eleanor roosevelt high school chin-sung lin. man invented machines…… extended the power of...

Binary World(Digital World)

Eleanor Roosevelt High School

Chin-Sung Lin

Man invented machines……

extended the power of muscle

Man invented computers……

extended the power of brain

The World of 1 and 0

Digitization

Digital Technology

The World of 1 and 0

Digitization

Digital Technology

Binary Numbers

The world of 1 and 0……

…... starts from counting……

represent “2” by “00110”

represent “5” by “11111”

represent “7” by “00011”

represent “3” by “?????”?

How many numbers can be represented by 5 fingers?

Answer: 32 numbers

2 x 2 x 2 x 2 x 2 = 25 = 32

00000 ----- 0

Binary Numbers

00001 ----- 1

00010 ----- 2

00011 ----- 3

00100 ----- 4

00101 ----- 5

00110 ----- 6

00111 ----- 7

01000 ----- 8

Binary Numbers

01001 ----- 9

01010 ----- 10

01011 ----- 11

01100 ----- 12

01101 ----- 13

01110 ----- 14

01111 ----- 15

Binary-to-Decimal Conversion

Binary-to-Decimal Conversion

3 2 0 1 ----- 3201

0 1 0 1 ----- 5

101 100102103

21 202223

3 x 103 + 2 x 102 + 0 x 101 + 1 x 100 = 3000 + 200 + 0 + 1 = 3201

0 x 23 + 1 x 22 + 0 x 21 + 1 x 20 =0 + 4 + 0 + 1 = 5

Binary-to-Decimal Conversion

1 0 1 0 -----1 x 23 + 0 x 22 + 1 x 21 + 0 x 20 = 8 + 0 + 2 + 0 =

21 202223

Binary-to-Decimal Conversion

1 0 1 0 ----- 101 x 23 + 0 x 22 + 1 x 21 + 0 x 20 = 8 + 0 + 2 + 0 = 10

21 202223

Binary-to-Decimal Conversion

1 1 1 1 -----1 x 23 + 1 x 22 + 1 x 21 + 1 x 20 = 8 + 4 + 2 + 1 =

Binary-to-Decimal Conversion

1 1 1 1 ----- 151 x 23 + 1 x 22 + 1 x 21 + 1 x 20 = 8 + 4 + 2 + 1 = 15

Binary-to-Decimal Conversion

1 0 0 1 -----1 x 23 + 0 x 22 + 0 x 21 + 1 x 20 = 8 + 0 + 0 + 1 =

Binary-to-Decimal Conversion

1 0 0 1 ----- 91 x 23 + 0 x 22 + 0 x 21 + 1 x 20 = 8 + 0 + 0 + 1 = 9

Binary-to-Decimal Conversion

1 1 0 1 ----- 1 x 23 + 0 x 22 + 0 x 21 + 1 x 20 = 8 + 4 + 0 + 1 =

Binary-to-Decimal Conversion

1 1 0 1 ----- 131 x 23 + 0 x 22 + 0 x 21 + 1 x 20 = 8 + 4 + 0 + 1 = 13

Decimal-to-Binary Conversion

Decimal-to-Binary Conversion

7Decimal: 7

Binary:

Decimal-to-Binary Conversion

7 2Decimal: 7

Binary:

Decimal-to-Binary Conversion

7

3

2Decimal: 7

Binary:

1

Decimal-to-Binary Conversion

7

3 2

2Decimal: 7

Binary:

1

Decimal-to-Binary Conversion

7

3

1

1 2

2Decimal: 7

Binary:

1

Decimal-to-Binary Conversion

7

3

1

1 2

2Decimal: 7

Binary: 1 1 1

1

Decimal-to-Binary Conversion

1 4Decimal: 1 4

Binary:

Decimal-to-Binary Conversion

1 4 2Decimal: 1 4

Binary:

Decimal-to-Binary Conversion

1 4

7

2 0Decimal: 1 4

Binary:

Decimal-to-Binary Conversion

1 4

7 2

2 0Decimal: 1 4

Binary:

Decimal-to-Binary Conversion

1 4

7

3

1 2

2 0Decimal: 1 4

Binary:

Decimal-to-Binary Conversion

1 4

7

3

1 2

2 0Decimal: 1 4

Binary: 2

Decimal-to-Binary Conversion

1 4

7

3

1 2

2 0Decimal: 1 4

Binary:

1

1 2

Decimal-to-Binary Conversion

1 4

7

3

1 2

2 0Decimal: 1 4

Binary: 1 1 1 0

1

1 2

Decimal-to-Binary Conversion

2 5Decimal: 2 5

Binary:

1

Decimal-to-Binary Conversion

2 5

1 2

6

3

1

0

0

2

2

2

2

Decimal: 2 5

Binary: 1 1 0 0 1

1

Decimal-to-Binary Conversion

2 4 0Decimal: 2 4 0

Binary:

0

2

1

Decimal-to-Binary Conversion

2 4 0

1 2 0

6 0

3 0

1 5

7

3

1

1

1

0

0

2

2

2

2

2

2

Decimal: 2 4 0

Binary: 1 1 1 1 0 0 0 0

0

Binary Arithmetic

0 0 1 0 1 ----- 5

+ 0 0 0 1 0 ----- +2

0 0 0 1 1 ----- 3

Binary Addition

0 1 0 0 0 ----- 8

+ 0 0 0 1 1 ----- +3

0 0 1 0 1 ----- 5

Binary Addition

1 0 0 0 0 ----- 16

+ 0 0 1 1 1 ----- +7

0 1 0 0 1 ----- 9

Binary Addition

0 0 0 1 0 ----- 2

- 0 0 1 0 1 ----- -5

0 0 1 1 1 ----- 7

Binary Subtraction

0 0 1 1 1 ----- 7

- 0 0 0 0 1 ----- -1

0 1 0 0 0 ----- 8

Binary Subtraction

0 0 1 1 1 ------ 7

- 0 0 0 1 1 ----- -3

0 1 0 1 0 ----- 10

Binary Subtraction

Hexadecimal Numbers

0 1 2 3 4 5 6 7 8 9 A B C D E F

Number Systems

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7

0 1

Hexadecimal

Decimal

Octal

Binary

Hex Numbers

0 0 0 0 ----- 0

0 0 0 1 ----- 1

0 0 1 0 ----- 2

0 0 1 1 ----- 3

0 1 0 0 ----- 4

0 1 0 1 ----- 5

Hex Numbers

1 0 1 0 ----- A

1 0 1 1 ----- B

1 1 0 0 ----- C

1 1 0 1 ----- D

1 1 1 0 ----- E

1 1 1 1 ----- F

Binary-to-Hex Conversion

00110001 ----- ?

00110001 ----- ?

00110001 ----- 31H

00110001 ----- 31H

Binary-to-Hex Conversion

01011100 ----- ?

01011100 ----- ?

01011100 ----- 5CH

01011100 ----- 5CH

Binary-to-Hex Conversion

11011010 ----- ?

11011010 ----- ?

11011010 ----- DAH

11011010 ----- DAH

Hex-to-Binary Conversion

34H ----- ?

34H ----- ?

34H ----- 00110100

34H ----- 00110100

Hex-to-Binary Conversion

A2H ----- ?

A2H ----- ?

A2H ----- 10100010

A2H ----- 10100010

Hex-to-Binary Conversion

FBH ----- ?

FBH ----- ?

FBH ----- 11111011

FBH ----- 11111011

ASCII Code

Binary Characters

00111111 --- ?

00100100 --- $

01100101 --- e

01000001 --- A

ASCII Code

Binary Switches

Binary Switches

Binary Switches

Binary Switches

Binary Switches

Binary Switches

The World of 1 and 0

Digitization

Digital Technology

Black and white image

Digitization

Black and white image

Digitization

Black and white image

Digitization

Gray level image

Digitization

Gray level image

Digitization

Digitization

0000

00010010

00110100

01010110

0111

1000

1001

1010

Digitization

10011100101010010010001001110001000100011010010100101011001001001

1,000 x 1,000 x 4 =

4,000,000 (bits)

Digitization

Color image

Digitization

10011100101010010010001001110001000100011010010100101011001001001

10011100101010010010001001110001000100011010010100101011001001001

10011100101010010010001001110001000100011010010100101011001001001

Digitization

Color video

Digitization

Sound

1001110010101001001000100111000100010001101001010010101100100100110011100101010010010001001110001000100011010010100101011001001001

Digitization

Shape

Motion

Relation

Digitization

Digital information

Digitization

10011100101010010010001001110001000100011010010100101011001001001100111001010100100100010011100010001000110100101001010110010010011001110010101001001000100111000100010001101001010010101100100100110011100101010010010001001110001000100011010010100101011001001001

Digital instruction

Digitization

10011100101010010010001001110001000100011010010100101011001001001100111001010100100100010011100010001000110100101001010110010010011001110010101001001000100111000100010001101001010010101100100100110011100101010010010001001110001000100011010010100101011001001001

Digital tools

Digitization

Digital world

Digitization

The World of 1 and 0

Digitization

Digital Technology

Titan super computer: 18,688 CPUs paired with an equal number of GPUs to perform at a theoretical peak of 27 petaFLOPS

Digital Technology

High-speed computation

Weather forecasting

Digital Technology

Pharmaceutical research

Digital Technology

Flight simulation

Digital Technology

Animation

Digital Technology

NSA Utah Data Center has storage capacity between 3 and 12 exabytes

Large amount storage

Digital Technology

The Indexed Web contains at least 3.81 billion pages (Thursday, 19 September, 2013)

Global connection

Digital Technology

Digital Technology

Digital life

Digital Technology

Digital life

Digital Technology

Digital life

Digital Technology

Digital life

Digital Technology

Digital life

Digital Technology

Digital life

Digital life

Digital Technology

Digital life

Digital Technology

The World of 1 and 0

Digitization

Digital Technology

Q & A

Binary World