HOW TRANSISTORS RUN CODE?
Summary
TLDRThis video, sponsored by Brilliant, explores the role of transistors in computing. It explains how transistors, acting as electronic switches, can be used to perform complex tasks like arithmetic and interpreting instructions. The video delves into the basics of transistors, their three terminals, and how they can be configured to create logic gates. It further discusses how these gates can be combined to form adders and other circuits, essential for computer operations. The script also touches on the importance of managing operation overflows and hints at the role of memory in future episodes.
Takeaways
- ๐ Transistors function as electronic switches, allowing electricity to flow when current is applied to the base terminal.
- ๐ง A single transistor can act as an insulator or a conductor, effectively acting as a switch controlled by electrical signals.
- ๐ก By using transistors, simple gates like an inverter or NOT gate can be created, which is fundamental to digital logic.
- ๐ Multiple transistors can be connected to form more complex logic gates, such as AND and OR gates, which are essential for computer operations.
- ๐ค Logic gates can be combined to create more complex circuits, like an XOR gate, which is significant in computer science.
- ๐ง The concept of abstraction allows us to represent complex circuits with simple symbols, making it easier to understand and work with.
- ๐ข Adders are circuits that can perform binary addition, which is crucial for arithmetic operations in computers.
- ๐ Full adders are used for multi-digit binary addition, taking into account both the bits being added and the carry from previous additions.
- ๐ Proper management of operation overflows is critical to avoid undefined behavior and potential system failures.
- ๐ ๏ธ Binary decoders enable selection among multiple options based on input, which is essential for interpreting different types of machine code instructions.
Q & A
What is the primary function of a transistor?
-A transistor functions as an electronic switch, allowing electricity to pass through when current is applied to one of its terminals.
What are the three terminals of a transistor?
-A transistor typically has three terminals: a collector, an emitter, and a base.
How can a transistor act as a switch in a circuit?
-A transistor can act as a switch by acting as an insulator when no current is applied to the base terminal, preventing electricity from flowing between the collector and emitter. When a small current is applied to the base, it acts as a conductor, allowing electricity to flow.
What is a simple gate in the context of transistor circuits?
-A simple gate is a basic circuit configuration using a transistor where the input is applied to the base terminal and the output is represented by the state of an LED, which can be on or off.
How does an inverter or NOT gate function with a transistor?
-An inverter or NOT gate is a transistor circuit where the LED is on when the input is zero, and the LED turns off, indicating an output of zero, when the input is set to one.
What is an AND gate in digital logic and how can it be created with transistors?
-An AND gate is a digital logic gate that outputs a one if and only if all its inputs are one. It can be created with transistors by connecting them in series, where both inputs must be one for the output to be one.
How does an OR gate differ from an AND gate in terms of transistor configuration?
-An OR gate can be created with transistors connected in parallel, where the output is one if at least one of the transistors acts as a conductor, which can happen if either or both inputs are one.
What is the purpose of a binary decoder in a computer circuit?
-A binary decoder is a circuit that receives a binary number as input and activates a specific output corresponding to the binary number, while deactivating all other outputs.
How does a full adder circuit differ from a half adder?
-A full adder circuit can handle two bits being added and also take into account the carry from a previous addition, unlike a half adder which only accepts two inputs and does not account for a carry.
What is the role of an arithmetic logic unit (ALU) in a CPU?
-An arithmetic logic unit (ALU) in a CPU takes input values and an operation code (OP code) that specifies the arithmetic operation to be performed. It then produces the result of the operation along with additional information such as the sign or overflow status.
Why is managing operation overflows important in computer operations?
-Managing operation overflows is crucial because neglecting them can lead to undefined behavior and potentially severe consequences, such as system crashes or incorrect data processing.
Outlines
๐ Understanding Transistors and Logic Gates
The video, sponsored by Brilliant, introduces transistors as fundamental electronic components that act as switches. It explains how transistors can be used to perform complex tasks such as mathematics and instruction interpretation. The host, George, discusses the three terminals of a transistor and how they can be manipulated to control the flow of electricity, thus acting as a switch. The video demonstrates how a single transistor can be used to create a simple gate, like an inverter, and how multiple transistors can form more complex logic gates such as AND and OR gates. The concept of abstraction is introduced to simplify the understanding of these circuits, allowing viewers to think in terms of logic gates rather than individual transistors.
๐งฎ Binary Addition and Logic Gates
This section delves into binary addition, comparing it to decimal addition and explaining how it works. It introduces the concept of overflow and the need for additional bits to represent values. The video then describes how to create a circuit that can add two single-digit binary numbers, focusing on the sum and carry outputs. It explains the use of XOR and AND gates to achieve this. The concept of a half adder is introduced, which can only add two bits without considering a carry from a previous addition. To overcome this, the video presents the full adder, which can handle both the bits being added and the carry from a previous addition. The video also touches on the importance of managing operation overflows to avoid undefined behavior and potential consequences, such as the 1996 rocket accident.
๐ก Building Complex Circuits with Logic Gates
The video continues by discussing how logic gates can be used to build more complex circuits, such as full subtractors and 8-bit subtractors. It then explores how these components are integrated within a CPU. The concept of binary decoders is introduced, explaining how they can activate specific outputs based on binary inputs. The video uses the example of assembly code and machine code to illustrate how a CPU identifies which circuit corresponds to a specific instruction. It discusses the use of NOR gates and opcodes to determine the type of arithmetic operation to be executed. The video concludes by introducing the arithmetic logic unit (ALU), which performs arithmetic operations based on input values and an opcode. It also hints at the importance of memory in computer operations, which will be explored in a future video.
Mindmap
Keywords
๐กTransistors
๐กElectronic Switches
๐กLogic Gates
๐กAND Gate
๐กOR Gate
๐กNOT Gate (Inverter)
๐กAbstraction
๐กAdders
๐กHalf Adder
๐กFull Adder
๐กBinary Decoders
๐กArithmetic Logic Unit (ALU)
Highlights
Transistors act as electronic switches, enabling the flow of electricity when current is applied to their base terminal.
Transistors can be used to perform complex tasks like arithmetic and interpreting instructions.
A single transistor has three terminals: collector, emitter, and base, functioning as a switch controlled by electrical signals.
Transistors can mimic a simple gate, acting as an insulator or conductor based on input signals.
An inverter or NOT gate is created when a transistor's LED turns off with an input of one, indicating an output of zero.
Multiple transistors in series can create an AND gate, which outputs one only when both inputs are one.
Transistors in parallel form an OR gate, outputting one if at least one input is one.
Logic gates are fundamental circuits that can be combined to achieve more complex behaviors.
An XOR gate requires a specific combination of transistors to output one only when the inputs differ.
Adders are circuits that perform binary addition, producing a sum and a carry output.
A half adder can only add two single-digit binary numbers without considering carry from previous operations.
A full adder is capable of adding three single-digit binary numbers, including carry from previous operations.
An 8-bit adder is a component that adds two 8-bit numbers, providing sum and overflow signals.
Binary decoders select one output among multiple options based on the input binary number.
Arithmetic logic units (ALUs) perform specified arithmetic operations based on input values and an OP code.
CPUs use binary decoders to identify which internal circuit corresponds to a specific instruction.
The video concludes with a teaser for a future episode on memory, a crucial concept in computer operations.
Transcripts
this video is sponsored by brilliant
transistors are very simple components
they are basically electronic switches
when we apply current to one of its
terminals a transistor lets electricity
pass through but how can this simple
Behavior make computers
possible in today's video we are going
to learn how transistors can be used to
achieve more complex
tasks like doing math and even
interpreting
instructions hi friends my name is
George and this is core dumped before we
begin just a reminder that you can find
me on social media and our Discord
server where I'm available to answer
your questions and by the way I keep
getting requests to use my own voice
instead of using text to speech the
reason I don't record myself is because
I grew up in South America and I'm not a
native English speaker so I hope you
like modern family cuz once I start
recording myself that's what it will
sound
like Anyway let's start a single
transistor typically has three terminals
a collector an emitter and a base in a
circuit it can act as an insulator
preventing electricity from flowing
between the collector and emitter
terminals but if we apply a small
current to the base terminal it acts as
a conductor allowing electricity to
flow essentially a transistor can be
seen as a switch but instead of
mechanical movement it operates by using
electrical
signals in this example circuit we are
using a transistor to turn on and off an
LED by utilizing the base terminal as an
input and the emitter terminal as an
output signal we can mimic the input
signal with a switch and visually
represent the output signal with the
LED let's dub this a simple gate in a
simple gate when the input is zero the
output is zero when the input is one the
output is
one now let's tweak things a bit here
when the input is zero the LED is on due
to the way it is arranged within the
circuit but pay attention to this
setting the input to one causes the LED
to turn off indicating to us the output
is a zero this setup is commonly
referred to as an inverter or a not
gate this may seem a bit confusing this
video I found on Twitter is a perfect
example of this
effect and if you want more details you
can watch this video by Ben eer where he
explains all this using real
components we're not limited to just one
transistor by using multiple transistors
we can achieve more complex Behavior if
two transistors are connected in series
when both inputs are zero the output
will be zero because both transistors
act as insulators similarly if either
input is zero the output will be zero
the only way to obtain a one in the
output is by having both transistors act
as conductors which happens when both
inputs are set to one
this is where we begin to apply a
powerful concept called abstraction
instead of focusing on the individual
transistors in the circuit we can
abstract this into a white box a box
that consistently outputs a specific
value based on two given
inputs this is known as an and gate an
and gate outputs a value of one if and
only if both inputs are one otherwise
the output will be
zero if we connect the transistors in
parallel when both transistors act as
insulators electricity cannot
flow but in this setup having any
transistor acting as conductor is enough
to allow electricity to
flow so in this arrangement to get an
output of one is not strictly necessary
to set both inputs to
one once more we can abstract this
circuit into a box known as an or gate
an or gate outputs a value of zero if
and only if both inputs are zero
otherwise it outputs a value of
one these circuits known as logic gates
are so fundamental that instead of
representing them with boxes each one is
assigned a dedicated
symbol notice that since inputs and
outputs are electrical signals we can
connect the output of one logic gate to
the input of another this allows us to
combine logic gates to achieve even more
complex
behavior for example if we desire this
particular Behavior we can combine logic
G Gates accordingly to achieve
it this is where we begin to see the
power of abstractions while this setup
is ultimately composed of transistors
it's much simpler to understand what's
happening by thinking in terms of logic
gates this circuit is known as an xor
gate and it is also very important in
computer science so it has its own
symbol and now that we understand what
logic gates are let's use them to create
more use ful things let's start with
adders adding binary numbers is actually
quite simple in fact binary addition
works just like decimal addition 0 + 0 =
0 0 + 1 = 1 1 + 0 = 1 and 1 + 1 = two
however the value two cannot be
represented with a single binary digit
when this occurs we say the addition has
overflowed meaning we require an
additional bit to represent the value so
what we're aiming for is a circuit that
takes two input values and produces two
outputs the sum and the
carry let's break down the
sum but before a quick message from
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dumped or by using the link in the
description below and now back to the
video let's break down the sum we
require a circuit that outputs zero when
both inputs are the same and one when
they differ does this sound familiar
it's precisely what an exor gate
accomplishes so we've already solved
half of the puzzle for the carry output
we need a circuit that outputs the value
one only when both inputs are
one this matches the behavior of and
gate and there we have it we've crafted
a circuit capable of adding two singled
digigit binary
numbers okay but what about multi-digit
binary
addition well let's try since we have to
add numbers in each row using one Adder
for each row seems logical it works well
for the first row but when we move to
the second row there's an
issue we need to consider that the
previous row might have created a carry
but because the adder circuit only
accepts two inputs it doesn't account
for this carry because of this
limitation this circuit is known as a
half adder and it is not useful in this
scenario what we need is a full adder a
circuit that can handle not only the two
bits being added but also take into
account the carry from a previous
addition here's the circuit we're
working towards think of it as a circuit
capable of adding three singled digigit
binary
numbers to simplify matters we can
encapsulate this in a box which we'll
call a full
adder with full adders we can now add
multi-digit binary
numbers the carry output of each full
adder feeds directly into the carry
input of the next full adder as shown
here in this
animation to add binary numbers of n
digits in one go n full adders are
needed for example if we aim to add two
8 bit numbers we'll need eight full
adders remember that values are
represent Ed here using electrical
signals since electricity moves at
incredible speed once we alter the input
the output changes almost instantly and
this is what makes transistors ideal for
this job while logic gates can be
crafted from other components like
relays and even fancy 3D printed Parts
powered by weird stuff like marbles or
even water none of this matches the
speed and compactness of
transistors before Things become overly
complex we can one more time package all
of this functionality into a special
component known as an 8bit
Adder an 8bit Adder takes two 8-bit
numbers as input and produces the sum of
the inputs as another 8bit number it
also provides an overflow signal which
is essentially the carry out output of
the last full adder inside this overflow
signal is crucial because it informs us
whether the storage capacity being
utilized is adequate to represent the
result of the
operation in this example both inputs
are one bite long but if we attempt to
store the output in just one bite we
will miss information resulting in an
incorrect
value by monitoring the Overflow output
we can recognize the need for an extra
bite to accurately store the
output believe it or not neglecting to
manage operation overflows can lead to
undefined Behavior sometimes with severe
consequences like this rocket accident
in
1996 and we can continue to move to
higher levels of abstraction if we want
to make a circuit that increments an
input value we can simply use an adder
and set the second input to always be
one we've only talked about adders in
detail but in the end it's all about
logic gates with them we can make more
useful things like a full subtractor
that then can be used to build an 8 bit
subtractor and from there we could keep
going and make even more complicated
stuff as you may have guessed inside the
CPU there's a special component that
houses all these circuits for now let's
call it our mysterious
component the question we want to answer
now is when a CPU reads an instruction
how does it identify which one of these
circuits corresponds to that specific
instruction how does the computer
discern adding numbers upon encountering
a particular instruction and subtract
them upon encountering
another I mean some instructions aren't
even arithmetic
operations the last type of component we
are covering today are binary
decoders let's take a look at this
circuit and examine the output for every
input combination the first thing we can
notice here is that each combination
triggers a specific output to activate
while deactivating all other
outputs another way to see it is that
the circuit receives the binary number
that corresponds to the position of the
output we wish to
activate this is what binary decoders do
when it receives an input one and only
one output has the value of one with all
others outputting the value of zero
if we have a decoder with three inputs
we can control which of eight outputs
turns
on four inputs well we can control 16
outputs and so
on this is huge because it means that we
are also capable of creating circuits
that can select among multiple
options now remember that assembly code
is just a humanfriendly representation
of machine code the actual code
consisting of ones and zeros that
computers comprehend
not all instructions are arithmetic
operations some of them are instructions
dedicated to fetch and write data to
memory and other stuff like that let's
imagine a very basic architecture where
if the first two bits of an instruction
are zeros the computer interprets them
as arithmetic operation
instructions in this example to verify
this we could employ nor Gates given the
scope of this video at the moment we are
not concerned with instruction that
signifies something else but at least we
know how to identify between them
in this example architecture the third
and fourth bits will determine the type
of arithmetic operation to be executed
for instance if those bits are 0 0 it
means addition if 01 it represents
subtraction and so forth this is
commonly known as an OP code each op
code is associated with one and only one
kind of arithmetic
operation when the CPU has determined
that the current instruction is an
arithmetic operation Our Mysterious
component receives this op code and
internally links those two bits to a
decoder which is used to identify the
desired internal
operation the straightforward approach
here would be by allowing all circuits
to receive the inputs and generate their
respective outputs but the outputs of
the decoder are interconnected in a way
that allows only the output of the
selected operation to pass through this
component keep in mind that there are
more efficient ways to do this but here
we focus on
Simplicity Our Mysterious component can
also be enclosed with within a box this
is a rudimentary and somewhat incomplete
version of something known as an
arithmetic logic
unit we'll talk about this component in
more detail in a future episode where we
discuss how CPUs execute instructions
but beforehand an arithmetic logic unit
takes input values and an OP code that
tells the internal circuitry what
arithmetic operation to perform between
those values it then produces the result
of the specified operation along with
additional information such as whether
the result is negative 0 or if it has
overflowed and this was a very very very
brief introduction to how computers use
transistors to do math and follow
instructions well sort of because we
completely avoided an important concept
memory but that's a topic for a future
video so make sure to subscribe because
you don't want to miss it and that's it
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