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

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1 Chapter 2: Basics on computers and digital information coding Information Technology and Arts Organizations 1

2 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) 2

3 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 Applications... 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 3

4 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 (Von Neumann, 1940) 4

5 The Von Neumann Machine (1940) John Von Neumann ( ) 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 electronic implementation of a Von Neumann machine is called hardware The set of programs executed by a computer is called software 5

6 A Mobile Phone as a computer (Execute) (Store data and programs) Input Input/Output Ouput Keyboard GPS SD/CF/MicroSD USB Display Vibro-Tactile Camera Tilt sensor Microphone HSDPA/UMTS/GPRS Speakers 6

7 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: Computers exchange information with the external world 7

8 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 Bytes Since a Byte is a sequence of 8 zeros and ones, GIOCA s logo can be represented with a sequence of 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 zeros and ones 8

9 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, redyellow, green-yellow 9

10 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 decrease in uncertainty 10

11 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 11

12 Data vs. Information Information: The meaning that a human assigns to data by means of the known conventions used in their representation (codes) 12

13 Codes on the sea 13

14 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 Binary code Strings of bits

15 INFORMATION CODING 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) 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 The table above shows the encoding of the door states (open/closed) with one bit Let s try, now, to encode the four cardinal points N E S and W 15

16 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, x 0 ) N 00 E 01 S 10 W 11 The table above maps the 4 cardinal points onto the 4 cofigurations of 2 binary variables: cardinal points may be encoded with 2 bit 16

17 Definition of n bit binary configuration An n bit binary configuration is a sequence of n 0 and 1 E.g. : 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 With n bit we can represent one out of 2 n alternative options 17

18 FUNDAMENTAL INEQUALITY FOR CODING How many bit are required to encode M different items? 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 An n bit code with n > n min is called a redundant code 18

19 The Power of Two n 2 n n 2 n n 2 n = (2K) K M M K K (= 1K) K = (1M) 30 Please complete the table above J 19

20 A redundant code for alphanumeric characters visualisation M = 26 (lower case) è n min =?? M = 52 (up-lower case) è n min =?? Bit map: a 64 bit code 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 + numbers è n min =?? Black & white pixel matrix: for example 8x8 20

21 Common Information Measurement Units 1 Kilobit = 2 10 bit= 1024 bit (Kb): just over one thousand (10 3 ) bit 1 Megabit = 2 20 bit = bit (Mb): just over one million (10 6 ) bit 1 Gigabit = 2 30 bit: = bit (Gb): just over one billion (10 9 ) bit 1 Terabit = 2 40 bit: = Gb (Tb): just over one thousand of billion (10 3 * 10 9 ) bit 1 Byte = 2 3 bit = 8 bit 1 KiloByte = 2 10 Byte = 1024 Byte (KB): 1 KB is equivalent to 8 Kb lowercase (b): bit ; uppercase (B): Byte The speed of data communication links is expressed in bps (bit per second) The size of a memory area is expressed in Byte 21

22 Example: codes for the decimal figures Decimal figures zero one two three four five six seven eight nine BCD out of 10 22

23 7 segments based coding Decimal figures abcdefg f a b zero one two three four five six seven eight nine e d g c 7 segments 23

24 Coding example: bar code Digit L Pattern R Pattern bit L Pattern R Pattern 3 bit (101) 3 bit (101) 6 bit (01010) 24

25 Coding example: Identification è RFID CHIP + Antenna Radio Frequency IDentification uses a 96 bit code called Electronic Product Code (EPC) EPC allow to encode up to 2 32 x 2 32 x 2 32 different information (products) ~ 4.3 Billion 2 32 ~ 4.3 Billion 2 32 ~ 4.3 Billion Internet Of Things? 25

26 Text encoding: 8 bit ASCII code Hexadecimal code: it uses 16 figures to represent numbers 8 bit is 0 8 bit is 1 26

27 Hexadecimal code to binary code Decimal Hexadecimal Binary A B C D E 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 27

28 Have a look inside files ASCII Code 28