Hello and welcome to the first
video on Boolean logic.

And Boolean expressions. You
might know this topic in an

alternative name because the
same topic sometimes also

referred to as digital Logic or
Boolean algebra or algebra of

proposition. What this topic is
looking at is looking at a

collection of input values.

A collection of operators.

That sometimes we refer to as
logic gates and looking at what

happens at the end, what is a
particular set of of these

inputs and operators? What kind
of outputs you can end up with?

Now the origonal part of this
coming from the at the very very

beginning, the computer has been
built up from logic circuits.

Tiny, tiny little circuits and
then depending on which circuits

you connected together, you were
able to tie the computer to do

different things so.

The input and output values can
be recorded in a number of

different ways. Again, there are
two common ways.

One is the true for set up and
the other one is the 1 zero set

up again. It comes from the fact
that logic circuits can be

turned on or off true and one is
equal to the on position and

force in OR equal to the off
position. Remember circuits turn

it on or turn it off. So let's

look at. What are the
basic Boolean operations? The

first Boolean operation?

Is the end operation now this
end operation sometimes just

written out as end in capital
letters sometimes is referred to

as this symbol?

And sometimes it's referred to
as a multiplication simple

symbol because it works like
ordinary multiplication within

the binary system. Now it also
has got in digital logic. If

you're looking at the circuits
themselves. If you're looking

at how to build boards
together, it has got a logic

gate symbol and that logic
gate symbol is this one.

Now this tells you that this
endgate can take a minimum

of two input values and it
will give you always one

output value.

So what does the end gate do
now? The end gate is actually

working as if you had a water
pipe fixed with two taps on it,

one after the other.

So when we have water flow
through, the water will flow

through only if both of the
tabs are open. If I turn

this tab off.

The voter will stop here if I
turn this step on when I leave

this tab of the water will stop
here, so water still doesn't

flow through an. Obviously, if
I have both taps turned off,

the water doesn't go further
than here. So what are we only

go through if all of these
steps are on, so would have can

go through only this way. Now
how can we sort of summarize

this information in a nice and
simple visual format? That's

why truth tables.

Has been invented through.
Tables are simple tables which

tells you what are the input
values or other possible input

values that can come. What is
the logic gate or what is the

Boolean operation that we use
here and then? What will be the

end result of that Boolean
operation for every possible

income combinations? Now let's
look at the simple examples.

Let's see how does the P&Q

operation works. B is an input
queue, is a different input.

What happens if I combine them
together? What will be the

common output so P.

And Q.

And here will be my output.

Now what kind of setups can the
two taps have? While I can turn

both of them on?

I can turn one of them on
the other one off, all in

the other combination.

Or I can have both
of them turned off.

So what did we say? The water
can only go through if both of

the taps are on?

Every other combination will
stop the water from flowing, so

this is the truth table
accompanying the end.

Operation. With this Boolean
trip tables, you need to know

them. You need to understand
them because later on we'll be

combining more than just one
single operation together and

see what happens if we start to
mix them up. So this was the

first one, the end operation.
Let's have a look at the next

one, which is the OR operator.
Now the symbol for the OR

operator can be this small away.
The opposite, the turned upside

of the end or the addition
because it works.

Like the audition.

And if you are coming from
the engineering background.

You can see either this.

Symbol or this symbol?

For the OR gates, again it
takes in at least two

incoming values and gives you
one outgoing value, so at

least two inputs, one output.

You can think about the OR gate.

As water pipes but fixed

now. In a different way now
these water pipes I fixed

together in a parallel
fashion and on each branch

we have got a tap.

So what happens in this case?
Now if I turn this tap off, stop

the water flowing here, but I
don't turn this stuff off.

The water will be able to bypass
that turned side and fluid flow

through. Here the same the other
way around. And obviously if

both of the tabs are open then
the voter have got the choice of

flowing through one or the
other, so the OR operation.

Opposite to what the end does,
it only stops the water. In one

case it stops the water if both
of the taps are turned off.

So what does it look like in the
truth table fashion? So again.

P or Q. What are the possible
income combinations and what are

the possible outcome
combinations of these? So again,

I can have two values.

Two input values P.

K.

So again, what are the different
input combinations for these two

values? The P&QA quick trick.

True, true Force Force 3434.
This fact comes from I've

got two input values.

P or K, but all both of them can
be true or false, so I only have

got two possible switch stands.
So 2 to the power of two gives

me 4, but two is the number of
input values and two is the

number of possible outcomes like
trues or force.

So what did we establish if
both of the taps are turned

on, then the voter can flow
through. If one of the taps

are turned on, then the water
can flow through that branch

and bypass the off tab.

But if both of the taps are
turned off than the water it

stopped. So that's when this
this operation is forced.

So the next operation that I
would like to talk about is the

not operation, which sometimes
also used this symbol.

Sometimes this symbol and
sometimes it used just by a bar

over the input for the pictorial
symbol for the Northgate. For

engineers is this it's a little
triangle with a little circle at

the end now.

Compared with the others, the
not operation only have one

input and has one output.

OK, so that state to wait as you
something. So if I have got just

one input then that input P.

Can only be true or false and
then not P.

But what is not true? What
is not true is force and

what is not force is true.
So the not operation has

got a very special role. It
flips it inverts it changes

the input to its opposite.

The next simple operation
is the X or.

Which has got this symbol, so it
doesn't have that many symbol as

the not. So that's easier. And
the exors pictorial symbol for

joining as circuit.

Is the OR gate?

But with an extra leg added to
it so it can take again at least

two inputs. Or if we use the
alternative way of the X or.

And it would look.

Something like that.

OK, now this is called the
axle operation because it's

exclusive.

Or

so it's exclusively one or the
other input, so the xclusive

or the X or operation filters
out the input values when the

inputs are the same. So what
do I mean by that? If I have

got inputs P&Q?

What will the acts or do
to them?

So again, be can be true
to force force and Q is

true force three force.

So exclusive, or if the inputs
are the same, which is this

case? Because both of them are
true. The Exor Gate gives you a

4th signal. Basically the axle
gates stops the signal going

through. If one is to the other
one is forced then that's when

the signal can go through and
again because force enforces the

same input value that the EXOR
gate stops your signal going

through. And remember that I
mentioned at the beginning of

this video. These are based on
the electric circuits and then

you wanted to manipulate at the
very, very early stages or

lippit stages of computing you
wanted to manipulate where the

electrical signal goes doesn't
go through here doesn't go

through that you wanted to
manipulate and filter out

certain inputs in favor of other
inputs. So these different gates

give you that kind of option of
turning them around. Saying, I

don't want this input, I want
that that input combination to

go through and nothing else.

There are a couple of more
operations that I would like

to talk about. These are
slightly more complicated. I

can't really give you any nice
and simple example of why they

work in here. We just have to
learn that this is the way

that they work, so one of them
is that you've done.

And the symbol for that
is this forward error.

So again. I've got inputs P&Q.

And then what will be
the Alpha output of the

P IF then Q operation?

So true true Force force
three force, three force.

Sometimes this also
called the implies.

So true implies true, that is

true. But true cannot imply
force, so this one is force

force can imply true.

And force can imply force
that's true. Again, this is

probably going to be the most
difficult gate to understand

why this works. You just have
to learn the truth tables, and

once you know the truth
tables, you can apply it to

any kind of combinations.

And the last operation that I
would like to talk about is that

if and only if.

And the symbol for that is
an arrow that goes both

ways. So if I have got the
two inputs again P&Q.

The P if and only Q
will work this way.

33443434.

This one is only true.

If both inputs are the same, so
true and true are the same, so

this will be true. True annefors
are different, so the output

will be force same for the third
right and for some for side the

same. So this is true in here.
Now if you look at this one and

if you remember the X or you can
support that these two

operations if and only if an the
X or are doing exactly the

opposite in this using this.

Operation I can filter out the
same input values and stop the

different input values.

So that's again a very useful
operation to have.

This short video was intended to
expose you to the basics of the

Boolean logic or digital logic
and show you had the truth.

Tables can be built up and what
are the most commonly used

operations to be able to follow
up on digital logic? You will

need to be able to know this by
heart, so these are different

operations that every time you
need to apply them you will be

have to be very, very confident
knowing these operations how

they work. What they do? What
kind of inputs they let

through an? What kind? What
kind of inputs they stop from

going through? And again, as I
mentioned at the beginning,

this is all coming from the
basic principles that went

first. Human started team when
the computers they build them

together from very tiny basic
circuits.