Combinational Logic Video Lecture | Digital Electronics - Electrical Engineering (EE)

good day this is Jim Pytel from Columbia
Gorge Community College or renewable
energy technology program this et1 21
digital one today we were moving into
Chapter five
we're going to discuss basic
combinational logic circuits okay so
we've been kind of dealing with the
smaller picture you know we've been
dealing with single gates you know what
combinational logic is is just bigger
picture it's combination of single gates
hence the name combinational logic
chapter 5 should be relatively easy
considering what we've gone through in
chapter 3 and 4 but again we're looking
at the big picture combinations of
single gates so we've talked about our
end or gates in exhaustive detail with
the SOP the semi-products and here right
here in our first diagram the end or
combinational it is an SOP so all this
is saying here is for a 4 input end or
combinational logic circuit to have a
high output both a and B have to be high
or both C and D have to be high ok if
you think about that when a and B are
both high you're getting a high right
here one doesn't matter what C and D are
doing it's 1 or whatever well that's a 1
so for input end or out excuse me for a
for input and or combinational logic
circuit for the output to be high both a
and B have to be high or both seen do
you have to be high what happened there
someone black I hope you can see this
okay so ah and-or-invert
okay this is where it gets you have to
start putting your thinking cap on here
you can use an end or invert to
implement the product of sums the POS
implementation okay this seems kind of
weird at first but now think about this
this right here in our SOP this output x
equals a and B or C and D nothing
nothin too complicated about this but
now check this out here the output is
inverted of that same expression now use
demorgan's theorum where we can get rid
of this over bar negation and then get
rid of those again oops
I want my footing to see in there that
needs to be so what does that look like
well that's a sum that's a sum ended
together that's the POS the product or
sums where this was up here was the sum
of products pretty cool huh
so N or invert can be used to implement
POS expressions the way to think about
this the output is low if both a and B
are high or both C and D are high I mean
just think about this if a is high it's
a 1 so not a a would be 0 B is high so
not B would be 0 0 or 0 would be a 0 and
do it with anything is it low okay so
both the output is low if both a and B
are high or both C and D are high okay
we're going to talk a little bit about
the exclusive or and the exclusive nor
using combinational logic we've kind of
already discussed this here and if
you've been paying attention in chapter
3 and 4 this should not be a big stretch
for you so exclusive or our truth table
a B X 0 1 1 0 1 1 X output is high only
when they're different right there make
a semi-products expression of this well
it's not a and B or
a and not B that's our X so how does
that look like in an end or situation
well invert our a B that's our X pretty
cool huh so it's just and or summer
products okay so now exclusive nor
actually here wait one thing I want to
discuss remember when I was saying
earlier is yes you can write the
exclusive or this way and you've got
your exclusive or gate here so this is
equivalent you can write the exclusive
or as a single gate or that's a and B
output X you can also write the
exclusive or as a combination of ends or
combinational logic
um additionally my light there is a
symbol it is a circled or symbol so
that's a exclusive or B you can
sometimes see that in the boolean
expressions okay so exclusive nor so
this is a pretty cool example of how you
can use and or and N or inverts to
implement the same thing so exclusive
nor it's just the inverted expression of
this guy here of the exclusive or so
let's start off a sweet not a and B or a
and not B equals exclusive nor let's
call that why does that I want you to
confuse but it's inverted okay so using
and or logic excuse me and or invert
logic it's the same thing as it was
upstairs
except this output here is inverted so
that's in or invert logic but now we can
use demorgan's theorum to walk through
this whole thing
get rid of our double negatives there to
come up with a product of sums
implementation so this right here
and-or-invert
is the expression of that product of
sums but let's say that we do not want
to do a product of sums or an and or
invert we want to do end or
combinational logic well keep on going
just do the foil method for this first
outer inner last
but check these guys out those are
zeroes according to our laws of boolean
algebra and we get + B or not B and not
a
so what does this look like well it is
still an and/or implementation of
combinational logic ok so not too hard
considering what we've gone through in
Chapter three and four so let's move on
in chapter five and talk about some more
combinational logic circuits