June 26, 2023 • 16 mins
Jonathan is loopy, but he's also logical. Or he tries to be. Between pop culture references and dad jokes, Jonathan explains what logic gates are and how they work.
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Speaker 1 (00:04):
Welcome to Tech Stuff, a production from iHeartRadio. Hey thereon
Welcome to Tech Stuff. I'm your host, Jonathan Strickland. I'm
an executive producer with iHeartRadio. And how the tech are you?
So I threatened? Sorry, I mean I mentioned last week
(00:25):
that I planned to do an episode about logic gates,
which light at the heart of computer processing. So today
we're going to do a quick overview of logic gates
and what they do. And originally I was going to
run reruns this week because I'm actually on vacation as
you listen to this, but I had a little extra
pizazz in my step that I'll talk about in a second.
(00:46):
But yeah, let's talk about logic gates and what they do.
And first up, you should know that logic gates are
based off of Boolean algebra. This branch of math was
invented by the guy that it was named after, George Algebra.
Just kidding. His name was George Bull. Bull was born
in England in eighteen fifteen, as so many were. He
(01:07):
died forty nine years later in Ireland. And I can
understand why. I guess this is where I should mention.
I'm writing this episode while under the influence of advil
PM because I grabbed the wrong tablets while trying to
treat a headache. So that's going to be a factor
for the rest of this episode, just like you know. Anyway,
George Bull helped establish symbolic logic, which, by the way,
(01:31):
I loved that subject in college. It was a math
course that I excelled at. In fact, I would only
show up to class on Thursdays and Fridays. We met
every day of the week, but there was no attendance policy.
So Thursday I would show up to find out which
chapters that the professor had gone over, and then Friday
(01:52):
I would show up because there was a quiz for
that week's lessons. And symbolic logic made so much sense
to me that I could just show up on Thursday
to see which chapters that needed to read, show up
Friday and do the work. And I aced that class.
Now this is not to say that I'm a genius.
I am not. Just for some reason or another, symbolic
(02:15):
logic clicked with me in a way that a lot
of subjects never did. Anyway, symbolic logic would become a
fundamental foundation for digital circuits. Years later, my guess is
he didn't know that was going to happen because computers
weren't a thing yet. So what had happened was Bull
mostly learned mathematics all on his own. He received some
(02:35):
tutoring from his father, who was a tradesman, and he
did go to a couple of schools, but no like
secondary formal education. Mainly he was self taught, and he
actually began teaching around various schools in his region when
he was just sixteen years old, not only because he
(02:55):
was brilliant, but also because it was necessary. His father's
business had slowed down and his family needed the income.
So the gig economy has been around for a while,
I guess is what I'm saying. In the eighteen forties,
Bull submitted papers to the Cambridge Mathematical Journal on subjects
ranging from differential equations to calculus, you know, light reading.
(03:17):
In eighteen forty seven, he published a work titled the
Mathematical Analysis of Logic Being an Essay toward a Calculus
of Deductive reasoning. This landed him a university teaching gig,
even though he had never earned a college degree of
his own. In eighteen forty five, he published a further
treatment of his ideas titled an Investigation into the Laws
(03:39):
of Thought on which are founded the mathematical theories of
logic and probabilities Real Page Turner. In eighteen forty six
he married Mary Everest, the daughter of Mount Everest. Okay, wait, no, sorry, no,
she was the daughter of George Everest. It's just that
Mount Everest is named after George Everest. That's actually true.
(04:02):
I got a little confused there. Sorry, I'm blaming the ADVILPM.
At this point, Boole used mathematical symbols to represent logical
arguments and showed that by encoding an argument as a
series of equations, one could check to see if the
argument was sound or not, if it were true, or
if it were false. So, for example, maybe you were
(04:27):
saying something like all cats are mammals, Old Greg is
a cat, therefore old Greg is a mammal. Well, you
could actually represent those statements as equations, and then you
could solve to show that the conclusion is contained within
the premises. So if the premisses contained the conclusion and
(04:47):
everything lines up, you would say it's logically sound. It
is a true argument. However, if you said all cats
are mammals. Old Greg likes to sip Bailey's out of
a shoe. Therefore, Old Greg is a mammal. Well, that
wouldn't fly because you haven't established that Old Greg is
a cat or any other kind of mammal for that matter.
He's Old Greg. So what does this have to do
(05:10):
with computers. Well, Old Greg will have nothing to do
with computers, probably because he lives at the bottom of
a lake and his computer with short circuit immediately. But
boolean logic would underpin the concept of logic gates, which
in turn would allow a computer to process information in
a meaningful way. And this brings us to the concept
of actual logic gates. PCMag dot com defines logic gates
(05:34):
as quote a collection of transistors and resistors that implement
boolean logic operations in a digital circuit. Logic gates have
one or two zero or one inputs, but only one
zero or one output, as in the following examples, which
they then list to continue the quote. Transistors make up gates,
(05:57):
Gates makeup circuits, and circuits may up electronic systems. End quote.
So a typical logic gate usually accepts two inputs and
produces a single output, and that output is based both
upon the nature of the inputs and the nature of
the gate itself. I say typically, because of course there
(06:18):
are exceptions, but for the purposes of simplicity, we're mainly
focusing on the typical example of two inputs enter, one
output leaves. So yeah, I am going thunderdome with these rules.
The output that a logic gate produces, like I said,
depends both upon the value of the inputs and the
type of logic gait that we're talking about. So you
(06:40):
can think of logic gates being kind of like a
physical gate that leads into, say a courtyard, and this
particular gate has a bouncer standing outside of it. The
bouncer enforces the rules. So you come up to the gate,
and if you meet certain criteria, the bouncer lets you through,
and if you do not meet the criteria, the bouncer
(07:01):
turns you away. This analogy isn't perfect, because really the
logic gates allow a value to pass through no matter
what it's just what value is that going to be?
Will it be a zero or will it be a one.
So the bouncers in circuits are electronic components, and the
rules depend upon the type of gait. And we are
talking physical structures here in a circuit. We're actually talking
(07:23):
about transistors and resistors. So the way the gates work
is dependent upon voltage. So each input can have one
of two values. Either zero volts is applied to the input,
which would then represent an input of zero, or five
positive volts are inputed into that input and then that
(07:46):
represents a one. The output produces a value of either
zero volts, so a zero in logic, or five volts
again meaning a one in logic. Now, if we just
talking two inputs, you can have four possible combinations, right,
So each input can have one of two states, either
a zero or a one. And if we start to
(08:09):
group these two inputs together, that gives us four potential combos.
You could have both input A and input B B zero,
so that's one value. Or you could have both of
them be one that's a second value. Or you could
have input A B zero, input B is one that's
a third value. Or you could have input A B
(08:32):
one and input B is zero that's your fourth value.
So four possible combinations zero, zero, zero, one, one zero
or one one. Now, those are the basics when we
come back. We're gonna talk about the different kinds of
logic gates, and we'll build from the most basic to
the more complicated. But first let's take this quick break
(08:55):
to thank our sponsor. We're back, So now we're going
to talk about logic gates, and the first one up
is the and logic gate. The and logic gate will
produce a one result as the output only if both
(09:19):
inputs are also one. So if input A is one,
an input B is one, then the output is also one.
Any other combination, whether it's zero, zero, zero, one, or
one zero, will have an output of zero. So an
and gate will produce a one if both inputs are
also one. Next up, we've got the or gate. This
(09:42):
one will produce a zero output if both inputs are
also zero, so any other combination will create a one output.
It's kind of the opposite of the AND gate in
many ways. Then we have the exclusive or, which is
agreed not to date other people. I'm sorry, that's the
nighttime advil talking. The exclusive or x or produces a
(10:06):
one only if one input is a one and the
other one is a zero. So if you have one,
zero or zero, one is the inputs that produces a
one output. The zero zero and one one inputs would
produce a zero output. I know this starts getting confusing,
but this is just for the purposes of explaining the
different types of logic gates. Next up, we've got the
(10:29):
logical inverter. So a logic inverter is someone who stands
mister spot on his head. No, actually no, it's a
not git and this only has a single input. So
it's one of those exceptions I was talking about a
few moments ago. So an inverter does exactly what you
would expect. It produces an output that's the opposite of
the input. So if you have a one coming into
(10:51):
a not git, a zero is coming out, or vice versa.
Now we're going to get into a few gates that
combine some of the more simple verse into something a
little more sophisticated. So first up, we've got the nand gate,
the NA in D gate. This behaves as if it
is an and gate immediately followed by a not gate.
(11:13):
So the nand gate will create a zero output only
if both inputs are one, so one one creates a
zero output. Any other combination would produce a one output.
Then we have the nore gate, which is an or
gate followed by an inverter. It will only produce a
one if both inputs are zero, So zero zero creates
(11:36):
a one output. Every other combination creates a zero output.
Now let's go crazy Broadway style. We got the exclusive
nore or x nore gate, which will produce an output
of one if both inputs are the same. So a
zero zero input will create a one output, but then
(11:57):
so will a one one input. Now a one zero
or a zero one input that would create a zero.
So yes, I know that sounded like a lot of
zeros and ones, but that's what we've got to work with.
And these logic gates are what make up digital circuits.
You can combine them in all sorts of different configurations,
with the only real limit being that we are talking
(12:19):
about physical structures producing these outputs, right, we are talking
about actual transistors and resistors. So eventually you do start
to run out of physical space. So they do take
up space, very little space because these are very very
very tiny components, but they do take up space. You
also run into issues like how much heat you're producing
when you're providing power to the circuit, so that can
(12:42):
also be a limiting factor, but otherwise you can get
into lots of complex orientations and configurations. Now, the cool
thing about this is you could actually write out the
string of logic gates that your circuits follow. Though you
would need an awful lot of paper to do anything
like a modern circuit, you could do it, however. The
(13:04):
point is that logic gates represent specific rules, and these
rules determine the output produced based upon the input received.
And that's the very basic foundation of digital computers. Though
obviously it gets a lot more complicated from there, but
that's something I'll just have to tackle on a day
when I'm not on ADVILPM, which is not a sponsor,
(13:24):
I should add, it's just the reason this episode turned
out the way it did, so my apologies on that one. Anyway,
that's the basics of logic gates. You can get a
lot more detailed, as I said, and I know it
gets really confusing hearing all those ones and zeros. I
recommend looking up truth tables for different logic gates so
(13:45):
that you can get a better understanding. It helps me,
at least when I'm able to see visualizations of this
in various charts, and that lets me get a better
understanding of what output you're going to get based upon
the input going in. So yeah, this is like the
core foundation of processing. So you combine that with the
(14:06):
element of binary information where your values can either be
a zero or one. Then you start grouping bits together
to make more meaningful representations of info. Couple that with
the process of logic gates, and you start to see
how computers actually start physically handle this information in the
(14:26):
form of voltages. It's really incredible, like when you start
to break it down, because we deal with such an
abstraction of what computers are doing when we're running any program, right,
We're just focusing on whatever the program does. We're not
necessarily thinking what is going on at the circuit level
to make this happen. Well, logic gates are really the
(14:50):
basis for that. So I hope this was interesting. I'm
sure it was at least cringe worthy and maybe in
a retaining as well due to my aduled state thanks
to the nighttime medication I accidentally took. And it's still
doing a number on me, y'all. I've had two full
cups of coffee to push through this, So blame my
(15:15):
foolish on grabbing the first headache medicine that I wasn't
within reach for me to deal with my headache. That's
the reason. All right, We've got a couple more new
episodes this week before we get into rerun territory. I've
got a new episode for tomorrow and for Wednesday, so
hope you enjoy those. They will also be on the
(15:35):
shorter side, which was necessary for me to be able
to get everything done before I headed off on vacation.
And I hope you are all well. I hope I'm
well right now. I should be kind of leaning back
in a hammock in the Blue Ridge Mountains somewhere hopefully
at this point, unless the weather's terrible, which is probably
(15:57):
will be, and that case, I'll just be inside watching
the rain. Either way sounds good to me. And I
will talk to you again really soon. Tech Stuff is
an iHeartRadio production. For more podcasts from iHeartRadio, visit the
iHeartRadio app, Apple Podcasts, or wherever you listen to your
(16:20):
favorite shows.
Welcome to Tech Stuff, a production from iHeartRadio. Hey thereon
Welcome to Tech Stuff. I'm your host, Jonathan Strickland. I'm
an executive producer with iHeartRadio. And how the tech are you?
So I threatened? Sorry, I mean I mentioned last week
(00:25):
that I planned to do an episode about logic gates,
which light at the heart of computer processing. So today
we're going to do a quick overview of logic gates
and what they do. And originally I was going to
run reruns this week because I'm actually on vacation as
you listen to this, but I had a little extra
pizazz in my step that I'll talk about in a second.
(00:46):
But yeah, let's talk about logic gates and what they do.
And first up, you should know that logic gates are
based off of Boolean algebra. This branch of math was
invented by the guy that it was named after, George Algebra.
Just kidding. His name was George Bull. Bull was born
in England in eighteen fifteen, as so many were. He
(01:07):
died forty nine years later in Ireland. And I can
understand why. I guess this is where I should mention.
I'm writing this episode while under the influence of advil
PM because I grabbed the wrong tablets while trying to
treat a headache. So that's going to be a factor
for the rest of this episode, just like you know. Anyway,
George Bull helped establish symbolic logic, which, by the way,
(01:31):
I loved that subject in college. It was a math
course that I excelled at. In fact, I would only
show up to class on Thursdays and Fridays. We met
every day of the week, but there was no attendance policy.
So Thursday I would show up to find out which
chapters that the professor had gone over, and then Friday
(01:52):
I would show up because there was a quiz for
that week's lessons. And symbolic logic made so much sense
to me that I could just show up on Thursday
to see which chapters that needed to read, show up
Friday and do the work. And I aced that class.
Now this is not to say that I'm a genius.
I am not. Just for some reason or another, symbolic
(02:15):
logic clicked with me in a way that a lot
of subjects never did. Anyway, symbolic logic would become a
fundamental foundation for digital circuits. Years later, my guess is
he didn't know that was going to happen because computers
weren't a thing yet. So what had happened was Bull
mostly learned mathematics all on his own. He received some
(02:35):
tutoring from his father, who was a tradesman, and he
did go to a couple of schools, but no like
secondary formal education. Mainly he was self taught, and he
actually began teaching around various schools in his region when
he was just sixteen years old, not only because he
(02:55):
was brilliant, but also because it was necessary. His father's
business had slowed down and his family needed the income.
So the gig economy has been around for a while,
I guess is what I'm saying. In the eighteen forties,
Bull submitted papers to the Cambridge Mathematical Journal on subjects
ranging from differential equations to calculus, you know, light reading.
(03:17):
In eighteen forty seven, he published a work titled the
Mathematical Analysis of Logic Being an Essay toward a Calculus
of Deductive reasoning. This landed him a university teaching gig,
even though he had never earned a college degree of
his own. In eighteen forty five, he published a further
treatment of his ideas titled an Investigation into the Laws
(03:39):
of Thought on which are founded the mathematical theories of
logic and probabilities Real Page Turner. In eighteen forty six
he married Mary Everest, the daughter of Mount Everest. Okay, wait, no, sorry, no,
she was the daughter of George Everest. It's just that
Mount Everest is named after George Everest. That's actually true.
(04:02):
I got a little confused there. Sorry, I'm blaming the ADVILPM.
At this point, Boole used mathematical symbols to represent logical
arguments and showed that by encoding an argument as a
series of equations, one could check to see if the
argument was sound or not, if it were true, or
if it were false. So, for example, maybe you were
(04:27):
saying something like all cats are mammals, Old Greg is
a cat, therefore old Greg is a mammal. Well, you
could actually represent those statements as equations, and then you
could solve to show that the conclusion is contained within
the premises. So if the premisses contained the conclusion and
(04:47):
everything lines up, you would say it's logically sound. It
is a true argument. However, if you said all cats
are mammals. Old Greg likes to sip Bailey's out of
a shoe. Therefore, Old Greg is a mammal. Well, that
wouldn't fly because you haven't established that Old Greg is
a cat or any other kind of mammal for that matter.
He's Old Greg. So what does this have to do
(05:10):
with computers. Well, Old Greg will have nothing to do
with computers, probably because he lives at the bottom of
a lake and his computer with short circuit immediately. But
boolean logic would underpin the concept of logic gates, which
in turn would allow a computer to process information in
a meaningful way. And this brings us to the concept
of actual logic gates. PCMag dot com defines logic gates
(05:34):
as quote a collection of transistors and resistors that implement
boolean logic operations in a digital circuit. Logic gates have
one or two zero or one inputs, but only one
zero or one output, as in the following examples, which
they then list to continue the quote. Transistors make up gates,
(05:57):
Gates makeup circuits, and circuits may up electronic systems. End quote.
So a typical logic gate usually accepts two inputs and
produces a single output, and that output is based both
upon the nature of the inputs and the nature of
the gate itself. I say typically, because of course there
(06:18):
are exceptions, but for the purposes of simplicity, we're mainly
focusing on the typical example of two inputs enter, one
output leaves. So yeah, I am going thunderdome with these rules.
The output that a logic gate produces, like I said,
depends both upon the value of the inputs and the
type of logic gait that we're talking about. So you
(06:40):
can think of logic gates being kind of like a
physical gate that leads into, say a courtyard, and this
particular gate has a bouncer standing outside of it. The
bouncer enforces the rules. So you come up to the gate,
and if you meet certain criteria, the bouncer lets you through,
and if you do not meet the criteria, the bouncer
(07:01):
turns you away. This analogy isn't perfect, because really the
logic gates allow a value to pass through no matter
what it's just what value is that going to be?
Will it be a zero or will it be a one.
So the bouncers in circuits are electronic components, and the
rules depend upon the type of gait. And we are
talking physical structures here in a circuit. We're actually talking
(07:23):
about transistors and resistors. So the way the gates work
is dependent upon voltage. So each input can have one
of two values. Either zero volts is applied to the input,
which would then represent an input of zero, or five
positive volts are inputed into that input and then that
(07:46):
represents a one. The output produces a value of either
zero volts, so a zero in logic, or five volts
again meaning a one in logic. Now, if we just
talking two inputs, you can have four possible combinations, right,
So each input can have one of two states, either
a zero or a one. And if we start to
(08:09):
group these two inputs together, that gives us four potential combos.
You could have both input A and input B B zero,
so that's one value. Or you could have both of
them be one that's a second value. Or you could
have input A B zero, input B is one that's
a third value. Or you could have input A B
(08:32):
one and input B is zero that's your fourth value.
So four possible combinations zero, zero, zero, one, one zero
or one one. Now, those are the basics when we
come back. We're gonna talk about the different kinds of
logic gates, and we'll build from the most basic to
the more complicated. But first let's take this quick break
(08:55):
to thank our sponsor. We're back, So now we're going
to talk about logic gates, and the first one up
is the and logic gate. The and logic gate will
produce a one result as the output only if both
(09:19):
inputs are also one. So if input A is one,
an input B is one, then the output is also one.
Any other combination, whether it's zero, zero, zero, one, or
one zero, will have an output of zero. So an
and gate will produce a one if both inputs are
also one. Next up, we've got the or gate. This
(09:42):
one will produce a zero output if both inputs are
also zero, so any other combination will create a one output.
It's kind of the opposite of the AND gate in
many ways. Then we have the exclusive or, which is
agreed not to date other people. I'm sorry, that's the
nighttime advil talking. The exclusive or x or produces a
(10:06):
one only if one input is a one and the
other one is a zero. So if you have one,
zero or zero, one is the inputs that produces a
one output. The zero zero and one one inputs would
produce a zero output. I know this starts getting confusing,
but this is just for the purposes of explaining the
different types of logic gates. Next up, we've got the
(10:29):
logical inverter. So a logic inverter is someone who stands
mister spot on his head. No, actually no, it's a
not git and this only has a single input. So
it's one of those exceptions I was talking about a
few moments ago. So an inverter does exactly what you
would expect. It produces an output that's the opposite of
the input. So if you have a one coming into
(10:51):
a not git, a zero is coming out, or vice versa.
Now we're going to get into a few gates that
combine some of the more simple verse into something a
little more sophisticated. So first up, we've got the nand gate,
the NA in D gate. This behaves as if it
is an and gate immediately followed by a not gate.
(11:13):
So the nand gate will create a zero output only
if both inputs are one, so one one creates a
zero output. Any other combination would produce a one output.
Then we have the nore gate, which is an or
gate followed by an inverter. It will only produce a
one if both inputs are zero, So zero zero creates
(11:36):
a one output. Every other combination creates a zero output.
Now let's go crazy Broadway style. We got the exclusive
nore or x nore gate, which will produce an output
of one if both inputs are the same. So a
zero zero input will create a one output, but then
(11:57):
so will a one one input. Now a one zero
or a zero one input that would create a zero.
So yes, I know that sounded like a lot of
zeros and ones, but that's what we've got to work with.
And these logic gates are what make up digital circuits.
You can combine them in all sorts of different configurations,
with the only real limit being that we are talking
(12:19):
about physical structures producing these outputs, right, we are talking
about actual transistors and resistors. So eventually you do start
to run out of physical space. So they do take
up space, very little space because these are very very
very tiny components, but they do take up space. You
also run into issues like how much heat you're producing
when you're providing power to the circuit, so that can
(12:42):
also be a limiting factor, but otherwise you can get
into lots of complex orientations and configurations. Now, the cool
thing about this is you could actually write out the
string of logic gates that your circuits follow. Though you
would need an awful lot of paper to do anything
like a modern circuit, you could do it, however. The
(13:04):
point is that logic gates represent specific rules, and these
rules determine the output produced based upon the input received.
And that's the very basic foundation of digital computers. Though
obviously it gets a lot more complicated from there, but
that's something I'll just have to tackle on a day
when I'm not on ADVILPM, which is not a sponsor,
(13:24):
I should add, it's just the reason this episode turned
out the way it did, so my apologies on that one. Anyway,
that's the basics of logic gates. You can get a
lot more detailed, as I said, and I know it
gets really confusing hearing all those ones and zeros. I
recommend looking up truth tables for different logic gates so
(13:45):
that you can get a better understanding. It helps me,
at least when I'm able to see visualizations of this
in various charts, and that lets me get a better
understanding of what output you're going to get based upon
the input going in. So yeah, this is like the
core foundation of processing. So you combine that with the
(14:06):
element of binary information where your values can either be
a zero or one. Then you start grouping bits together
to make more meaningful representations of info. Couple that with
the process of logic gates, and you start to see
how computers actually start physically handle this information in the
(14:26):
form of voltages. It's really incredible, like when you start
to break it down, because we deal with such an
abstraction of what computers are doing when we're running any program, right,
We're just focusing on whatever the program does. We're not
necessarily thinking what is going on at the circuit level
to make this happen. Well, logic gates are really the
(14:50):
basis for that. So I hope this was interesting. I'm
sure it was at least cringe worthy and maybe in
a retaining as well due to my aduled state thanks
to the nighttime medication I accidentally took. And it's still
doing a number on me, y'all. I've had two full
cups of coffee to push through this, So blame my
(15:15):
foolish on grabbing the first headache medicine that I wasn't
within reach for me to deal with my headache. That's
the reason. All right, We've got a couple more new
episodes this week before we get into rerun territory. I've
got a new episode for tomorrow and for Wednesday, so
hope you enjoy those. They will also be on the
(15:35):
shorter side, which was necessary for me to be able
to get everything done before I headed off on vacation.
And I hope you are all well. I hope I'm
well right now. I should be kind of leaning back
in a hammock in the Blue Ridge Mountains somewhere hopefully
at this point, unless the weather's terrible, which is probably
(15:57):
will be, and that case, I'll just be inside watching
the rain. Either way sounds good to me. And I
will talk to you again really soon. Tech Stuff is
an iHeartRadio production. For more podcasts from iHeartRadio, visit the
iHeartRadio app, Apple Podcasts, or wherever you listen to your
(16:20):
favorite shows.
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Daniel Jeremiah of Move the Sticks and Gregg Rosenthal of NFL Daily join forces to break down every team's needs this offseason.
Dateline NBC
Current and classic episodes, featuring compelling true-crime mysteries, powerful documentaries and in-depth investigations. Follow now to get the latest episodes of Dateline NBC completely free, or subscribe to Dateline Premium for ad-free listening and exclusive bonus content: DatelinePremium.com
Las Culturistas with Matt Rogers and Bowen Yang
Ding dong! Join your culture consultants, Matt Rogers and Bowen Yang, on an unforgettable journey into the beating heart of CULTURE. Alongside sizzling special guests, they GET INTO the hottest pop-culture moments of the day and the formative cultural experiences that turned them into Culturistas. Produced by the Big Money Players Network and iHeartRadio.