
Welcome to the next video. In
the Boolean series. In this

video I'm going to show you what
Boolean expressions are and how

we can use the laws of logic to
make them simpler.

But I've shown you a lot of
Lowe's and I've shown you a lot

of operations, but what are
actually Boolean expressions?

But Boolean expressions are
basically just input values.

Peace, QS, and Rs combined
together with all these logical

operations, so different letters
representing different input

values and combined together
with these logical operations

just like in algebra for

example. P&Q
XRR is a Boolean expression,

another somewhat more
complicated Boolean expression

is something like P&Q.

Call

Not Q&R Or
P if then K.

And not Q.

If an only if R, so whichever
operation you want to put

together, and then how many
inputs are there, it is again

different for each expressions.
As I mentioned, these different

expressions will carry out
different instructions for the

computer, so the computer can do

different things. And allow
through certain input

combinations and stop certain
input combinations from going

through in the circuit.

Now let's talk a little bit
about the rules of the brackets.

So if I have got the expression
of not P&Q, and if I have got

the expression of not P&Q, what
is the difference in here? What

am I doing by placing the
bracket? Well, just as in

algebra by pressing a bracket
somewhere, I'm emphasizing

priority in this expression. The
knot is only applied to pee and

to be able to calculate the.

Overall, output of this
expression. I need to

calculate not P and combine it
together with the key using

the end operation as opposed
to hear hear the bracket is

applied to the P&Q. So I need
to calculate the P&Q 1st and

then the note is applied to
the all of it with the

bracket. So once I found the
P&Q output values then I need

to invert them. I need to
apply the not operation to

those output values to get to
the whole output so it will be

very different in the two
different cases.

Similarly, if I have got P&Q.

X or R or P&QX or R. The bracket
tells me what I need to do

first. Here I need to use the
end operation and combined

together P&Q then find the
output and combined it together

with the I using the axe or
while in this case is the

opposite way around. I need to
use the exit gate combined Q&R

together 1st and then use the
end operation to combine output

from here. Which P to get to
the final output of the

overall Boolean expression.

Now the last thing I'd like to
show you in this video is how we

can use these laws of logic to
reduce the Boolean expressions.

So I have this expression not P
or not Q. So how can I use the

lose of logic to reduce this
expression? Now I can use the

Morgan low to distribute the not
over the bracket. So what does

the De Morgan do? I can break it
up into not P and not not.

Cute and then I can use the
double negation and applied the

not not key so that gives me not

P&Q. Well, I think he would like
to agree with me that instead of

this bracketed expression, this
expression is rather similar.

One more example, not.

Key or P?

Or

Not P&Q What I have
here is key or P and I have

here not P&Q. So I have got
the same things in here but I

have got them in the opposite
order so why can do? First I

can apply the commutative low
and bring them up in the same

kind of order.

Then what I can use next is the
Morgan loads to distribute the

not inside the bracket. So that
gives me not P and not Q.

Or Not P&Q now what
I have in here now. It's like

in algebra you spot.

That the first term here.

Is the same, so you can do
something called in algebra,

factorization and in this case I
can use the backwards operation.

The backwards version of the
distributive law so I can bring

out the note P.

And the end.

And what remains is the not

Q. Or key.

Now what do I know about not Q

or key? But I know about Nokia
or cubes that that is always

true because it doesn't matter
which not Q or Q is force, the

other will be always true and
true. Or force always gives you

true. So this is also the same
as not P and true.

And.

Not P and true.

That is always equal to not pee.
I can apply the identity law

here, which states that P and
two is always P for the special

case of not PN 2 is always not
paying. So this long complicated

expression is actually nothing
else but not P.

I hope that you now have a
good idea of how to use the

lose of logic to simplify
Boolean expressions in the

next slide you will have some
questions to allow you to do

some practice on your own and
you will find the answers to

these questions shortly after.

So these are the practice
questions.

And here are the answers.