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Hello and welcome to the first
video on Boolean logic.

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And Boolean expressions. You
might know this topic in an

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alternative name because the
same topic sometimes also

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referred to as digital Logic or
Boolean algebra or algebra of

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

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collection of input values.

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A collection of operators.

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

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

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

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

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

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Tiny, tiny little circuits and
then depending on which circuits

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

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different things so.

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

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different ways. Again, there are
two common ways.

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

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

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

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

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it on or turn it off. So let's

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look at. What are the
basic Boolean operations? The

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first Boolean operation?

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Is the end operation now this
end operation sometimes just

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written out as end in capital
letters sometimes is referred to

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as this symbol?

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And sometimes it's referred to
as a multiplication simple

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symbol because it works like
ordinary multiplication within

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

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

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

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gate symbol and that logic
gate symbol is this one.

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Now this tells you that this
endgate can take a minimum

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of two input values and it
will give you always one

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output value.

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

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

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one after the other.

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

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

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this tab off.

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

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

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

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

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

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

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

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why truth tables.

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Has been invented through.
Tables are simple tables which

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tells you what are the input
values or other possible input

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

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

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end result of that Boolean
operation for every possible

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

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Let's see how does the P&Q

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

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

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common output so P.

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And Q.

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And here will be my output.

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

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both of them on?

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

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the other combination.

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Or I can have both
of them turned off.

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

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the taps are on?

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Every other combination will
stop the water from flowing, so

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this is the truth table
accompanying the end.

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

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

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combining more than just one
single operation together and

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

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

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

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

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of the end or the addition
because it works.

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Like the audition.

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And if you are coming from
the engineering background.

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You can see either this.

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Symbol or this symbol?

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

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incoming values and gives you
one outgoing value, so at

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least two inputs, one output.

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You can think about the OR gate.

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As water pipes but fixed

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

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together in a parallel
fashion and on each branch

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we have got a tap.

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

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

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

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

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

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

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

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

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

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

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the possible outcome
combinations of these? So again,

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I can have two values.

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Two input values P.

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K.

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

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values? The P&QA quick trick.

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

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got two input values.

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

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

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

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number of possible outcomes like
trues or force.

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

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

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

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and bypass the off tab.

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

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

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

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not operation, which sometimes
also used this symbol.

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Sometimes this symbol and
sometimes it used just by a bar

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

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

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the end now.

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Compared with the others, the
not operation only have one

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input and has one output.

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

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one input then that input P.

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Can only be true or false and
then not P.

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

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

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

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the input to its opposite.

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The next simple operation
is the X or.

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

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

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joining as circuit.

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Is the OR gate?

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

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

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And it would look.

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Something like that.

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

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exclusive.

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Or

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

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

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

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got inputs P&Q?

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What will the acts or do
to them?

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

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true force three force.

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

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

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

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

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the signal can go through and
again because force enforces the

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same input value that the EXOR
gate stops your signal going

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through. And remember that I
mentioned at the beginning of

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

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

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lippit stages of computing you
wanted to manipulate where the

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

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through that you wanted to
manipulate and filter out

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

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

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

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go through and nothing else.

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There are a couple of more
operations that I would like

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to talk about. These are
slightly more complicated. I

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

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

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

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And the symbol for that
is this forward error.

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

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And then what will be
the Alpha output of the

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P IF then Q operation?

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So true true Force force
three force, three force.

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Sometimes this also
called the implies.

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So true implies true, that is

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

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force can imply true.

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

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probably going to be the most
difficult gate to understand

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

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

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any kind of combinations.

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

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if and only if.

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And the symbol for that is
an arrow that goes both

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

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The P if and only Q
will work this way.

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33443434.

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This one is only true.

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

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

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

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

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

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

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opposite in this using this.

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

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different input values.

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

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

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

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

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

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

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

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have to be very, very confident
knowing these operations how

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

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

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

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this is all coming from the
basic principles that went

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first. Human started team when
the computers they build them

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together from very tiny basic
circuits.