HOW TRANSISTORS RUN CODE?

Summary

This 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

• 😀 Transistors function as electronic switches, allowing electricity to flow when current is applied to the base terminal.
• 🔧 A single transistor can act as an insulator or a conductor, effectively acting as a switch controlled by electrical signals.
• 💡 By using transistors, simple gates like an inverter or NOT gate can be created, which is fundamental to digital logic.
• 🔗 Multiple transistors can be connected to form more complex logic gates, such as AND and OR gates, which are essential for computer operations.
• 🤖 Logic gates can be combined to create more complex circuits, like an XOR gate, which is significant in computer science.
• 🧠 The concept of abstraction allows us to represent complex circuits with simple symbols, making it easier to understand and work with.
• 🔢 Adders are circuits that can perform binary addition, which is crucial for arithmetic operations in computers.
• 🔄 Full adders are used for multi-digit binary addition, taking into account both the bits being added and the carry from previous additions.
• 🚀 Proper management of operation overflows is critical to avoid undefined behavior and potential system failures.
• 🛠️ 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

00:00

🔌 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.

05:02

🧮 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.

10:02

💡 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.

Keywords

💡Transistors

Transistors are semiconductor devices used to amplify or switch electronic signals and electrical power. They are the fundamental building blocks of modern electronic devices. In the video, transistors are described as simple electronic switches that can control the flow of electricity. They are used to explain the basic operation of computers, where they can act as insulators or conductors based on the input signal, thus enabling complex tasks like arithmetic operations and processing instructions.

💡Electronic Switches

An electronic switch is a device that can open or close an electrical circuit. In the context of the video, transistors function as electronic switches, allowing or blocking the flow of current based on a small current applied to the base terminal. This functionality is crucial for creating logic gates, which are the basis for all digital circuits in computers.

💡Logic Gates

Logic gates are basic building blocks of a digital circuit that implement logical operations. They are used to model complex Boolean algebraic expressions. The video explains how transistors can be arranged to form logic gates such as AND, OR, NOT, and XOR gates, which are essential for performing computations and making decisions within a computer.

💡AND Gate

An AND gate is a logic gate that outputs true or one only when all of its inputs are true or one. The video uses the AND gate as an example of how multiple transistors can be connected to create a circuit that outputs a one only when both inputs are one, illustrating the concept of abstraction in digital circuit design.

💡OR Gate

An OR gate is a logic gate that outputs true or one if at least one of its inputs is true or one. In the video, the OR gate is explained as a circuit where an output of one is produced if either or both inputs are one, showcasing how transistors can be connected in parallel to achieve this functionality.

💡NOT Gate (Inverter)

A NOT gate, also known as an inverter, is a logic gate that outputs the inverse of its input. If the input is true, the output is false, and vice versa. The video demonstrates how a transistor can be used to create a NOT gate by turning an LED on when the input is zero and off when the input is one.

💡Abstraction

In the context of digital circuits, abstraction refers to the concept of hiding the complexity of a system and exposing only the necessary elements. The video discusses how complex circuits of transistors can be abstracted into simpler representations like logic gates, making it easier to design and understand digital systems.

💡Adders

Adders are digital circuits that perform the arithmetic addition operation. The video explains how adders can be constructed using logic gates and transistors, with examples of half adders and full adders. These circuits are essential for performing arithmetic operations in computers.

💡Half Adder

A half adder is a simple digital circuit that adds two bits and produces a sum and a carry output. The video clarifies that a half adder does not account for a carry from a previous addition, making it insufficient for multi-digit binary addition.

💡Full Adder

A full adder is a digital circuit that adds three bits: two input bits and one carry-in bit, and produces a sum and a carry-out bit. The video demonstrates how full adders can be used to perform multi-digit binary addition by considering the carry from previous additions.

💡Binary Decoders

Binary decoders are digital circuits that convert binary-encoded signals into a form where their individual elements can be separately observed or acted upon. The video uses binary decoders to explain how a computer can select which operation to perform based on the opcode received from the CPU, highlighting their role in interpreting instructions.

💡Arithmetic Logic Unit (ALU)

An Arithmetic Logic Unit is a digital circuit that performs arithmetic and logical operations. The video introduces the concept of an ALU as a component that takes input values and an opcode to perform specified operations, producing results and flags indicating overflow or negative values.

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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