Chapter 2: Basics on computers and digital information coding. A.A Information Technology and Arts Organizations

Chapter 2: Basics on computers and

digital information coding

Syllabus (1/3)

1.  Introduction on Information Technologies (IT) and Cultural Heritage (CH)

1.  The role of Cultural Heritage

2.  Safeguarding and management

3.  Context aware multimedia guides

4.  The role of technology

2.  Basics on Computers and digital information coding

1.  Reference model: the Von Neumann Machine 2.  Information and its measure

3.  Binary information encoding

4.  Binary codes: fundamental inequity for coding, examples (ASCII, 7 segment, numbers)

Why do computers and computer

industry develop so fast?

Because they share the same reference model

  Returns on investments on computers are continuously

reinvested on the same reference model, leading to reduced

recurring costs and increased performance.

  This leads to new applications, increased turnover and new

opportunities for further investments that are always redirected to the same reference model, with further virtuous

improvements in performance and costs

So, what is a computer?

A computer is just an information

processing machine, where

information is represented through

sequences of “0”s and “1”s

COMPUTER REFERENCE MODEL

A computer is a machine with the following properties:

•  It is digital

•  It is programmable

•  Its programs are set of instructions executed

sequentially

•  Its programs and its data are stored on a memory

support

Therefore we say that a computer is a stored program

sequential digital machine

  John Von Neumann (1903-57) proposed in 1940 the model of a general

purpose programmable digital machine

  The Von Neumann machine was adopted by the industry as the computer

reference model

  Again, the essential features of the Von Neumann machine are:

  It is digital

  It is a general purpose machine and the desired functionality is assigned by

an instruction sequence named program

  The program is stored on a memory support

  Therefore:

the function performed by a computer may be changed by changing its program

The Von Neumann Machine (1940)

The electronic implementation of a Von Neumann machine is called “hardware” The set of programs executed by a computer is called “software”

A Mobile Phone as a computer

USB SD/CF/MicroSD GPS Keyboard _Display Vibro-Tactile Speakers

Input Input/Output Ouput

What happens to information inside a

computer?

•  Text is information

•  Images are information

•  Spoken language is information

Inside a computer information is always represented through sequences of “zeros” and “ones”

Sequences of “0” and “1” are stored (Memory), processed (CPU) and

moved (BUS) inside a computer

Furthermore:

How many zeros and ones are required

to represent a specific information?

GIOCA

Gestione e Innovazione delle

organizzazioni culturali e

artistiche

This text can be represented with a sequence of approximately

500 “zeros” and “ones”

This logo is an image. Windows tells us that its size is “60005 Bytes”

Since a Byte is a sequence of 8 “zeros” and “ones”, GIOCA’s logo can be

represented with a sequence of 480.040 “zeros” and “ones”

The 5 seconds audio clip associated to the reading of the above text in the Italian language can be represented with a sequence of approximately 25000 “zeros” and “ones”

Examples of information

•  Information is an entity representing a choice among

alternative options

“Open”

or

“Closed”

“Turned on”

or

“Turned off”

4 options: N, E, S, W 8 options: N, NE, E, SE, S, SW, W, NW 16 options: N, NNE, NE, ENE, E, ESE, SE, SSE, S, SSW, SW, WSW, W, WNW,

NW, NNW

3 options: red, yellow, green

4 options: red, yellow, green,

flashing yellow

SW, W, NW

4 options: red, green, red

Information and messages

•  Information is a choice among a set of options

•  A message is a collection of information sent from an entity A

to an entity B

•  When a message is received, uncertainty decreases. The

amount of information

carried by a message goes with the

Measuring information

•  The information measurement unit is called bit

•  Definition: “A message specifying a choice between two

options with the same probability carries one bit of

information”

•  With reference to the previous “door state” example, if both

situations “door open” and “door closed” may occur with the

same probability, then the message “the door is open”

carries one bit of information

•  bit stands for binary digit, (“cifra binaria”); this name was

selected because one bit of information may be represented

with a single binary digit, i.e. a digit that can only take two

values: 0 or 1; so a binary digit, i.e. a “0” or a “1”, represents

one bit of information

Data vs. Information

Information

:

The meaning that a human assigns to

data

by means

of the known conventions used in their

“Codes on the sea”

Binary codes

A binary code is a map, i.e. a correspondence,

between the “symbols” of an alphabet and their

representation with strings of bits

Alphabet

≈

∂

∞

↨

€

Ω

☺

♠

♥

Strings of bits

0101 101 1101 11 1100 00 11111 010 1

Binary code

INFORMATION CODING

•  Suppose that we want to code a situation, that is the status of a door •  The door can be open or closed

•  We can map the status of the door onto the values of a single binary variable, for example, according to the following table:

door state x

door open 0

door closed 1

Let’s try, now, to encode the four cardinal points

N E S and W

The table above shows the encoding of the door states (open/closed) with one bit

Definition

a binary variable X is a variable that can only take two values: 0 and 1 ( i.e. it can only be x=0 or x=1)

Example: CODING the four cardinal

points

•  We may bind each cardinal point to a configuration of 2 binary

variables x1 e x0, according to the following arbitrary table:

Cardinal

Point Value for _(x

1 , x0)

N 00

E 01

S 10

W 11

The table above maps the 4 cardinal points onto the 4 cofigurations of 2 binary variables:

Definition of n bit binary configuration

•  An n bit binary configuration is a sequence of n “0” and “1”

•  E.g. : 001011 is a 6 bit binary configuration

How many n bit binary configurations exist?

2

n

•  There are two (i.e. 2

1

_{) configurations of one bit: “0” and}

“

1”

•  Anytime one bit is added, the amount of configurations

doubles: C

_n

= 2 * C

_n-1

•  In fact: adding one bit to a generic configuration

X of n-1

bit

_,

leades to the following two new configurations:

0

X

and

1

X

FUNDAMENTAL INEQUALITY FOR

CODING

As with n bit we can build 2

n

_{different n-bit binary configurations,}

then with n bit we can code up to 2

n

_{different items}

Therefore it must be:

M ≤ 2

n

The above is called the coding fundamental inequality

Let’s call n

_min

the smallest integer that verifies the inequality M ≤ 2

n

Ex: M = 3 è n

_min

= 2

M = 6 è n

_min

= 3

How many bit are required to encode M different items?

The Power of Two

n 2n _{n 2}n _{n 2}n 1 2 11 2048 = (2K) 21 2 4 12 22 3 8 13 8K 23 4 16 14 24 5 15 25 32M 6 16 26 64M 7 128 17 27 8 256 18 256K 28 9 19 512K 29 10 1024 (= 1K) 20 1024K = (1M) 30

A redundant code for alphanumeric

characters visualisation

Black & white pixel matrix: for example 8x8

This code is

“redundant” as its size (64 bit) is

larger than the minimum amount of bit required to code alphanumeric characters. Such a minimum may be evaluated applying the “fundamental coding inequality”

Bit map: a 64 bit code

M = 26 (lower case) è n_min = ??

M = 52 (up-lower case) è n_min = ??

Common Information Measurement

Units

•  1 Kilobit = 210 _{bit= 1024 bit (Kb): just over one thousand (10}3_{) bit}

•  1 Megabit = 220 _{bit = 1.048.576 bit (Mb): just over one million}

(106_{) bit}

•  1 Gigabit = 230 _{bit: = 1.073.741.824 bit (Gb): just over one billion}

(109_{) bit}

•  1 Terabit = 240 _{bit: = 1.024 Gb (Tb): just over one thousand of}

billion (103 _{* 10}9_{) bit}

•  1 Byte = 23 _{bit = 8 bit}

•  1 KiloByte = 210 _{Byte = 1024 Byte (KB): 1 KB is equivalent to 8}

Kb •  …

•  The speed of data communication links is expressed in bps (bit

per second)

•  The size of a memory area is expressed in Byte

Example: codes for the decimal figures

zero

one

two

three

four

five

six

seven

eight

nine

Decimal

figures

0000

0001

0010

0011

0100

0101

0110

0111

1000

1001

BCD

1000000000

0100000000

0010000000

0001000000

0000100000

0000010000

0000001000

0000000100

0000000010

0000000001

1 out of 10

7 segments based coding

g a f b e c d

zero

one

two

three

four

five

six

seven

eight

nine

Decimal

figures

1111110

0110000

1101101

1111001

0110011

1011011

0011111

1110000

1111111

1110011

7 segments

abcdefg

Coding example: bar code

Digit L Pattern R Pattern

0 0001101 1110010 1 0011001 1100110 2 0010011 1101100 3 0111101 1000010 4 0100011 1011100 5 0110001 1001110 6 0101111 1010000 7 0111011 1000100 8 0110111 1001000 9 0001011 1110100 3 bit (101) 6 bit (01010)

7 bit

3 bit (101) L Pattern R Pattern

Coding example: Identification è RFID

Radio Frequency IDentification uses a 96 bit code called Electronic Product Code (EPC)

EPC allow to encode up to 232 _{x 2}32 _{x 2}32 _different

information (products) 232 _{~ 4.3 Billion} 232 _{~ 4.3 Billion} 232 _{~ 4.3 Billion}

Internet Of Things?

http://www.epcglobalinc.org/home http://en.wikipedia.org/wiki/Electronic_Product_Code CHIP + Antenna

Text encoding: 8 bit ASCII code

Hexadecimal code: it uses 16 figures to represent numbers

Hexadecimal code to binary code

Decimal Hexadecimal Binary

0 0 0000 1 1 0001 2 2 0010 3 3 0011 4 4 0100 5 5 0101 6 6 0110 7 7 0111 8 8 1000 9 9 1001 10 A 1010 11 B 1011 12 C 1100 13 D 1101 14 E 1110 15 F 1111

We have 16 information (the

first 16 decimal numbers)

We need 4 bits to encode

such information. In fact, we

need to find the minimum

value of n that verify the

inequity 2

n

_{≥ 16}

Have a look inside files…