INTRODUCTION TO DIGITAL ELECTRONICS

Chapter 6

KMEM4110

INTRODUCTION TO DIGITAL 1s AND 0s

Chapter 6

A large part of the worldwide telecommunications system falls in the category of digital systems.

It started as a simple digital system that used only two states to represent information.

A telegraph system consisted of a battery, a code key (normally open,

momentary contact switch), a telegraph wire, and an electromagnetic clacker.

INTRODUCTION TO DIGITAL 1s AND 0s

Chapter 6

The telegraph system used two distinct symbols to transmit any word or number

Short & long electric pulses, the dots & dashes of Morse codea digital representation of information.

The electric signal is either on or off at all times.

This relates to modern digital systems that use electrical signals to represent 1s and 0s.

A timing diagram shows which state (1 or 0) the system is in at any point in time.

And shows the time when a change in state occurs.

INTRODUCTION TO DIGITAL 1s AND 0s

Chapter 6

By displaying one or more digital signals using test instruments such as an oscilloscope, we can compare actual signals to expected operation.

NUMERICAL REPRESENTATIONS

Chapter 6

Physical systems use quantities which must be manipulated arithmetically.

Quantities may be represented numerically in either analog or digital form.

Here, a quantity is represented by a continuously variable, proportional indicator

Sound through a microphone causes voltage changes.

Automobile speedometer changes with speed.

Mercury thermometer varies over a range of values with temperature.

Here, the quantities are represented by symbols called digits

Varies in discrete (separate) steps.

Passing time is shown as a change in the display on a digital clock at one minute intervals.

A change in temperature is shown on a digital display only when the temperature changes at least one degree.

Analog Representation

Digital Representation

ADVANTAGES OF DIGITAL

Chapter 6

Ease of design

Well suited for storing information

Accuracy and precision are easier to maintain

Programmable operation

Less affected by noise

Ease of fabrication on IC chips

DIGITAL NUMBER SYSTEMS

Many number systems are use in digital technology.

The most common are: Decimal 10 symbols (base 10)

Binary 2 symbols (base 2)

Hexadecimal 16 symbols (base 16)

DECIMAL SYSTEM

Chapter 6

10 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Decimal system is also called the base-10 system because it has 10 digits

It is a positional-value system in which the value of a digit depends on its

position.

MSD: Most significant digit

LSD: Least significant digit.

Positional value may be stated as a digit multiplied by a power of 10.

Fig 1: Decimal position values as

powers of 10

DECIMAL COUNTING

Chapter 6

With two decimal places, we can count through 102 = 100different numbers (0 to 99)

In general, with N places or digits, we can count through

10 different numbers, starting with and including zero.

Characteristic

BINARY SYSTEM

Chapter 6

There are 2 symbols in the Binary (base 2) System: 0, 1

Lends itself to electronic circuit design since only two voltage levels are required.

Binary system is also a positional-value system, where each binary digit has its own

value or weight expressed as a power of 2.

Term binary digit is often abbreviated to the term bit.

MSB: Most significant bit

LSB: Least significant bit Fig 2: Binary position values as powers of 2

BINARY COUNTING

Chapter 6Fig 3: Binary counting sequence

Characteristic

By using N bits or places, we can go through 2 counts.

Example: 22 = 4 counts (002 through 112)

The last count will always be all 1s and is equal to 2 1 in the decimal system