so any

switch any switch if it is closed closed means connected so if the switch is closed that we will

call 1 this is your input a or b and if the switch is open as it is shown in this figure

so it is open so that we will call 0 so if you take this as the meaning of

one and 0 then you can see that if a is 0 and b is 0 if a is 0 and b is 0 so it is open

both switches are open and then the lamp is not glowing and you say that y is equal to 0

and if one of the switches closed other switches open so a is 1 and b is 0 so a is 1 and b is 0

so that case also there is no current in the circuit the lamp is off and therefore y is equal to 0

if it this is open and that is closed then also the same story and if both the switches are closed

so that this a is 1 and b is 1 then it glows and if it glows if it is on then we say that y is

1 so 1 and 1 is 1 so this is the meaning of this add you can now make this add

digital circuit using p n junction diodes let us see how

so let me take two diodes one diode here p n junction this is p side this is inside

you remember that another diode here join this together and put a resistance

and then a battery cell here could be two volts three volts and this is our ground this is our

ground and let these two be the input points a and b and let this be the output point y

and see if this can do that and operation what is that and operation the and operation is

if a is 0 b is 0 y is 0 then if a is 0 b is 1 then y is 0 if this is 1 this is 0 then this is 0

and if this is 1 this is 1 then this is 1 that is the end operation so what happens if this a is 0

and this b is 0 that means this is given 0 volts this is given 0 volts I am connecting this to the ground

I am connecting this to the ground remember this kind of symbol it means that this is connected

to this line here and this is also connected to that same line here so in this case both the

diodes are forward biased you have a higher voltage here and a lower voltage here so it is

forward biased and therefore you have current through this diode the current goes like this and then

it comes back and goes into the battery the current goes like this and comes back and goes into

the battery and since the current is going it is forward biased the drop here on this p and junction

is very small 0.2 volts 0.3 volts 0.5 volts or more than that 0.6 volts maximum so if this is 0

this will only be a small voltage here and for digital operations that is same as 0 low so this is

low voltage and therefore y is 0 y is 0 and then what happens if a is 0 and b is 1 a is 0 means

a remains grounded but now b is at 5 volts this b is at 5 volts let us say 5 volts

so if we have put 5 volts here that means we have put a battery another battery here and that

battery is connected to this negative here and this is a plus 5 going that what happens this becomes

reverse bias you have put full 5 volts here no current through this no current through this

but does it matter this is still grounded a is 0 this is still grounded and therefore this

higher voltage this is lower voltage this is forward biased and therefore the current will still

be there and once the current is there once again the same story this is this is 0 and this only

a small voltage which is 0 and here it is 5 volt there need to be 5 volt this is the no current

is going so it is just possible this side is 5 and this point is very small volt so that is fine

so this is low so this is a low and similarly if a is 1 and b is 0 then this will be 0 you are

changing the these two swapping these two put 5 volt here put 0 volt here then this will

be reverse to bias no current from here and the current will be only from here what happens if

a is 1 and b is 1 this one a is 1 and b is 1 so I am giving 5 volt to a and 5 volt to b

now both the diodes are reversed bias no current going from here no current going from here

and therefore no current going from here gets off junction rule no current going from here so

whatever is this voltage that same will be this voltage and therefore this will be high and hence

you have 1 1 and 1 so this is how this and can be implemented using this diodes I can also do this using

transistors we had shown how that switches can be used to light that lamp and that equivalence

of that answer kit and transistor can be used as a switch so that same switch circuit I can

put 2 transistors and then make this and circuit using those so next time I will show that

and then we will talk about several other gates and their circuits.