Digital Logics and Data Representation

Summary

This session delves into the physics of digital computers, contrasting them with analog computers and highlighting digital's precision and reliability. It traces the evolution from abacuses to modern transistor-based systems, explaining the fundamental concepts of voltage and current. The script explores the role of MOSFET transistors in digital logic, the significance of logic gates, and the construction of memory elements like registers and flip-flops. It also discusses binary counters, clock signals for synchronization, and Moore's Law, providing a comprehensive foundation in digital logic.

Takeaways

• 🌟 Digital computers are referred to as such because they perform computations on data with discrete values, as opposed to analog computers that work with continuously varying values.
• 🔢 The term 'digital' implies precision and accuracy in computation, which has led to the widespread adoption of digital computers over analog ones due to their reliability and cost-effectiveness.
• 👨‍🏫 A brief history of computing devices includes the abacus, mechanical gears, and levers, electronic computers with vacuum tubes, and the advent of transistors post-1947 which revolutionized computing.
• 🔋 Voltage and current are fundamental concepts in electrical engineering, with voltage representing potential difference and current representing the flow of electrons, analogous to water pressure and flow.
• 💡 The transistor, a semiconductor device, is the building block of digital systems, controlling the flow of electrical current and functioning as an on/off switch in digital circuits.
• 🛠️ MOSFETs, or Metal Oxide Semiconductor Field Effect Transistors, are a type of transistor used in digital circuits that can be either 'on' or 'off', controlled by the gate voltage.
• 🔄 CMOS technology utilizes complementary transistors that can be turned on by positive or zero gate voltages, offering low power consumption and high reliability in digital logic circuits.
• 📚 Logic gates, derived from Boolean algebra, are the basis for digital hardware and can be implemented using transistors to perform basic functions like AND, OR, and NOT.
• 🔄 Latches and flip-flops are sequential circuits that store data and have outputs dependent on previous inputs, essential for creating memory elements like registers in processors.
• 🔢 Binary counters are circuits that accumulate numeric values, counting the number of input transitions and providing an output that represents the count in binary form.
• ⏲ Clocks are essential for the automatic operation of digital computers, providing a regular sequence of signals that synchronize the operation of digital logic circuits.

Q & A

What is the fundamental difference between a digital computer and an analog computer?

A digital computer performs a sequence of computational steps on data items with discrete values, while an analog computer operates on values that vary continuously over time.

Why are digital computers considered more precise than analog computers?

Digital computers are more precise because they can be very accurate with discrete values, unlike analog computers that deal with continuous values which can be less exact.

What is the significance of the invention of the transistor in the history of computing?

The invention of the transistor between 1947 and 1950 changed computing dramatically by replacing vacuum tubes and improving the computing power and reliability of electronic devices.

What is the role of voltage and current in the context of digital logic?

Voltage and current are quantifiable properties of electricity used in digital logic to represent the potential difference and the flow of electrons, respectively, which are essential for the operation of digital circuits.

How does the analogy of water help in understanding voltage and current?

Voltage can be compared to water pressure, and current to the amount of water flowing through a pipe, helping to visualize the concepts of electrical potential and flow.

What is a transistor and how is it used in digital circuits?

A transistor is a semiconductor device used to control the flow of electrical current. In digital circuits, it functions as an on/off switch, controlled electronically.

What are the two types of MOSFET transistors used in digital logic, and what is their significance?

The two types of MOSFET transistors are those that turn on when the gate voltage is positive and those that turn on when the gate voltage is zero. They are significant in CMOS technology, which allows for low-power consumption circuits.

What is a latch in digital systems and what is its basic function?

A latch is a basic sequential circuit with an input, output, and an enable line. Its function is to store a value and output it when the enable line is set to a logical one.

How are registers different from latches in terms of their role in a processor?

Registers are short-term storage units within the CPU that hold multiple bits and are used in computations, whereas latches are basic circuits that can store a single bit of data.

What is a flip-flop and how does it differ from a latch?

A flip-flop is a circuit where the output depends on the previous input as well as the current input, acting like a toggle switch. Unlike latches, flip-flops respond to a sequence of inputs and can change state with each input transition from 0 to 1.

What is the purpose of a binary counter in digital systems?

A binary counter accumulates numeric values, providing a numerical total in binary form, unlike a flip-flop which only offers two possible output values. It is used to count the number of input transitions from 0 to 1.

How does a clock function in a digital logic circuit?

A clock in a digital logic circuit provides a regular sequence of alternating ones and zeros, which allows the hardware to take action without requiring an input to change. It is essential for the automatic operation of a digital computer.

What is Moore's Law and how has it been revised over time?

Moore's Law is the observation that the number of transistors on a silicon chip doubles approximately every 18 months, initially stated as every year. It signifies the rapid growth in the density of integrated circuits.

What are the different levels of abstraction in understanding digital circuits, and why are they important?

The different levels of abstraction in digital circuits include the circuit boards, the processor, the gate, and the transistor levels. They are important for understanding the underlying hardware details and for building practical structures in digital logic design.

Outlines

00:00

💻 Introduction to Digital Logic and Computers

This paragraph introduces the fundamentals of digital logic, aiming to understand the physics behind computer operations. It explains the distinction between digital and analog computers, emphasizing the precision and reliability of digital computation due to their discrete data values. The paragraph also touches on the historical development of computing devices, from the abacus to electronic computers using vacuum tubes and transistors. The importance of reliability in computation is highlighted, as a single error can lead to failure. Voltage and current are introduced as key concepts in electrical engineering, with an analogy comparing voltage to water pressure and current to water flow through a pipe.

05:06

⚡ Understanding Voltage, Current, and Transistors

The second paragraph delves into the concepts of voltage and current, which are essential to comprehend digital logic. It explains how electrical engineers use these terms to describe properties of electricity, with voltage measured in volts representing potential difference and current in amperes representing the flow of electrons. The concept of ground as a reference point for voltage measurement is introduced. The paragraph then transitions to discussing transistors, which are semiconductor devices used to control electrical current. Metal-Oxide-Semiconductor Field-Effect Transistors (MOSFETs) are highlighted as a key component in digital systems, functioning as switches that can be turned on and off electronically.

10:06

🛠 The Building Blocks of Digital Systems: Logic Gates and Transistors

This paragraph explores the construction of digital systems using logic gates, which are based on Boolean algebra functions such as AND, OR, and NOT. These functions form the basis for digital hardware and can be implemented using transistors. The discussion includes how positive voltage represents a Boolean '1' and zero voltage represents a '0'. The paragraph also introduces the concept of latches, which are basic sequential circuits with an enable input, allowing for memory creation in digital systems. Registers are explained as short-term storage units within the CPU, holding multiple bits and commonly being either 32-bit or 64-bit in size.

15:07

🔄 Registers, Flip-Flops, and Memory in Digital Systems

The fourth paragraph continues the discussion on digital system components, focusing on registers and their role in holding values for computation. It explains how registers can be constructed from one-bit latches and how they operate with enable lines to store and maintain values. The concept of flip-flops is introduced as circuits with outputs dependent on previous inputs, functioning like a power switch that toggles state with each input pulse. The paragraph also touches on the graphical representation of flip-flop operation and the use of additional inputs like reset in these circuits.

20:10

🔢 Binary Counters and Clocks in Digital Logic Design

This paragraph introduces binary counters, which extend the functionality of flip-flops by offering multiple output values and the ability to accumulate input transitions, providing a numerical total in binary form. The discussion includes the practical aspects of electronic counters, such as reset inputs and overflow detection. The paragraph then moves on to the concept of clocks, which are essential for the automatic operation of digital computers, providing a regular sequence of signals to synchronize circuit operations. The function of clocks in digital logic is explained, along with their creation using inverters or quartz crystals.

25:11

🕰 Clocks, Sequences, and the Operation of Digital Circuits

The sixth paragraph discusses the role of clocks in digital circuits, explaining how they enable a sequence of operations without human intervention. It describes how a computer might start, with a series of steps that are performed one second apart, using a clock to control the timing. The paragraph introduces the concept of building a circuit to perform a sequence of steps using a clock, a binary counter, and a decoder or multiplexer. The explanation includes how these components work together to create a timed sequence of operations.

30:12

📈 Moore's Law and the Evolution of Integrated Circuits

The final paragraph discusses Moore's Law, which predicts the doubling of transistors on a chip approximately every 18 months, leading to increased functionality and performance. It outlines the categories of integrated circuits, from small-scale integration to very large scale integration (VLSI), and mentions the use of complementary metal-oxide-semiconductor (CMOS) technology in IC manufacturing. The paragraph also touches on the process of creating wafers containing multiple IC designs and the abstraction levels involved in circuit board and processor design. It concludes with a summary of the importance of digital logic in constructing computer systems and the role of Boolean algebra in circuit design.

Keywords

💡Digital Computer

A digital computer is a device that processes data by performing a sequence of computational steps on discrete values. It is characterized by its precision and accuracy, which is why it has largely replaced analog computers in most applications. In the video, digital computers are contrasted with analog computers, which operate on continuously varying values over time. The script emphasizes the importance of digital computers due to their reliability and precision, which are critical for complex computations involving billions of steps.

💡Analog Computer

An analog computer is a type of computer that operates on data represented by continuously varying quantities, as opposed to digital computers that work with discrete values. The script mentions that analog computers have been largely replaced by digital computers due to the latter's advantages in precision, cost-effectiveness, and reliability. However, analog computers are still used in very specific cases where their continuous operation is required.

💡Voltage

Voltage is a term used to describe the electric potential difference between two points, measured in volts. It is a fundamental concept in the script's discussion of electricity and its role in digital logic. Voltage is analogous to water pressure, where the potential difference drives the flow of electrons, similar to how water pressure drives the flow of water through a pipe. The script uses this analogy to help explain how voltage drops when current starts flowing through a wire.

💡Current

Current refers to the flow of electric charge, typically in the form of electrons, and is measured in amperes. In the context of the video, current is likened to the flow of water through a pipe at any given time. It is a key concept in understanding how electricity works within digital circuits and is essential for the operation of digital logic components like transistors.

💡Transistor

A transistor is a semiconductor device used to control the flow of electrical current. It is a fundamental component in digital systems, with the script highlighting its role in digital circuits, particularly in the form of metal-oxide-semiconductor field-effect transistors (MOSFETs). Transistors can act as switches, either allowing current to flow (on state) or preventing it (off state), which is crucial for the operation of digital logic gates.

💡MOSFET

MOSFET stands for Metal-Oxide-Semiconductor Field-Effect Transistor, a type of transistor used in digital circuits. The script explains that MOSFETs are the building blocks of modern digital computers, with their ability to control electrical resistance and thus act as switches. The term is used in the context of constructing digital systems and understanding the underlying physics of computer operation.

💡Logic Gates

Logic gates are the basic building blocks of digital circuits, implementing logical functions such as AND, OR, and NOT. The script discusses how these gates use voltage to represent binary values, with a positive voltage representing a logical '1' and zero voltage representing a logical '0'. Logic gates are essential for constructing more complex digital systems and are the foundation of digital logic design.

💡Latch

A latch is a basic sequential circuit with an input, output, and an additional 'enable' input. The script explains that latches are used to create memory within digital systems. When the enable input is set to a logical '1', the latch accepts the input bits and sets its output accordingly. Latches are fundamental in the construction of registers, which are short-term storage units within a CPU.

💡Register

A register is a short-term storage unit within a CPU that holds values used in computation. The script mentions that registers can hold multiple bits, with most computers having either 32-bit or 64-bit registers. Registers are constructed by replicating the circuitry that handles a single bit, illustrating the principle of digital hardware design where complex structures are built from simpler components.

💡Flip-Flop

A flip-flop is a circuit that has an output which depends on both the current and previous inputs. The script describes how a flip-flop changes its output state each time the input transitions from '0' to '1', acting like a toggle switch. Flip-flops are used to remember information in digital systems and are an essential part of sequential logic circuits.

💡Binary Counter

A binary counter is a digital circuit that accumulates input pulses and outputs a binary number representing the count. The script explains that unlike a single flip-flop, which only offers two output values (0 or 1), a binary counter can have multiple output lines, allowing it to count up to a maximum value. When the count exceeds this maximum, the counter typically resets to zero, indicating an overflow.

💡Clock

In the context of the video, a clock is a mechanism that provides a regular sequence of alternating '1's and '0's, allowing digital circuits to perform a series of steps without human intervention. The script describes how clocks are essential for the automatic operation of digital computers, synchronizing the operation of individual components to ensure they work together as intended.

💡CMOS

CMOS stands for Complementary Metal-Oxide-Semiconductor, a technology used to create integrated circuits. The script mentions CMOS as the chief advantage for MOSFET arrays because it allows for extremely low power usage. CMOS technology is crucial for the construction of modern digital computers, providing the ability to build complex and power-efficient circuits.

💡Moore's Law

Moore's Law is the observation that the number of transistors on a silicon chip doubles approximately every 18 months. The script refers to Moore's Law to illustrate the rapid pace of advancement in digital logic and computer hardware. This law has been a driving force behind the increasing capabilities and decreasing costs of digital electronics.

Highlights

Understanding the distinction between digital and analog computers, with digital computers handling discrete data values and analog computers operating on continuously varying values.

The precision advantage of digital computers over analog, due to their bit accuracy and reliability.

The historical evolution of computing devices from the abacus to electronic computers constructed from vacuum tubes and the invention of the transistor.

The fundamental role of transistors in modern digital computers, especially metal oxide semiconductor field effect transistors (MOSFETs).

The function of transistors as on/off switches in digital circuits, controlled by the gate terminal.

The two types of MOSFET transistors used in CMOS technology, which enable low power consumption in digital logic circuits.

The conceptual basis of digital hardware in Boolean algebra functions: AND, OR, and NOT.

The construction of efficient circuits implementing Boolean functions using transistors.

The use of latches to create memory in digital systems, with an explanation of their operation and the enable line.

Registers as short-term storage units within the CPU, holding multiple bits and their construction from one-bit latches.

The concept of flip-flops in digital circuits, which have outputs dependent on previous inputs and current states.

Binary counters as an extension of flip-flops, offering multiple output values and accumulating input transitions.

The importance of clocks in digital logic, providing a regular sequence of operations without human intervention.

The use of Moore's Law to describe the historical trend of increasing transistor density on integrated circuits.

The categorization of integrated circuits based on complexity, from small scale integration to very large scale integration.

The process of IC manufacturing, involving the creation of wafers containing multiple copies of IC designs.

The multi-level abstraction in digital logic design, from circuit boards to individual transistors and gates.

The significance of digital logic in constructing digital systems and the role of Boolean algebra in circuit design.

Transcripts

welcome to another session for

fundamentals of digital logic today we

want to understand the underlying

physics behind uh the computers and how

computers

operate

so the first positive button uh thing

that you're going to do is understanding

why a computer is referred to are either

a digital computer or a nanolog computer

so uh when you use the term digital

computers we want to refer to a device

that performs a sequence of computation

computational steps on data items that

have discrete values

and the alternative of that is an analog

computer that operates on values that

vary on a continuously over time

so the digital computation has the

advantage of being very very precise or

in other words to say a bit accurate

compared to the analog computer

because digital computers have become

both inexpensive and highly reliable

analog computers

has been navigated to a few very very

special cases

uh the need of reliability arises

because of computation can entail of

billions of individual steps if a

computer if a computer misinterprets a

value or a single instruction it is said

to fail therefore computers are designed

for failureates of much less than one

billion so uh

the purpose of a digital computer is to

increase their reliability and uh of the

output of a user so a brief history of a

computer you can see Abacus relied on

humans to move beats to keep track of

the sun uh the early 20th century and

mechanical gears and levels were being

used to produce cash registers and

adding machines in 1940s uh the Aria

electronic computers were being

constructed from vacuum tubes and the

invention of the transit assistance

between 1947 and 1950 emerged and this

is this changed Computing dramatically

um the modern digital computers are

built from electronic circuits that use

transistors so after the vacuum tubes we

had now the transistors reached to the

improved the computing power of the

machine if you want to understand more

about it just read more about the

history of computers and understand more

about that so there's some terms that I

use used in Computing which are referred

to as the voltage and current and

um

when we depend most of the time about

the physics or the physical phenomena

have associated with the electricity

so Engineers use the terms voltage and

current to refer to quantifiable uh

properties of electricity

the voltage between two points is

measured in volts and represent the

potential uh difference and the current

uh on the other side is mentioned in

amperes that represent the flow of elect

electrons along the path EG are y

a good analogy can be made with water

right what is the best example that we

can use

um

voltage corresponds to maybe the water

pressure

and the current uh corresponds to the

amount of water

are flowing through a pipe at any given

time

if a tank develops a hole and the water

begins to flow through the hole the

water pressure will drop and if the

current start flowing through the wire

the voltage will drop

right I think that's uh the best uh

analogy to really understand so the most

important thing to know about electrical

voltage is that the voltage can only be

measured has the difference between two

points

right uh for your information the

measurement is relative and thus

voltmeter is used which is uh to measure

the voltage and always has to uh

to probability which are

the meter does not register voltage

until both probes have been connected

right so you have to check on the two

points so electrical engineers use the

term ground to refer to the point that

is measured to the point of zero voltage

um we can understand the search of

digital logic without uh we cannot

understand

um the digital logic without knowing

more about voltage and current and we

only need to understand how electricity

flow uh through a different meetings

so we can move on now that you

understand

um

the definition of voltage in current so

there's an element that we always refer

to as the transistors or something we've

discussed about so a transistor

um

is used to control the flow of

electrical current is mostly a

semiconductor average device so the

mechanical the mechanism used to control

flow of electrical current is a

semiconductor device known as the

transistors so

at the lowest level All Digital systems

are composed of transistors in

particular digital circuit use a form of

transistors known as metal oxide

semiconductor Field Effect trans trans

transistor so this is the

abbreviated as m-o-s-f-e-t

right so I miss Earth m m or s

f e t

uh can be from

uh can be formed on um

uh on a silicon Foundation

which has the two layers which is p and

n-type silicon a silicon insulating

layer which can be either a glass in the

metal for wires that conduct that

connect the transistor to the rest of

the circuit uh so the transistors are

used in digital circuit to function

as an on and or in on and off battle

right on end of battle uh which

I it's noted uh a transistor can be a in

in Ada on option or an off uh option

which is operated electronically instead

of mechanically

right so each transistor has three

terminals has three terminals

um

that provide connection to the list of

Destruction the two terminals are

associated brain have a channel between

them on which the electrical resistance

can be controlled

internet systems is low the electronic

current flows from the soils to the

drain and if the resistance is high no

current flows

well plus okay so the

um the term that that terminal is also

known as the gate the gate controls the

resistance in the

um

we will see on how switching transistor

can be used to build more complex

components that are used to build

digital system but you have to

understand about the three uh parts of

our

um

of the transistor the terminals in the

gate and W going to move on uh well

so

the more the

m-o-s-f-e-t transistors uh come in two

types both are used in digital Logics

and we have

um the two types of transistors used in

logical circuit the type are we would uh

mostly or are referred to as turn on

when the git voltage is positive or turn

on when they get voltages are zero the

two forms are known as complementary and

they overrated technology is all known

as the CMOS or CMOS or

as complementary methoxide semiconductor

um

these you're going to the chief

advantage of the CMOS arrays is because

the circuits can be diverse that use

extremely low power right right so these

are just a Somali opportunity to know

about the transistors and how they come

in two types one to make sure that it's

on and off and all that so we go next to

the logic uh Gates our transistor has to

possible State current is uh flowing or

no current is Flowing or on and off

right so

um the circuit type design designed

using the two valued mathematical system

borrowed from the boring algebra most

programmers are familiar with the three

uh basic burning functions and all and

not right if you understand the

borrowing functions and or and not

and these are the possible input and the

results of each function the borrowing

function provide the conceptual basis

for a digital Hardware more important

it's possible to use transistors to

construct efficient circuits that

Implement each of the borrowing function

um

for example or a good example is when

you consider you know the boring note

typical Logics that you use a positive

voltage to represent a boring one and

zero voltage to represent a boring zero

right using zero voltage volts to

represent zero under positive voltage to

represent one meaning which means a

circuit

meaning that a circuit that computes

boring

cannot be cannot not can be constructed

from two transistors

that is the circuit

um will take on him input on one wire

produce an output on another wire where

the output is always the opposite of the

input

in fact I'm right here when a voltage is

placed on the input the output will be

zero and when the zero voltage is placed

on input the output will be positive

right so the these uh if you look here

the typical logic circuit user voltage

to represent 0 and to represent a

balanced zero using a zero voltage to

represent zero and the positive voltage

to the present one it means the circuit

that computes by computes borrowing not

can be constructed from the true

transistors

right after the summary so

um you can move in you can we can move

on

with um

um

understanding about a few concept that

uh

um

uh used indeed

in the Logics about the

using latches to create a memory we

don't want to go so much deep enough

uh in understanding uh

the logic of the physics because it's

not so these are computer class it's not

a physics class so a latch is one of the

most basic of the sequential circuits

the idea of a large is straightforward

that has an input

has an input in the output a large has

an extra input

called enable line right referred to as

an enable

um

not right so in other things that um

the minute just trying to get a very

good example

of the whole thing so that you can

understand

or better so I sent you to handle

multiple bits is constructed

okay fine let me just explain about

using latches to create a memory uh

um any time you we discuss about the

processor we have an element of memory

which are commonly referred to as

registers that cover the short-term

storage units within the CPU so

registers hold values that are used in

computation

that will be added together each

register holds multiple bits uh most

which most computers have either a

32-bit or a 64 bit register the circuit

for register illustrate an important

principle of the digital Hardware design

uh so uh I thank you to handle multiple

bit is constructed by physically

replicating a circuit that handles one

bit so I started to handle much copy is

construction is constructed by

physically dedicating a circuit that

handles one bit uh registers on the

other hand hold values that are used in

computation register that holds multiple

beats and most computers are either a

32-bit or a 64-bit uh register that's

why you hear someone asking or most

powerful fears are you ask whether it's

supporting a 32-bit or 64 uh your

register so I'm sure there is an

illustration

to understand the principle behind it so

um

which shows a 4-bit registers can be

constructed from one bit latches all

right so in the figure that we have here

they enable lines of all four latches

are

connected together to

to form and enable input for the

register

although the hardware consists of the

four independent circuits before

independent circuit

connected to a neighbor knife means that

the four latches act in unison right

these aren't in unison all right when

the nipple line

um is set to set logical the logic one

the register accept the four input bits

and

said for and set the four outputs

accordingly

when the label line becomes zero the

output remain fixed right the output

becomes fixed so this is how you explain

uh

uh that so the register has told

whatever value has was present on its

input and the output will not change

until the enable line becomes uh one

again so the point here is that a

register of one of the key comp is one

of the key components in a processor and

is a hardware mechanism that uses that

is to store digital values so uh this is

the explanation of what we've been

discussing uh that's the literature so

the next thing that is very very key

um if you have understood

uh this process is about the free probes

and maybe the transition

um

a flip flop is a flip flop is another

circuit in which output depends on the

previous input as well as the current

output or input sorry there are various

forms one act exactly like the power

switch on a computer the time it is its

input becomes one the free Pro the free

prop turns uh the output on and the

second time the input becomes one the

free flop times the output off

make a push button

so we choose to control the power a free

Pro 4 does not respond to a continuous

input the input must Return To Zero

before a value 1 will cause the free

flop to change the state

so whenever the input transition from

one to zero the fifth the free form

changes its output from the current

state to the opposite state

um I really love explaining or for you

just to have a common understanding

about uh how uh the zeros and that and

one as growing up you've tried maybe to

balance the uh the bulb you know the the

bad switch or uh to try balancing to see

whether the electricity can the bug or

the bug can be halfway on one off I'm

sure no one has ever succeeded on that

because it responds to

um are to a sequence of freeform it is

not possible for combination of of the

circuit so a free-form cannot be

constructed from a single gate something

to note however

Africa can be constructed from a pair of

latches

uh

for you to be in a position to

understand

better a free prop Works

um

with the plot of input and output in a

graphical form that is indicated uh uh

here on these diagram

so

um

that's how it is explained uh in a

nutshell so this illustration of the

transition diagram that shows how free

properties to a series of input marks

the

um and the exercise indicator

um

indicate the times each corresponds to

the one clock tick

uh sometimes the free forms include

additional inputs named reset that

places the output in a state zero

um

in addition to several other variants of

freeform that exist right

so um

if you understand that that process uh

we go to something that is very very

important which is referred to as

the binary counters the binary counters

so after a single free flow only offers

two possible output values which are

zero or one however a set of three

probes cannot be connected in a series

to form a binary counter and accumulates

um numeric or total like a free fall the

counter has a single input unlike

unlike the freeform variable account

that has multiple

um

output and the output account

the output count how many input passes

have been detected by giving a numerical

total in a binary

right so we think of the output as the

starting at the zero and adding one to

each time the input transition from 0 to

1 a quarter that has three output lines

can accumulate at a top between zero

to seven right so what you're talking or

what am I trying to explain is this

until

we have the binary counter here so uh

this is an illustration of a binary

counter

here and the sequence of input values

and the corresponding output uh the

current report

decimal give the

decimal gives the decimal equivalent of

the outputs right

um

in real life or in in practice an

electronic path that implements a binary

counter has several additional features

uh eg a counter has additional input is

to reset the count are

to zero and me

may have input the temporarily stop to

the counter

more importantly because it has a fixed

number of output each counter has a

maximum value which can represent when

the accumulation count exceed the

maximum value

the counter resets the output to zero

and this is the additional output and it

decades data flow overflow has occurred

right

so uh if you understand about the uh the

binary the binary countries that's the

summary about from the free probs binary

counter so we go to the clock clocks and

the secret sequences

uh so um

we have seen the basic building block of

digital logic one additional feature is

a position as it's a absolutely

essential for a digital computer

automatic operation that is a computer

must be able to execute a sequence of

instruction without any uh input

changing

so the digital logic circuit discussed

previously or use the property that they

respond to changes in one of one of

their inputs they do not perform any

function until an input changes

uh so how can a digital logic perform a

series of steps without uh maybe a human

intervention

um the answer is very simple and it's

something referred to as a clock so

which allowed acrylic allows the

hardware to take action without

requiring an input to change in fact

most digital logic circuits are used to

be clocked which means that they that

the cloud signal they use the clock

signal

rather than the changes in input

controls and synchronize the operation

of individual components and ensure that

they work together in an intended way

right so that's a very good explanation

or an overview or what is a clock so

what is a clock it's uh it really fast

to an electronics that that circuit that

oscillates at a regular rate the

oscillations are converted to a sequence

of alternative one and zeros right

so

um although a clock can be created from

an inverter most Club use uh quartz

crystal which is the oscillation

oscillation that is natural

to provide the signal to a precise

frequency

right

so it is difficult for any human to

imagine it's actually changing of the

such high rate to make it clear clock is

available that operates extremely slow

at maybe one heart so the speed of a

call is measured by heart the number of

times per second the clock

Cycles to the one followed by a zero

think that should be clear so a computer

must perform the following sequence of

steps

or

how does the alternative sequence of

zeros and value make the circuits more

powerful to understand you will consider

um below

uh how a computer starts so you can see

the first procedure is the you test the

the battery power on power

on self-test of the memories that the

discs cleaning power about the screen

read the boot sector and then you start

the CPU to simplify the explanation you

need to assume that each step requires

you uh one second to complete before the

next one can start uh thus with the

circuit that one it has been started

will perform the six steps in a sequence

at one second intervals with no further

changes

for now we will focus on the essence of

the circuit and consider how it can be

started a circuit to handle the task of

Performing six steps in a sequence can

be built from three building block we

have

um we have the three building blocks

right so these are the three building

blocks we have the clock

we have the binary counter

and we have the decoder or multiplexer

all right so I barely counter and the

device known as the which is uh

abbreviated at the max

we have already considered a counter and

we'll assume that the clock is available

that generates digital output at a rate

exactly one cycle per second

all right so uh and then something I

record that is very very necessary to

um to do the whole process so uh

this is uh how the whole uh illustration

of how a clock can be used to create a

suction a circuit that performs a

sequence of the six steps I'll put lines

from the counter correct that that

connect directory to the input uh

lines right

uh something to note is for you to

understand how the circuit operator

assumed that the counter has been reset

of two to zero

right

or when I decoder the device merely

selects one input output when used to

the uh as a decoder the device takes an

extra input which passes to the select

output both the decoder functions are

more complex uh the multiplexer function

can be construction from the boring uh

Gates right so this is how it is um

this is how

the six steps are multiplier are

are represented

so uh the next thing is um just to

understand about the circuit size A

month's law

for you to understand a little bit

so the code the

the good amount the co-founder of entire

Corporation is attributed with having

itself that the the density of silicon

circuit measured in the number of

transistors per square inch would double

every year so the observation known as

malt law was revised in 1970 when the

Aged slot to building uh doubling every

18 months so as the number of

transistors on a single chip increase

the vendors took advantage of the

capability to add more and more

functionality some very the industry

created a multiple CPU Chief by

replacing the multiple copies of their

CPU called the call

Corner single chip and providing

interconnection of the of the code so um

just the integrated circuit can be

divided into four categories so this is

the we have the small scale integration

integration integration

we have the median Square integration

and the large-scale integration and we

have the VL it's high a very large

integral integrated

uh

circuit so this is um

I see the integrated circuit of often

created by using the complementary metal

oxide semiconductor technology the

Silicon is due to the impurities to give

it negative or positive ionization

right so the resulting substance are

known as The Entity silicon or the

p-type Silicon

um the p-type Silicon

uh when arranging layer the n-type and P

type to become form the transistors

so uh something to note is the IC

manufacturers do not create single ICS

at any given time instead

the manufacturers create the offer that

is between 12 and 18 inches diameter

that contain many copies of the IC

design

so um when you look more about the most

Cloud you're going to find about

different levels of abstraction which

will be discussing about the circuit

boards uh the processor revealed there's

chip the gate the transistor and in that

so to summarize whatever I've just

mentioned today is a digital logic

refers to the pieces of Hardware used to

construct digital systems such as a

computer as we have seen the coronary

algebra is an important tool in digital

circuits uh design uh there is a direct

relationship between borrowing functions

and it gets used to implement the

combinational digital circuits we have

also seen the boring logic values that

can be described using the true tables

clock is a mechanism that that emits

pulses at a regular intervals to form a

signal of alternating ones and zeros a

clock allows the digital circuit output

to be function of or function of time as

well as the logic input a clock can be

used to provide synchronization among

multiple parts of the circuits

Authority digital uh logic of former

mathematical point of view building

practical structures involved

understanding the underlying Hardware

details in particular uh the basic

correctness Engineers must be content

with the problem of distribution and

park script so

um thank you uh for listening to me

um see you in the next class