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.