ECE-0832: Digital World 2020

Fall 2017

Assignment #1

Directions: Project report and presentation slides are expected to be organized in a typical format. As an

example, a report may include sections like: Introduction/Background, Body, Conclusion, and

References. The presentation will be done in groups but the report will be individual. All submissions (in

PDF format) are accepted electronically using Canvas.

In this assignment, the essay question is “Do we live in a Digital or Analog world?” You can make a

powerful case for either option (both or none as well). To answer the essay question, use the material you

learned in class as well as your own (from your field). Although this topic is broad, be concise and use

specific examples to present your view and relate it to your major. There is no wrong answer, just need

the relevant evidence to back up your findings. The essay report should be done individually.

Your PowerPoint presentation must be at least 15 slides. Your group will have a maximum of 20 minutes

to present. All members of the group must take an equal role in the presentation and incorporate the

findings of your reports. There is no specific format required. Students choose the design of the slides

(colors/fonts). You may use the textbook or the Internet. Students will work together in teams of three or

four. Group members will use visual aids such as images, tables, graphs, handouts or videos to structure

their remarks and underscore key points.

Your paper should be 1-2 pages long, with one inch margins, Times New Roman 11pt font, 1.5 spacing,

and single column. No plagiarism, use your own words, references and quotations. Everyone must

submit their own essay to Canvas by the due date. Only one person from each group needs to submit the

PowerPoint presentation to Canvas by the due date.

You will be graded based on 1) research contents, 2) outline and organization, 3) presentation argument,

4) relevance to major and 5) essay.

Digital World 2020

ECE-0832

Fall 2019

Goals and Objectives of This Course

For non-engineering students from diverse disciplines

◼ Taking the mystery out of modern day Digital Technology

◼ Understanding Digital Technology from basic concept to

application

◼ Digital Technology past, present, and future

◼ If you understand it, you can appreciate it, gain a leg up

Digital Technology is here to stay. Always ask yourself:

How is this relevant,

How am I influenced by this,

How can I influence this?

Technology Trends:

IEEE

(Institute of Electrical and Electronics Engineers)

2018

1. Accelerators

2. 3D

3. Robotics

4. Cybersecurity

5. AI (Artificial Intelligence)

6. Industrial Internet of Things (IoT)

7. AR/VR (Augmented Reality/Virtual

Reality)

8. Deep Learning

9. Transportation

10. Blockchain

11. Digital Currency

12. Ethics

1.

2.

3.

4.

5.

2019

Deep Learning Accelerators –

with faster hardware (HW)

Assisted Transportation –

assisted driving

Internet of Bodies (IoB)

Social Credit Algorithm – Using

computer to judge people,

impartially?

Advanced (Smart) Materials

and devices – self-destructing

packaging, env friendly material)

3

Technology Trends:

CES (Consumer Tech Assoc)-2018

https://www.forbes.com/sites/danielnewman/2018/01/16/top-18-tech-trends-at-ces2018/#44e83b28452f

1.

2.

3.

4.

5.

6.

7.

8.

9.

Convertible tablets and laptops

Smart Home Devices

Augmented Reality

Companion Robots

Chip Wars

Artificial Intelligence (AI) in Everything

Health Sensors

5G Technology (5th Generation wireless)

Smarter Cars

10.Facial Recognition

11. Virtual Reality

12. Smart Cities

13. Connected Devices Every where (IoT)

14. Wireless Charging

15. LED (Light Emitting Diode) TV

16. 3D printing more than plastic

17. Boosted Performance Analysis in Sports Tech

18. Drones (UX=User Experience, UI=User

Interface)

“From a budging standpoint to simply knowing what’s around the corner in your

industry, keeping up with enterprise tech trends is a key to staying competitive in

the digital world.” – Daniel Newman, CEO of Broadsuite Media Group, principal

analyst at Futurum and author of Futureproof.

4

Week1:

Information Revolution

Outline

◼ What exactly do scientists and engineers do?

◼ Definition of information, message and signal

◼ Components of Communication Systems

◼ Birth of the Digital Age

◼ Introduction to digital representation of signals

◼ Examples of analog and digital systems

◼ Moving forward in digital information technology

Making Dreams a Reality?

◼

◼

◼

◼

◼

Can you imagine what your life be like without TVs,

radios, computers and automobiles?

What would your life be like if you could not text or

snapchat your family and friends?

What if there no X-rays and CAT scans to help

doctors diagnose injuries and illness?

What if the only way for you to get to school were to

walk or ride a horse?

We often take today’s great creations for granted

Making Dreams a Reality?

◼

◼

◼

What new high-tech health treatment,

communications device, transportation vehicle or

digital entertainment experience will we all take for

granted in the coming years?

Computers that talk to us or even “think” for us? Cars

that drive themselves?

Engineers are already working on these devices

today!

What makes engineers different from

scientists?

◼

Primary purpose of science and math is to help

humans understand and describe our world

◼

◼

◼

◼

◼

How do cells divide?

What makes objects fall to the ground?

What are the basic building blocks of life?

What is the distance between the Earth and the Moon?

To answer these questions, scientists have followed

the scientific method

Scientific Method

1) Observe some aspect of the universe

2) Invent a tentative description (hypothesis)

consistent with what you have observed

3) Use the hypothesis to make predictions

4) Test those predictions by experiments or further

observations, and modify the hypothesis in light of

your results

5) Repeat steps 3 and 4 until there are no

discrepancies between theory and experiment or

observation

What makes engineers different from

scientists?

◼

While scientists seek to explain how the world works,

engineers attempt to create new objects and devices

◼

◼

◼

◼

◼

Cutting edge medical devices

Innovative video games

Safer cars

High-tech communication devices

While scientists rely on the scientific method,

engineers rely on engineering design and test

algorithms

Engineering Design & Test

Algorithms

1) Identify the problem or design objective

2) Define the goals and identify the constraints

3) Research and gather information

4) Create potential design solutions

5) Analyze the viability of solutions

6) Choose the most appropriate solution

7) Build or implement the design

8) Repeat ALL steps as necessary

Example: Designing a cell phone

◼

Step 1: Identify the design objective

◼

◼

Step 2: Define goals and constraints

◼

◼

Movement, size, form, energy use, cost…

Step 3: Research and gather information

◼

◼

Build something that will allow humans to communicate with one another at

any time

Wireless radio telephones were being researched by the American

Telephone and Telegraph Company in 1930s, but these systems were more

like “walkie-talkies” than cell-phones

Step 4 to 8: Create, analyze, choose, build and test

◼

International companies such as Sony, Nokia, Samsung, Qualcomm and

Motorola completed these steps

Information Revolution

◼

Information (Latin: idea, conception)

◼

◼

◼

◼

Knowledge communicated or received concerning a particular fact or

circumstance

The information revolution has just begun

The changes we’ve seen during the past ten years are hardly the

beginning

We are headed toward an unprecedented change in every aspect of

how we communicate, educate, track information, solve medical

problems, and manage every aspect of life

Historical Perspective

◼

Information and its uses have always been an integral part of

mankind

◼

◼

◼

◼

The very first indication of information communication/storage/retrieval

is considered to be through cave drawings

Mankind later developed pictures, words and subsequently languages to

more efficiently communicate with each other

Information sharing was made possible by the invention of the printing

press in the early 1450’s by Johannes Gutenberg through the process of

printing and distributing manuscripts

The printing press is widely thought of as

the origin of mass communication

Information Technology Timeline

Egyptian Book

of the Dead

75,000

B.C.

Rock

Carvings

1500 B.C.

(8 x 103) + (2 x 102) + (3 x 101) + (4 x 100)

10 raised to the power of …

◼

◼

◼

◼

◼

◼

◼

◼

100 =1

101 =10

102 =10×10=100

103 =10x10x10=1,000

104 =10x10x10x10=10,000

and so on

Also called Base-10 system

We have ten fingers

and use ten digits!

Coincidence?

There are other ways of representing numbers other

than using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9

7

Comparing decimal and binary

systems

◼

◼

◼

◼

While people routinely use decimal digits,

computers use binary digits.

The decimal system uses ten numbers (0,

1, 2, 3, 4, 5, 6, 7, 8, 9) to represent all

values. The binary system uses two

numbers (0 and 1) to represent all values.

In other words, computers use the “base-2”

system rather than the “base-10” system.

Counting in binary is simple (different, but

simple) because you use powers of two

instead of ten. Example follows.

8

Binary to decimal conversion

The same as calculating the value of a decimal system number

except use powers of two instead of powers of ten.

•

The binary number 1101 can be converted to decimal as follows:

(1×23) + (1×22) + (0x21) + (1×20) = 8 + 4 + 0 + 1 = 13

•

For understanding binary, it’s helpful to have a good command of

powers of 2:

20 = 1

21 = 2

22 = 2×2 = 4

23 = 2x2x2 = 8

24 = 2x2x2x2 = 16

25 = 2x2x2x2x2 = 32

26 = 2x2x2x2x2x2 = 64

27 = 2x2x2x2x2x2x2 = 128

28 = 2x2x2x2x2x2x2x2 = 256

29 = 2x2x2x2x2x2x2x2x2 = 512

210 = 2x2x2x2x2x2x2x2x2x2 = 1024

and so on…

9

Binary conventions

◼

Most Significant Bit (MSB) and Least Significant Bit (LSB)

◼

Binary: 1000000

◼

◼

◼

◼

◼

◼

If there is a “1” in the LSB of a binary number, then its decimal equivalent

is an odd number

If there is a “0” in the LSB of a binary number, then its decimal equivalent

is an even number

Subscripts: Note that the subscript “2” makes it clear a number is in

binary format and the subscript “10” makes it clear a number is in

decimal format.

For example, 1101012 , 20310

◼

◼

1 on the left side is the MSB

0 on the right side is the LSB

We normally omit “10” in the subscripts for the base-10 in daily lives.

This avoids confusion between a number like 110101 which can either

be binary, written as 110101(2) or decimal, written as 110,101(10)

10

Example: Converting a Base-2

Number to a Base-10 Number

What is the binary number 1110 in base 10?

Solution:

To determine the base 10 value of 1110, we need to scale the

appropriate powers of 2 by the values 1, 1, 1, and 0:

1 × 23 or one 8

1 × 22 or one 4

1 × 21 or one 2

0 × 20 or one 1

Summing these results together, we get

1 × 23 + 1 × 22 + 1 × 21 + 0 × 20

= 1 × 8 + 1 × 4 + 1 × 2 + 0 × 1 = 14

◼

11

Let’s Use Binary to

“Command” a Machine

Turning “switches” to show decimal 9 in binary form

0

0

0

0

d0

0

0

1

OFF OFF OFF OFF OFF OF

OFF ON

Label for

the

9

switches→ 2

28

20 = 1

21 = 2

22 = 2×2 = 4

23 = 2x2x2 = 8

24 = 2x2x2x2 = 16

25 = 2x2x2x2x2 = 32

27

26

25

24

23

0

0

1

OFF OFF ON

22

26 = 2x2x2x2x2x2 = 64

27 = 2x2x2x2x2x2x2 = 128

28 = 2x2x2x2x2x2x2x2 = 256

29 = 2x2x2x2x2x2x2x2x2 = 512

210 = 2x2x2x2x2x2x2x2x2x2 = 1024

and so on…

21

20

12

Conversion Among Bases

◼

The possibilities:

Decimal

Octal

Binary

Hexadecimal

13

Decimal, Binary, Octal, and Hex

◼

Decimal is the number system that we use

◼

Binary is a number system that computers use

◼

◼

Octal is a number system that represents groups of binary numbers

(binary shorthand). It is used in digital displays, and in modern

times in conjunction with file permissions under Unix systems.

Hexadecimal (Hex) is a number system that represents groups of

binary numbers (binary shorthand). Hex is primarily used in

computing as the most common form of expressing a humanreadable string representation of a byte (group of 8 bits).

14

Decimal (base 10)

◼

◼

◼

The number system we are familiar with

Decimal number has base 10

Each digit is a number from 0 to 9

15

Binary

◼

◼

◼

◼

Binary number has base 2

Each digit is one of two numbers: 0 and 1

Each digit is called a bit

Eight binary bits make a byte

16

Octal

◼

◼

◼

◼

Octal number has base 8

Each digit is a number from 0 to 7

Each digit represents 3 binary bits

000=0

001=1

010=2

011=3

100=4

101=5

110=6

111=7

Was used in early computing, but was replaced by

hexadecimal

17

Hexadecimal

◼

◼

Hexadecimal number has base 16

Each digit is a number from 0 to 15: digits 0 to 9,

and the digits 10 through 15 are represented by A

through F

◼

◼

◼

◼

◼

◼

◼

A = 10

B = 11

C = 12

D = 13

E = 14

F = 15

Each digit represents 4 binary bits

0000=0

0001=1

0010=2

0011=3

0100=4

0101=5

0110=6

0111=7

1000=8

1001=9

1010=A

1011=B

1100=C

1101=D

1110=E

1111=F

18

Common Number Systems

System

Base Symbols

Used by

humans?

Used in

computers?

Decimal

10

0, 1, … 9

Yes

No

Binary

2

0, 1

No

Yes

Octal

8

0, 1, … 7

No

No

Hexadecimal

16

0, 1, … 9,

A, B, … F

Yes

Yes

19

Conversion Among Bases

◼

The possibilities:

Decimal

Octal

Binary

Hexadecimal

20

Quick Example

2510 = 110012 = 318 = 1916

Base

21

Decimal to Decimal

Decimal

Octal

Binary

Hexadecimal

22

Decimal to Decimal example

Weight

12510 =>

5 x 100

2 x 101

1 x 102

=

5

= 20

= 100

125

Base

23

Binary to Decimal

Decimal

Octal

Binary

Hexadecimal

24

Binary to Decimal

◼

Technique

◼

◼

◼

Multiply each bit by 2n, where n is the “weight” of

the bit

The weight is the position of the bit, starting from

0 on the right

Add the results

25

Example

Bit “0”

1010112 =>

1

1

0

1

0

1

Binary Tutorial –

x

x

x

x

x

x

20

21

22

23

24

25

=

=

=

=

=

=

1

2

0

8

0

32

4310

26

Decimal to Binary

Decimal

Octal

Binary

Hexadecimal

27

Decimal to Binary

◼

Technique

◼

◼

◼

◼

Divide by two, keep track of the remainder

First remainder is bit 0 (LSB, least-significant bit)

Second remainder is bit 1

Etc.

28

Example

12510 = ?2

◼

◼

◼

◼

◼

◼

◼

◼

Technique

125 ÷ 2 = 62 R 1

62 ÷ 2 = 31 R 0

31 ÷ 2 = 15 R 1

15 ÷ 2 = 7 R 1

7÷2= 3R1

3÷2= 1R1

1÷2= 0R1

12510 = 11111012

29

Example

12510 = ?2

2 125

2 62

2 31

2 15

7

2

3

2

1

2

0

1

0

1

1

1

1

1

12510 = 11111012

30

Hexadecimal to Decimal

Decimal

Octal

Binary

Hexadecimal

31

Hexadecimal to Decimal

◼

Technique

◼

◼

◼

Multiply each bit by 16n, where n is the “weight”

of the bit

The weight is the position of the bit, starting from

0 on the right

Add the results

32

Example

ABC16 =>

C x 160 = 12 x

1 =

12

B x 161 = 11 x 16 = 176

A x 162 = 10 x 256 = 2560

274810

Remember, in hexadecimal

A represents 10

B = 11

C = 12

D = 13

E = 14

F = 15

33

Decimal to Hexadecimal

Decimal

Octal

Binary

Hexadecimal

34

Decimal to Hexadecimal

◼

Technique

◼

◼

Divide by 16

Keep track of the remainder

35

Example

123410 = ?16

◼

◼

◼

1234 ÷16 = 77 R 2

77 ÷ 16 = 4 R 13

4 ÷ 16 = 0 R 4

Remember, in hexadecimal

A represents 10

B = 11

C = 12

D = 13

E = 14

F = 15

123410 = 4D216

36

Example

123410 = ?16

16

16

16

Remember, in hexadecimal

A represents 10

B = 11

C = 12

D = 13

E = 14

F = 15

1234

77

4

0

2

13 = D

4

123410 = 4D216

37

Binary to Hexadecimal

Decimal

Octal

Binary

Hexadecimal

38

Binary to Hexadecimal

◼

Technique

◼

◼

◼

Group bits in fours, starting on right

Convert to hexadecimal digits

Why group in 4 bits? Because each Hex needs 4 bits.

39

Example

10101110112 = ?16

10 1011 1011

2

B

B

10101110112 = 2BB16

40

Hexadecimal to Binary

Decimal

Octal

Binary

Hexadecimal

41

Hexadecimal to Binary

◼

Technique

◼

Convert each hexadecimal digit to a 4-bit

equivalent binary representation

42

Example

10AF16 = ?2

1

0

A

F

0001 0000 1010 1111

Remember, in hexadecimal

A represents 10

B = 11

C = 12

D = 13

E = 14

F = 15

10AF16 = 00010000101011112

43

Exercise (1) – Convert …

Decimal

33

Binary

Hexadecimal

1110101

451

1AF

Don’t use a calculator!

44

Exercise (1) – Convert …

Answer

Hexadecimal

Decimal

33

Binary

100001

117

1110101

75

451

111000011

1C3

170

000110101111

1AF

21

45

Exercise (2) – Convert …

Decimal

Binary

Hexadecimal

24

74

1B

10100110

Don’t use a calculator!

46

Exercise (2) – Convert …

Answer

Hexadecimal

Decimal

36

Binary

100100

74

1001010

4A

27

11011

1B

166

10100110

A6

24

47

Exercise (3) – Convert …

Decimal

Binary

Hexadecimal

C9

211

10

1011011

Don’t use a calculator!

48

Exercise (3) – Convert …

Answer

Hexadecimal

Decimal

201

Binary

11001001

211

11010011

D3

16

1000

10

91

1011011

5B

C9

49

End Note!

Hint: “10” is not “ten”

50

Purchase answer to see full

attachment

Fall 2017

Assignment #1

Directions: Project report and presentation slides are expected to be organized in a typical format. As an

example, a report may include sections like: Introduction/Background, Body, Conclusion, and

References. The presentation will be done in groups but the report will be individual. All submissions (in

PDF format) are accepted electronically using Canvas.

In this assignment, the essay question is “Do we live in a Digital or Analog world?” You can make a

powerful case for either option (both or none as well). To answer the essay question, use the material you

learned in class as well as your own (from your field). Although this topic is broad, be concise and use

specific examples to present your view and relate it to your major. There is no wrong answer, just need

the relevant evidence to back up your findings. The essay report should be done individually.

Your PowerPoint presentation must be at least 15 slides. Your group will have a maximum of 20 minutes

to present. All members of the group must take an equal role in the presentation and incorporate the

findings of your reports. There is no specific format required. Students choose the design of the slides

(colors/fonts). You may use the textbook or the Internet. Students will work together in teams of three or

four. Group members will use visual aids such as images, tables, graphs, handouts or videos to structure

their remarks and underscore key points.

Your paper should be 1-2 pages long, with one inch margins, Times New Roman 11pt font, 1.5 spacing,

and single column. No plagiarism, use your own words, references and quotations. Everyone must

submit their own essay to Canvas by the due date. Only one person from each group needs to submit the

PowerPoint presentation to Canvas by the due date.

You will be graded based on 1) research contents, 2) outline and organization, 3) presentation argument,

4) relevance to major and 5) essay.

Digital World 2020

ECE-0832

Fall 2019

Goals and Objectives of This Course

For non-engineering students from diverse disciplines

◼ Taking the mystery out of modern day Digital Technology

◼ Understanding Digital Technology from basic concept to

application

◼ Digital Technology past, present, and future

◼ If you understand it, you can appreciate it, gain a leg up

Digital Technology is here to stay. Always ask yourself:

How is this relevant,

How am I influenced by this,

How can I influence this?

Technology Trends:

IEEE

(Institute of Electrical and Electronics Engineers)

2018

1. Accelerators

2. 3D

3. Robotics

4. Cybersecurity

5. AI (Artificial Intelligence)

6. Industrial Internet of Things (IoT)

7. AR/VR (Augmented Reality/Virtual

Reality)

8. Deep Learning

9. Transportation

10. Blockchain

11. Digital Currency

12. Ethics

1.

2.

3.

4.

5.

2019

Deep Learning Accelerators –

with faster hardware (HW)

Assisted Transportation –

assisted driving

Internet of Bodies (IoB)

Social Credit Algorithm – Using

computer to judge people,

impartially?

Advanced (Smart) Materials

and devices – self-destructing

packaging, env friendly material)

3

Technology Trends:

CES (Consumer Tech Assoc)-2018

https://www.forbes.com/sites/danielnewman/2018/01/16/top-18-tech-trends-at-ces2018/#44e83b28452f

1.

2.

3.

4.

5.

6.

7.

8.

9.

Convertible tablets and laptops

Smart Home Devices

Augmented Reality

Companion Robots

Chip Wars

Artificial Intelligence (AI) in Everything

Health Sensors

5G Technology (5th Generation wireless)

Smarter Cars

10.Facial Recognition

11. Virtual Reality

12. Smart Cities

13. Connected Devices Every where (IoT)

14. Wireless Charging

15. LED (Light Emitting Diode) TV

16. 3D printing more than plastic

17. Boosted Performance Analysis in Sports Tech

18. Drones (UX=User Experience, UI=User

Interface)

“From a budging standpoint to simply knowing what’s around the corner in your

industry, keeping up with enterprise tech trends is a key to staying competitive in

the digital world.” – Daniel Newman, CEO of Broadsuite Media Group, principal

analyst at Futurum and author of Futureproof.

4

Week1:

Information Revolution

Outline

◼ What exactly do scientists and engineers do?

◼ Definition of information, message and signal

◼ Components of Communication Systems

◼ Birth of the Digital Age

◼ Introduction to digital representation of signals

◼ Examples of analog and digital systems

◼ Moving forward in digital information technology

Making Dreams a Reality?

◼

◼

◼

◼

◼

Can you imagine what your life be like without TVs,

radios, computers and automobiles?

What would your life be like if you could not text or

snapchat your family and friends?

What if there no X-rays and CAT scans to help

doctors diagnose injuries and illness?

What if the only way for you to get to school were to

walk or ride a horse?

We often take today’s great creations for granted

Making Dreams a Reality?

◼

◼

◼

What new high-tech health treatment,

communications device, transportation vehicle or

digital entertainment experience will we all take for

granted in the coming years?

Computers that talk to us or even “think” for us? Cars

that drive themselves?

Engineers are already working on these devices

today!

What makes engineers different from

scientists?

◼

Primary purpose of science and math is to help

humans understand and describe our world

◼

◼

◼

◼

◼

How do cells divide?

What makes objects fall to the ground?

What are the basic building blocks of life?

What is the distance between the Earth and the Moon?

To answer these questions, scientists have followed

the scientific method

Scientific Method

1) Observe some aspect of the universe

2) Invent a tentative description (hypothesis)

consistent with what you have observed

3) Use the hypothesis to make predictions

4) Test those predictions by experiments or further

observations, and modify the hypothesis in light of

your results

5) Repeat steps 3 and 4 until there are no

discrepancies between theory and experiment or

observation

What makes engineers different from

scientists?

◼

While scientists seek to explain how the world works,

engineers attempt to create new objects and devices

◼

◼

◼

◼

◼

Cutting edge medical devices

Innovative video games

Safer cars

High-tech communication devices

While scientists rely on the scientific method,

engineers rely on engineering design and test

algorithms

Engineering Design & Test

Algorithms

1) Identify the problem or design objective

2) Define the goals and identify the constraints

3) Research and gather information

4) Create potential design solutions

5) Analyze the viability of solutions

6) Choose the most appropriate solution

7) Build or implement the design

8) Repeat ALL steps as necessary

Example: Designing a cell phone

◼

Step 1: Identify the design objective

◼

◼

Step 2: Define goals and constraints

◼

◼

Movement, size, form, energy use, cost…

Step 3: Research and gather information

◼

◼

Build something that will allow humans to communicate with one another at

any time

Wireless radio telephones were being researched by the American

Telephone and Telegraph Company in 1930s, but these systems were more

like “walkie-talkies” than cell-phones

Step 4 to 8: Create, analyze, choose, build and test

◼

International companies such as Sony, Nokia, Samsung, Qualcomm and

Motorola completed these steps

Information Revolution

◼

Information (Latin: idea, conception)

◼

◼

◼

◼

Knowledge communicated or received concerning a particular fact or

circumstance

The information revolution has just begun

The changes we’ve seen during the past ten years are hardly the

beginning

We are headed toward an unprecedented change in every aspect of

how we communicate, educate, track information, solve medical

problems, and manage every aspect of life

Historical Perspective

◼

Information and its uses have always been an integral part of

mankind

◼

◼

◼

◼

The very first indication of information communication/storage/retrieval

is considered to be through cave drawings

Mankind later developed pictures, words and subsequently languages to

more efficiently communicate with each other

Information sharing was made possible by the invention of the printing

press in the early 1450’s by Johannes Gutenberg through the process of

printing and distributing manuscripts

The printing press is widely thought of as

the origin of mass communication

Information Technology Timeline

Egyptian Book

of the Dead

75,000

B.C.

Rock

Carvings

1500 B.C.

(8 x 103) + (2 x 102) + (3 x 101) + (4 x 100)

10 raised to the power of …

◼

◼

◼

◼

◼

◼

◼

◼

100 =1

101 =10

102 =10×10=100

103 =10x10x10=1,000

104 =10x10x10x10=10,000

and so on

Also called Base-10 system

We have ten fingers

and use ten digits!

Coincidence?

There are other ways of representing numbers other

than using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9

7

Comparing decimal and binary

systems

◼

◼

◼

◼

While people routinely use decimal digits,

computers use binary digits.

The decimal system uses ten numbers (0,

1, 2, 3, 4, 5, 6, 7, 8, 9) to represent all

values. The binary system uses two

numbers (0 and 1) to represent all values.

In other words, computers use the “base-2”

system rather than the “base-10” system.

Counting in binary is simple (different, but

simple) because you use powers of two

instead of ten. Example follows.

8

Binary to decimal conversion

The same as calculating the value of a decimal system number

except use powers of two instead of powers of ten.

•

The binary number 1101 can be converted to decimal as follows:

(1×23) + (1×22) + (0x21) + (1×20) = 8 + 4 + 0 + 1 = 13

•

For understanding binary, it’s helpful to have a good command of

powers of 2:

20 = 1

21 = 2

22 = 2×2 = 4

23 = 2x2x2 = 8

24 = 2x2x2x2 = 16

25 = 2x2x2x2x2 = 32

26 = 2x2x2x2x2x2 = 64

27 = 2x2x2x2x2x2x2 = 128

28 = 2x2x2x2x2x2x2x2 = 256

29 = 2x2x2x2x2x2x2x2x2 = 512

210 = 2x2x2x2x2x2x2x2x2x2 = 1024

and so on…

9

Binary conventions

◼

Most Significant Bit (MSB) and Least Significant Bit (LSB)

◼

Binary: 1000000

◼

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If there is a “1” in the LSB of a binary number, then its decimal equivalent

is an odd number

If there is a “0” in the LSB of a binary number, then its decimal equivalent

is an even number

Subscripts: Note that the subscript “2” makes it clear a number is in

binary format and the subscript “10” makes it clear a number is in

decimal format.

For example, 1101012 , 20310

◼

◼

1 on the left side is the MSB

0 on the right side is the LSB

We normally omit “10” in the subscripts for the base-10 in daily lives.

This avoids confusion between a number like 110101 which can either

be binary, written as 110101(2) or decimal, written as 110,101(10)

10

Example: Converting a Base-2

Number to a Base-10 Number

What is the binary number 1110 in base 10?

Solution:

To determine the base 10 value of 1110, we need to scale the

appropriate powers of 2 by the values 1, 1, 1, and 0:

1 × 23 or one 8

1 × 22 or one 4

1 × 21 or one 2

0 × 20 or one 1

Summing these results together, we get

1 × 23 + 1 × 22 + 1 × 21 + 0 × 20

= 1 × 8 + 1 × 4 + 1 × 2 + 0 × 1 = 14

◼

11

Let’s Use Binary to

“Command” a Machine

Turning “switches” to show decimal 9 in binary form

0

0

0

0

d0

0

0

1

OFF OFF OFF OFF OFF OF

OFF ON

Label for

the

9

switches→ 2

28

20 = 1

21 = 2

22 = 2×2 = 4

23 = 2x2x2 = 8

24 = 2x2x2x2 = 16

25 = 2x2x2x2x2 = 32

27

26

25

24

23

0

0

1

OFF OFF ON

22

26 = 2x2x2x2x2x2 = 64

27 = 2x2x2x2x2x2x2 = 128

28 = 2x2x2x2x2x2x2x2 = 256

29 = 2x2x2x2x2x2x2x2x2 = 512

210 = 2x2x2x2x2x2x2x2x2x2 = 1024

and so on…

21

20

12

Conversion Among Bases

◼

The possibilities:

Decimal

Octal

Binary

Hexadecimal

13

Decimal, Binary, Octal, and Hex

◼

Decimal is the number system that we use

◼

Binary is a number system that computers use

◼

◼

Octal is a number system that represents groups of binary numbers

(binary shorthand). It is used in digital displays, and in modern

times in conjunction with file permissions under Unix systems.

Hexadecimal (Hex) is a number system that represents groups of

binary numbers (binary shorthand). Hex is primarily used in

computing as the most common form of expressing a humanreadable string representation of a byte (group of 8 bits).

14

Decimal (base 10)

◼

◼

◼

The number system we are familiar with

Decimal number has base 10

Each digit is a number from 0 to 9

15

Binary

◼

◼

◼

◼

Binary number has base 2

Each digit is one of two numbers: 0 and 1

Each digit is called a bit

Eight binary bits make a byte

16

Octal

◼

◼

◼

◼

Octal number has base 8

Each digit is a number from 0 to 7

Each digit represents 3 binary bits

000=0

001=1

010=2

011=3

100=4

101=5

110=6

111=7

Was used in early computing, but was replaced by

hexadecimal

17

Hexadecimal

◼

◼

Hexadecimal number has base 16

Each digit is a number from 0 to 15: digits 0 to 9,

and the digits 10 through 15 are represented by A

through F

◼

◼

◼

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◼

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◼

A = 10

B = 11

C = 12

D = 13

E = 14

F = 15

Each digit represents 4 binary bits

0000=0

0001=1

0010=2

0011=3

0100=4

0101=5

0110=6

0111=7

1000=8

1001=9

1010=A

1011=B

1100=C

1101=D

1110=E

1111=F

18

Common Number Systems

System

Base Symbols

Used by

humans?

Used in

computers?

Decimal

10

0, 1, … 9

Yes

No

Binary

2

0, 1

No

Yes

Octal

8

0, 1, … 7

No

No

Hexadecimal

16

0, 1, … 9,

A, B, … F

Yes

Yes

19

Conversion Among Bases

◼

The possibilities:

Decimal

Octal

Binary

Hexadecimal

20

Quick Example

2510 = 110012 = 318 = 1916

Base

21

Decimal to Decimal

Decimal

Octal

Binary

Hexadecimal

22

Decimal to Decimal example

Weight

12510 =>

5 x 100

2 x 101

1 x 102

=

5

= 20

= 100

125

Base

23

Binary to Decimal

Decimal

Octal

Binary

Hexadecimal

24

Binary to Decimal

◼

Technique

◼

◼

◼

Multiply each bit by 2n, where n is the “weight” of

the bit

The weight is the position of the bit, starting from

0 on the right

Add the results

25

Example

Bit “0”

1010112 =>

1

1

0

1

0

1

Binary Tutorial –

x

x

x

x

x

x

20

21

22

23

24

25

=

=

=

=

=

=

1

2

0

8

0

32

4310

26

Decimal to Binary

Decimal

Octal

Binary

Hexadecimal

27

Decimal to Binary

◼

Technique

◼

◼

◼

◼

Divide by two, keep track of the remainder

First remainder is bit 0 (LSB, least-significant bit)

Second remainder is bit 1

Etc.

28

Example

12510 = ?2

◼

◼

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◼

◼

◼

Technique

125 ÷ 2 = 62 R 1

62 ÷ 2 = 31 R 0

31 ÷ 2 = 15 R 1

15 ÷ 2 = 7 R 1

7÷2= 3R1

3÷2= 1R1

1÷2= 0R1

12510 = 11111012

29

Example

12510 = ?2

2 125

2 62

2 31

2 15

7

2

3

2

1

2

0

1

0

1

1

1

1

1

12510 = 11111012

30

Hexadecimal to Decimal

Decimal

Octal

Binary

Hexadecimal

31

Hexadecimal to Decimal

◼

Technique

◼

◼

◼

Multiply each bit by 16n, where n is the “weight”

of the bit

The weight is the position of the bit, starting from

0 on the right

Add the results

32

Example

ABC16 =>

C x 160 = 12 x

1 =

12

B x 161 = 11 x 16 = 176

A x 162 = 10 x 256 = 2560

274810

Remember, in hexadecimal

A represents 10

B = 11

C = 12

D = 13

E = 14

F = 15

33

Decimal to Hexadecimal

Decimal

Octal

Binary

Hexadecimal

34

Decimal to Hexadecimal

◼

Technique

◼

◼

Divide by 16

Keep track of the remainder

35

Example

123410 = ?16

◼

◼

◼

1234 ÷16 = 77 R 2

77 ÷ 16 = 4 R 13

4 ÷ 16 = 0 R 4

Remember, in hexadecimal

A represents 10

B = 11

C = 12

D = 13

E = 14

F = 15

123410 = 4D216

36

Example

123410 = ?16

16

16

16

Remember, in hexadecimal

A represents 10

B = 11

C = 12

D = 13

E = 14

F = 15

1234

77

4

0

2

13 = D

4

123410 = 4D216

37

Binary to Hexadecimal

Decimal

Octal

Binary

Hexadecimal

38

Binary to Hexadecimal

◼

Technique

◼

◼

◼

Group bits in fours, starting on right

Convert to hexadecimal digits

Why group in 4 bits? Because each Hex needs 4 bits.

39

Example

10101110112 = ?16

10 1011 1011

2

B

B

10101110112 = 2BB16

40

Hexadecimal to Binary

Decimal

Octal

Binary

Hexadecimal

41

Hexadecimal to Binary

◼

Technique

◼

Convert each hexadecimal digit to a 4-bit

equivalent binary representation

42

Example

10AF16 = ?2

1

0

A

F

0001 0000 1010 1111

Remember, in hexadecimal

A represents 10

B = 11

C = 12

D = 13

E = 14

F = 15

10AF16 = 00010000101011112

43

Exercise (1) – Convert …

Decimal

33

Binary

Hexadecimal

1110101

451

1AF

Don’t use a calculator!

44

Exercise (1) – Convert …

Answer

Hexadecimal

Decimal

33

Binary

100001

117

1110101

75

451

111000011

1C3

170

000110101111

1AF

21

45

Exercise (2) – Convert …

Decimal

Binary

Hexadecimal

24

74

1B

10100110

Don’t use a calculator!

46

Exercise (2) – Convert …

Answer

Hexadecimal

Decimal

36

Binary

100100

74

1001010

4A

27

11011

1B

166

10100110

A6

24

47

Exercise (3) – Convert …

Decimal

Binary

Hexadecimal

C9

211

10

1011011

Don’t use a calculator!

48

Exercise (3) – Convert …

Answer

Hexadecimal

Decimal

201

Binary

11001001

211

11010011

D3

16

1000

10

91

1011011

5B

C9

49

End Note!

Hint: “10” is not “ten”

50

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