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Logic Gates and Truth Tables - Step-by-Step Lesson from the Classroom

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so chapter two Boolean operations simple

logic gates yes from this I'll give you

this book but we're going to be looking

at not just logic gates I think further

on in the book I'm not sure which page

but we're going to be looking at

at logic

gates and

okay give you

that don't get mixed up with Trace tables

tables

okay Trace tables are what we put

through if we've got some pseudo code or

or or a flow diagram something like that

then we get our our sort of test data

and we would put it through and record

that on a trace table this is not a

trace table this is a truth table

students get it mixed up don't get mixed

up so logic gates we've got to learn six

different logic gates okay first one

nice and

easy is one that looks like the letter

D okay uhhuh the next one is one that looks

looks

like looks like a triangle with a little

circle on the front like so and the last

one for these first three it's going to

be something that looks like a sting raid

raid

that okay Gates we're going to be

passing through in terms of the gate two

inputs on this one A and B and an output

is going to be X this one has only got

one input yeah one outut and one output

this one has got two inputs A and B and

one output I'm just going to make the

pen a bit smaller because that's a bit

but what is the difference between the

first one and this third one good

question this is an and

gate so if both of these are turned on

uhuh that's going to be turned on uhuh

this is a not

gate another name for not gate is an

invert inverter inverter we'll call it

an inverter could be an inverter and

this is an all

gate okay

if A's turned on c will be turned on or

if B's turned on c will be turned on or

and this is the nice thing about the or

gate if like the and gate if both of

them are turned on then X not c x will

on okay

so these are what they call logic gates

but each logic gate as it own what they

call a truth table

table

okay I'll do the first

one so if we've got a and b we've got four

four

possible scenarios uhuh we've got and

both been turned off okay we've got

eight been turned on and B been turned

off or a off B on or both of them turned

said that if both are turned off or for

gate that's going to be off yeah one's

turned on one's turned off so the the I

or the one and the zero are basically

the on and off it's on and off

because binary in terms of the computer

language of binary binary is just little

transistors little switches the computer

works inside the C you a billions of

these little transistors with zeros and

ones it's a bit like a record play with

the it's either a pit or a trough you on

a record so it's either one on generally

on or zero off okay that's how binary

works so that basically they say

computer is fulfilled of zeros and ones

is basically ons and offs in reality

yeah oh so zeros and ones yes it's on

now this one has only got one input M

how many possible options would there be

here um just one possible option that it

work one possible option option like

infinite we've got four options here

uhuh in that sense so it can be false or

true Okay so we've got

two two beautiful a x so if we if this

is off off then that's going to be on if

this is on that is going to be off uh

can it be determined like can be say

that if a was on then X be off or then a

is off X be1 is it determined or it's

not possible could say if x if aals 0 x

= 1 can you say that if if a is because

when a is off then it sense that the X

also be

up no Inver it Inver it it inverts

whatever's coming into here so it's the opposite

opposite

of it inverts whatever's coming in so

Zero's gone in it inverts it to one

one's gone in it inv to zero so if true

then false if false then true yeah okay

I got okay like the exclamation mark in Java

Java

basic there's exclamation mark true

okay so this one has got two inputs so

how many possible

scenarios well it has to it has two

hello every possible scenarios thank you

there's two inputs is going to have four

different potential

outputs okay A

B yeah 0 0 0 1 1 0 one one okay and this yeah

yeah

X this is an all gate so we said if a or

b are on or both then it will be on so

obviously the first one no but this B's

on true so that's true a is on Mr true

and one and one X that one is going to

be true as well but didn't we say first

of all it's C and then if both of them

are true then it's going to be X say

again like at the beginning we said that

the output is C and when the output is C

if one of them is true yeah if one of

them is true but with the all gate it

also works if both of them are true like

the am gate so it's all it's basically

there's three different um conditions

where it's where we're going to get a

one we're going to get a a positive

output yeah it's only when they both

turned off that that becomes off as well

but why did we say C is going to be the

answer if why are you talking about C

pret these are all the outputs X I made

a mistake that oh okay ab ab output x a

x AB output X okay okay so don't worry

about C okay okay yeah so they're the first

first

three yeah they're the easy ones okay

yes okay so we've done the first

three we've got another three to do but

I'm going to draw your attention to this gate

gate

here what gate was that uh the or the uh

the inverter or not gate beautiful

invert not gate now it's called not gate

generally all the KN Gates we've got all

the gates that

like know or

invert I've got a little circle here

yeah yeah yeah at the front so there are

three gates we're going to look at now

we've got a gate that looks like an an

gate but it's got a circle on the front

means

nor what's the

D what's this

shape it's it's like an and it's an and

yeah okay but it's got a circle on the front

front

and not what can that mean and not good

flip that round not and beautiful not

n nand n nand not and oh good so the not and

and

gate again we've got our

um impulse A and B as before

and we've got

here A to B so again exactly the same

there's two inputs so there must be four

different scenarios four different

um things what's what I'm looking for 0

0 0 1 1 0 can it predict the answer the

only thing that is going to be zero is

the last one beautiful is that correct

perfect because why because it's not n

anything except n so one one one one z z

okay which will if you look at the other

tr truth tables from the other three

this out these outcomes will not be part

of that yeah okay it's different so if

we've got not and the next one is going

to be draw this little sta shape here

Stingray what's that it was or so what

is it not or not or so basically

anything but or if that's called a n

what this what's this one going to be

uh uh noran no just no oh nor yeah no

okay so let's put these back

gate X the

output so Norgate if you remember from

before the or MH which was everything

apart from or the two

zeros so let's have a look at the

possible outcomes again 0 0 0 1 1 0 1

1 so if it's not all the the second and

the third one are zero what about this

one uh as well okay so these should be

all three should be zeros yes which

means the two

offs would be a one what does that

remind you of um not exactly if it's a

zero here it's going to be one there

it's almost inverted just that and it's

inverted everything else MH it's not

inverted because it's two different

inputs it gives four possible alol

that's similar to no but similar yeah

the last

one which you need to know doesn't look

like any of these sort of looks like

this the orgate but it's got this

special sort of another defense Shield here

here

yeah like a Stingray with a defense

Shield or an additional tail M A and B

again two

inputs and of course we've got our output

output

here this one is called it does look

like an or to a degree this one must be

called an or where at the front of it we

put an x s s gate or EXO or S yeah yeah

good now what the X means what the x is

is absolute all nothing else it's only

all only

all with that in mind the only or or is

only the answer or is only the answer

which is two probably the the middle ones

ones

beautiful beautiful

one so yes it can only be or so this and

this are ORS therefore this one it's an

and it worked okay for the or gate but

it's not in terms of this so this is our

s th

th s on

so there we go so here we've

got possibly three

outcomes with a nand little thing on the

front yeah little thing on the front for

the no gate not all only one outcome the

but opposite and we've got here only

only if you want to make a note of that

[Music]

good so part three I'm just going to

introduce you to this bit which is

basically we can join them both together

or can join Gates together to give us

different outcomes so for example if I

have here so I've got input a and input

B and I've got an output which is going

to be X again M but here what I'm going

to do is I'm going to put an and

gate yeah like so but here I can stick a

not gate into the

diagram okay yeah so that's going into

there into b and a is going to spread

into the am

gate okay now the way this would work if

I have a truth

table it wouldn't work why wouldn't work

because it's an end and

because only if B is zero it works and a

is one okay

so a and b

before so let's have a look at it this

way we could if I remove this just for

the time being and put C

yeah and put another column in here for

X so this time if I put C here which is

basically the opposite of B so now A and

C need to be both on in order for X to

be on yeah so I've added another column

in here so basically C is the opposite

of B I can put this in so one Z 1 Z

but now we've got a going into the

amgate and we've got C going into the

gate okay so we need to be looking here

and saying okay so both need to be on a

and C yes so that's not going to work

yeah that's not going to work but

here these are both on therefore it's

going to be that scenario there okay

okay A and C so we've change we've now

got another truth table which looks

different to the other six that we had

before but we can go a step

further okay I'll r that out for now we

can go a step

further or several steps

further now I'm going to

have a b and c as my inputs and I'm

going to have X

as an

output okay so we're going to start off

we'll have an hand gate

again but this time I can have let's put

in but I'm going to have a not gate

gate

here B is going to go into that b is

also going to go into that a is going to

that okay so we can expand it we can

have a vast

vast um logic circuit yeah based on

binary and based on the binary number

system how many possible scenarios do

you think we're going to get based on

the B three inputs so there four for two and

and uh

six think about the B number system or

eight beautiful we go one two and it

doubles every 10 yeah 8

16 32 and if we do an an8 bit number

system yeah 641

128 so with these doubling in time if

we've got three inputs we should in

theory get eight okay so that should be

for three that should be for two which

we've just done that is for the invert

the or gate yeah sorry not the or gate

not gate yeah which would just invert it

with two possible scenarios four

possible scenarios here we should get

eight different scenarios so let's have

okay

so 0 0 0 happy with that yeah 0 0

1 0

one0 one0 0 and that's our s of IND ones

then we can have 01

one 1 0

1 1 1 0 and one one and one one one 1 2

3 4 5 6 7even eight can't of anymore

okay beautiful so let's have a little

this eight and B and C we need to get

work out what x is

done this a bit wrong what I would what

I would rather do add

some so I would put D here and I would

possibly put an M here and an F

here okay all right how we're going to

do this so B some additional ones yes

those on the camera I have changed this

so I've added some extra ones so we can

see some extra bits so we know looking

at this that D and F are what we need to

consider in terms of what's going into

the an gate to get the output so this is

my little if you do a truth table my

little bit of working

working

space always useful and then I can put

in my D my e and my

f okay so really quickly if we've got A

or B going into this this is my orgate A

or B so either of these are on D should

be on happy with that yeah so looking

down here

no no yes yes yes no yeah yes yes uh and

it can be both yeah still Yes okay good

take e is basically the inverse of C

c 1 0 1 1 0 0 1 0 good f is going to

be b or or okay b o e so let's have look

yes uh no

yes uh yes

yes

yes uh yes yes yes yes yes okay so

what's F and

D so they have to be both they have to

be both so we're going to be focusing on this

this

column and this

column so

no no no yes yes yes uh yes yes yes yes

yes there's only in this case there's

only two possible scenarios where the

would would be

off so there we go mixing Toth tables

yeah sorry mixing expanding our circuit

diagram so we got more than one are you

photographing that beautiful okay so

that's how we would do that

now just I know it's we've run out of

time but what we could say we've got an

and gate

here we could write what we call a logic

statement so I'm going to write the word

and in the middle because that's the one

nearest to the X so it's going to be A or

B A

and what do you think and

and

and b b or c or

system or e or E Yeah well put e but

we're pretending these are our these are

the major yeah or inverse of

C which would be b or

or not

not

CC okay so that would be our statement

and I can go into more detail about put

little tags on top and everything we'll

save that for another day okay so that's

basics okay thank you very much please

continue to ask questions leave your

comments hit notifications and please

subscribe and finally if you wish to buy

me a coffee i' be truly grateful please

visit buy meac

coffee.com SL Learning Zone thank you

very much indeed see you next time bye

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