The worlds we live in. The worlds we live in

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1 The contents of this Supporting Material document have been prepared from the Eight units of study texts for the course M150: Date, Computing and Information, produced by The Open University, UK. Copyright The Open University, UK. Introduction The unit aims to: explain the concept of crossing the boundary between the computer s world and our own. explain the digital nature of the computer s world and contrast it with our analogue world of sense and motion. describe in detail how to transform features of our world into computer representation. look at ways in which digital information in the computer can be displayed for our eyes and ears. consider the amazing implications of being able to use the computer to manipulate and transform digital representations of our world. 1

2 The worlds we live in The computer is a tool like any other. The computer s job is to acquire, store, present, control, exchange and manipulate interesting characteristics of the natural world. Storage and presentation keeping copies of all your TMAs or letters or digital films; Control control programs in a washing machine; Exchange sending data between two computers linked by a network. Manipulation computer-aided design systems; The worlds we live in We live in an analogue world (a world of sensation) while the world of the computer is digital (a world of numbers). In order to capture pieces of reality on a computer, you have to move them from an analogue to a digital world inside the computer. You have to cross the boundary between two very different worlds. Humans (and all livings) have the ability to sense or perceive the world around them. We have five senses: vision, hearing, smell, taste and touch. The human perceptual system uses our five senses but is very strongly based on vision and hearing. Humans have learned to enhance their perceptual systems with instruments such as: Microscopes, Telescopes, Radar, Sonar, X-ray Devices, Hearing aids, etc. 2

3 Analogue information: digital representation Analogue quantities are ones that change continuously. Example1: Temperature is an analogue quantity. The analogue thermometer, that uses the length of a column of mercury or colored alcohol to indicate the temperature. There is an infinite number of possible temperatures between the two values 14 and 15 or any other two values. Temperature, goes up smoothly and progressively. Analogue information: digital representation Example2: Volume is an analogue quantity. The volume control of a radio or stereo with a simple knob. When the knob is rotated to increase the volume, the intensity of the sound does not increase in a series of jumps but goes up smoothly and progressively. Other examples on analogue quantities are: Brightness (of light), color, pitch (how high or low a musical note is), pressure, speed. 3

4 Analogue information: digital representation Discrete quantities are ones that change in a series of clear steps. Example1: The discrete volume control shown below. When the control is moved from click to click, you can hear the volume increasing not smoothly, but in a series of steps. Discrete quantities has a fixed number of possible values between any two points on its scale. Analogue information: digital representation Example2: The discrete thermometer below. shown Temperature and volume are fundamentally analogue quantities in that they are infinitely variable. But we may choose to measure them with discrete instruments for our own convenience. Other examples on fundamentally discrete quantities are: The number of people in a party; The number of bricks in a house. 4

5 Analogue information: digital representation Exercise 3.1: Which items in the following list are fundamentally analogue and which fundamentally discrete? 1. The price of petrol 2. The amount of heat from a fire 3. The speed of a car 4. The energy of a star 5. The size of the audience at a play 6. The pressure of the atmosphere. Answer: items 2, 3, 4 and 6 are definitely analogue, although we might choose to measure them with discrete instruments. Items 1 and 5 are discrete. Analogue information: digital representation The terms discrete and digital are often used interchangeably. Digital is a term that is used for any communication or computing technology whose data may only have a finite number of discrete values. The interior world of the computer is a discrete world, a digital world, a world of numbers, nothing but numbers! 5

6 Analogue information: digital representation We have different number systems. Decimal (Base 10) It uses 10 symbols (0, 1, 2, 3, 4, 5, 6, 7, 8 and 9). Binary (Base 2) It uses 2 symbols (0 and1). Octal (Base 8) It uses 8 symbols (0, 1, 2, 3, 4, 5, 6 and 7). Hexadecimal (Base 16) It uses 16 symbols (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F). Analogue information: digital representation Decimal (Base 10) System The system that is used worldwide. It uses ten digits (0 to 9) and each column counts groups ten times bigger than those counted in the column to its right. Examples: 37 = 7 + 3* = 5 + 4* * = 1 + 2* * *10 3 6

7 Analogue information: digital representation Octal (Base 8) System The system that is mostly used by computer scientist. It uses eight digits (0 to 7) and each column counts groups eight times bigger than those counted in the column to its right. Examples: 46 8 = 6 + 4*8 1 = = 5 + 2* *8 2 = Analogue information: digital representation Binary (Base 2) System The system that is used by the computer. It uses two digits (0 and 1) and each column counts groups two times bigger than those counted in the column to its right. Examples: = 0 + 1* *2 2 = = 1 + 0* * *2 3 =

8 Analogue information: digital representation A bit is short for binary digit and refers to a 1 or a 0 stored in the computer. A byte is a group of eight bits that can be used to represent numbers between 0 and 255. A byte looks like this: The largest number we can store in the a byte is = (255) 10. The smallest number we can store in the a byte is = (0) 10. Analogue information: digital representation A word is a group of four bytes. It is the largest data object a particular computer can process in a single operation. A word is 32 bits (4 x 8), so the largest binary number that a computer using a four-byte word can process in a single operation would be which is decimal 4,294,967,295. Computer s memory and hard drive is measured in: bytes = 8 bits kilobytes (KB) = 1024 or 2 10 bytes megabytes (MB) = 1024 KB = 2 20 bytes gigabytes (GB) = 1024 MB = 2 30 bytes 8

9 Crossing the boundary The computer handles everything in a binary form, i.e. in numbers. Therefore, to take the features of our analogue experience across the boundary into a computer means transforming these features into numbers. Text, pictures, moving pictures, diagrams and sound can all be reduced to numbers and stored inside the boundary in a computer s memory. Text Crossing the boundary Word processors enable us to enter text into the computer, edit it, store it and then print it out when we are satisfied with the result. Text exists inside the computer in the form of numbers. Each character (alphabets, parentheses, accents, spaces, etc..) has its numerical representation in the computer. If different computers used different numbers to encode the same character, people would not be able to read each other s documents. There have to be standards. ASCII Unicode 9

10 Crossing the boundary ASCII (American Standard for Computer Information Interchange) It was approved in ASCII uses 7 bits for 128 numbers, from 0 to 127, for upper and lower-case alphabetic characters, punctuation marks and some invisible characters, such as a carriage return (start a new line) and a tab. Unicode standard for character representation It certified in It preserves the ASCII numbers, but expands it. It uses 16 bits (two bytes) for 65,536 as follows: 8192 numbers for representing characters in the world s main languages for punctuation marks, graphics and special symbols for developers to define their own symbols. 27,000 or so for Han Chinese characters. the remainder for characters yet to be invented. Crossing the boundary Text Capture Devices Text capture devices are those used for transforming text into digital form inside the computer. These are: Keyboard, scanners (which produce an image of a page) and optical character recognizers (OCRs). Keyboards are still the main way of taking text across the boundary into the computer. When typing on a keyboard a program called BIOS (Basic Input/output System) will transform the signal from the pressed button to its appropriate numerical code and then other software will store it in memory. Scanners and OCRs provide faster and more efficient way of getting text into a computer than the keyboard. A scanner produces an image of the page. The image is passed to a computer program called OCR (Optical Character Recognition), which detects each letter on the page in turn and transforms it into a digital code. Recognizing characters is a difficult task for the computer because the same character can be represented in many different forms. 10

11 Crossing the boundary Graphics and Video: Images Vision is the most dominant sense for a human being. A visual field includes light, colors, shade, form, etc Such features need to be transformed into numbers in order to cross the boundary and enter the computer world. We ll start with a simple picture (a), place a border around it (b), to indicate the area of interested. Crossing the boundary Graphics and Video: Images Next, divide the picture into equal-sized squares over it (c). Examine each square (d): If the square is entirely grey make it white. If the square is entirely colored (mauve) make it black. If the square contains both grey and color, if more than the third of the square is mauve then it will become black otherwise it will become white. 11

12 Crossing the boundary Graphics and Video: Images Finally, map the square s color to a number by assigning the number 0 to it if it is colored white and 1 if it is colored black (e). This sort of encoding is referred to as a Bitmap or Raster Graphics. Each square that we have mapped to a 0 or a 1 is called a pixel (picture element). Bitmap is a method for storing images in computer memory in which the image is divided into rows of pixels and each pixel is represented by certain fixed number of bits. (e) Crossing the boundary Graphics and Video: Images One way to improve the quality of the image is to increase the number of squares and make each square smaller. This is called increasing the resolution of the picture. 12

13 Crossing the boundary Graphics and Video: Images Such simple method for encoding images is not satisfactory for more sophisticated pictures, such as these shown in figure below. It doesn t handle colors. It is plain black and white, which won t allow us to deal with shade and texture. In our simple method, we dedicated one bit to each pixel in our image. To accommodate a greater range of shades, we need to devote more bits to each pixel. Crossing the boundary Graphics and Video: Images Allocating 2 bits per pixel gives us 4 shades. 11 (black), 00 (white), 01 (light grey) and 10 (dark grey). 3 bits per pixel will give us 8 shades, from black to white. 4 bits per pixel gives us 16 shades. n bits give us 2 n shades. This mapping of shades of grey between black and white in a black and white bitmap is known as grayscale. The range of numbers to which a pixel can be mapped is termed the pixel amplitude. Pixel amplitude: The range of numbers available to represent a pixel digitally. A pixel amplitude of 2 allows only black and while representation. 13

14 Crossing the boundary Graphics and Video: Images Colors are represented in a different way. Any color can be made out of a mixture of three basic shades: Red, Green and Blue (R, G, B). Each shade is represented by a byte (8 bits), giving values ranging from 0 to 255. As a total we have 256 x 256 x 256 possible colors, reflecting every possible mixture of our three basic shades. Red is (255, 0, 0); Green is (0, 255, 0); Blue is (0, 0, 255); White is (255, 255, 255) and Black is (0, 0, 0). Each pixel in the above scheme is stored in 24 bits (or 3 bytes) Large amounts of memory are required. A more efficient way of storing visual information is needed. This way of representing color is called the RGB (Red, Green, Blue) model. Crossing the boundary Graphics and Video: Diagrams Diagrams can be represented more economically than in a bitmap. For the diagram shown below, all we care about are the objects shown (circle, a rectangle, a line, an arrow and a piece of text) the rest is just empty space. To reconstruct the diagram the only information we need about each of these objects is: what sort of object it is (e.g. line, square); its size and position on the page; details about its coloring, width of line (line weight), and so on. 14

15 Crossing the boundary Graphics and Video: Diagrams The method for encoding diagrams into numbers is easy. Assign a number to each type of object. Place two axes, x and y at right angles on the page to be able to record the size and position of each object. This depends on the object, as follows: A circle is defined by its radius and the coordinates of its center. A rectangle by the coordinates of its upper left and lower right corners. Lines and arrows by their starting and ending points. The text area by the coordinates of its top left corner. For each object, record details as the line color, fill color, line width, This sort of encoding is known as vector graphics. Crossing the boundary Graphics and Video: Diagrams Vector graphics is a form of digital representation of images, in which the picture is seen as a collection of geometrical objects, such as lines, squares, circles. Vector format graphic files are much more compact than raster graphics. Vector images are easily altered in scale. They are scalable, we can easily shrink or stretch the size of it without any loss of information. Vector graphics is of little use in representing complex, photorealistic image information. Programs that allow us to draw and display vector graphics are generally referred to as drawing packages. Systems for constructing and displaying raster graphics are usually called painting packages. 15

16 Crossing the boundary Graphics and Video: Movies A Video or a movie, is a series of images (frames) that slightly differ one from another, passing them one after the other at a certain speed (frame rate) will give the illusion of movement. Frame rate is the speed of flipping the frames one after the other. Films are usually shot and displayed at 24 frames a second (fps). TV pictures are presented at between 25 and 30 fps, depending on what country you live in. High definition TV, currently only available in Japan, uses 60 fps. Crossing the boundary Graphics and Video: Movies Computers use the same principle to display moving visual information. A series of images is taken from the computer s memory, or direct from a storage device such as a CD, and presented on the computer screen in quick succession. Each image is different from, but correlated with, the previous image; the illusion of smooth movement is created by our own eyes and brains. The problem here is generally with the size of digital encoding of images (see exercise 4.5). 16

17 Crossing the boundary Graphics and Video: Movies One approach of reducing the amount of storage that moving images need depends on the fact that frames are correlated (similar). Hence, if we fully encode the first frame and then just record the differences between it and the next frame, and so on, we will save huge amounts of space. Other ways to reduce image storage space is by compressing it. Whatever compression strategy we adopt we need to have agreements (standards). Other computers need to be able to decompress it again to display it. Crossing the boundary Exercise 4.5: Consider a two-hour film to be displayed on a computer at 24 fps. Each frame is 640 x 380 pixels and a 24-bit RGB color encoding is being used. How many bytes will be required to represent the whole film? The number of pixels in one frame = 640 * 380 = pixels. The number of bytes needed to represent one frame = * 3 = bytes. The number of seconds in 2 hours = 2 * 60 * 60 = 7200 seconds. The number of frames in 2 hours = 7200 * 24 = frames. The number of bytes needed to represent the whole film = * = bytes. = / 2 30 = GB. 17

18 Crossing the boundary Graphics and Video: Movies Most common compression standards are JPEG (Joint Photographic Experts Group) and GIF (Graphics Interchange Format). Both standards reduce the number of bits used to store each pixel. GIF condenses each pixel from 24 bits to 8, by reducing the set of colors used to a smaller set, called a palette. JPEG is designed to take advantage of certain properties of our eyes, namely, that we are more sensitive to slow changes of brightness and color than we are to rapid changes over a short distance. Image data can sometimes be compressed to one twenty-fifth of the original size. For video, the dominant standard is MPEG (Moving Picture Experts Group), which is now used in most digital camcorders. Crossing the boundary Graphics and Video Capture Devices The main devices used for transforming images and video into digital form inside the computer are scanners, digital cameras and camcorders. 1. Scanners: Can be used for images as well as text. A scanner works by moving a sensing point rapidly across the image, in a series of lines, as illustrated in the figure. This is known as raster scanning. 2. Digital cameras and camcorders: Digital still cameras usually compress their images into JPEG format and store them on a removable memory card inside the camera. Digital camcorders generally produce MPEG format, stored on a special tape. 18

19 Crossing the boundary Sound It is another analogue feature we rely on and we want to digitize it. If you cry out or hit a piano key, then you set particles of air shaking, and any ears will interpret this shake as sound. Vibrating a tuning fork makes pure sound that makes particles of air move backwards and forwards with the fork. One way to visualize this movement is to draw a graph of how far an air particle moves backwards and forwards (we call this its displacement) as time passes. The graph will look like the figure shown below. The distance it moves either way is known as the amplitude. The rate at which it completes one backwards and forwards movement is known as the frequency. Crossing the boundary Sound As with images, the process of digitizing a sound includes: Sampling and Quantization. In order to digitize a sound waveform, we take samples of the sound at small time intervals, such a process is called sampling. An image is sampled into rows of pixels (units of area). A waveform is sampled into a series of discrete time intervals (units of time). The number of times/second we take a sample is called the sampling rate. The smaller the interval is the better. It brings the encoding closer to the original sound. We can never make a perfect digital representation of an analogue quantity because we will always lose information between the times we sample a waveform. It is also impossible to make a perfect digital coding of an analogue picture, because we will always lose information between the pixels. 19

20 Crossing the boundary Sound Quantization is the second stage in the process of taking an image or sound wave across the boundary. It is the process of converting each sample into a suitable number for computer storage. The smaller the interval of taking the samples, the more accurate our representation of the analogue sound will be. Smaller intervals will mean, more samples and therefore more bits to quantize them, which means more storage space. Several formats exist for sound digitizing, depending on the allowed loss of precision (ex: mp3, wav, mid, etc ). Microphone is a sound capture device. Crossing the boundary A final world to say is that can take any feature (rather than visual or sound information) of our world that interests us into the digital world by following the same two-step process: 1. Breaking the target into parts (Sampling). 2. Mapping each part onto a binary number (Quantization ). Once this information has been captured in digital form, programs can be written that will change them in any way that suits us. 20

21 Going Back Digital representations (of pictures, movies, sound, ) are of no value to us unless we can take them back across the boundary into the human area. Sending a digital representation back across the boundary is a three stage process, consisting of: 1. Identifying the output device to be used. 2. Arranging the numbers into a form that can be handled by the output device. 3. Interpretation of the code by the output device. A computer uses different output devices such as: monitors (screens), printers, plotters, speakers,..etc. Going back Monitors: There are two main types of monitors: CRT (Cathode Ray Tube) Monitors The CRT monitor contains millions of tiny red, green, and blue phosphor dots that glow when struck by an electron beam that travels across the screen to create a visible image. The electron beam sweeps across the screen in the same raster scanning pattern. Pixels on CRT are formed by 3 colored phosphors. Professional graphic artists still favor CRT monitors for their color accuracy. LCD (Liquid Crystal Display) Monitors The LCD monitor uses a crystal liquid matrix between 2 opposite polarizing filter sheets. A backlight creates light that passes through the first sheet. At the same time, electrical currents cause the liquid crystal molecules to align to allow varying levels of light to pass through to the second sheet and create the colors and images that you see. Pixels on LCD are made of the crystal molecules. LCD monitors are to be preferred over CRT monitors as they use much less power; take up little space; and are free from flicker and hence less tiring to work on. Monitors of both types supply digital display. 21

22 Going back Printers: There are two main types in use today: Inkjet Printers Inkjet printers work by firing tiny droplets of ink at the paper from a moving print head to create an image. Such printers can print in both color and black and white. Its color cartridge comes in three parts: cyan, magenta and yellow, indicating the color model (CMYK) that the printer uses. Laser Printers Laser printers produce very high quality print by firing a laser beam at a rotating, light-sensitive drum. In this way, the laser draws a negative electrostatic image on the surface of the drum. The charged drum is then rolled in a positively charged toner, a dry powder type of ink, which sticks to the charged image on the drum. The toner is transferred onto a paper using heat and pressure. Laser printers generally print only in black and white but color lasers are available, but are rather expensive for individual users. Both types of printers produce a digital output, as they make graphics and text by firing the laser, or ink, through a square matrix of tiny holes (pixels). Going back Plotters A plotter is a special type of printing device mostly used by architects, engineers and map makers. The printed output is produced by moving a pen across the paper. (several differently colored pens are also available). Plotters are most suitable for line drawings, which is why architects, for instance, use them. Plotters produce an analogue output directly. Loudspeakers Speakers also produce an analogue output. The audio program inside the boundary converts the digital encoding of the sound to a series of electrical pulses that are sent to the speaker, where they cause a cone of stiffened paper (or some synthetic material) to vibrate in and out. This makes the air vibrate in the characteristic sound wave. 22

23 More on numbers systems To convert from binary to decimal a method known as Positional notation can be used. The below figures illustrate the method with an example of how to convert to decimal. Reference: More on numbers systems One of the easy methods used to convert from decimal to binary is comparison with descending powers of two and subtraction. The below figure shows how to convert the decimal number to binary. Reference: 23

24 More on numbers systems To convert from octal to decimal the following formula can be used: Decimal Form = Ʃ(a i x 8 i ) Where, 'a' is the individual digit being converted, while 'i' is the number of the digit counting from the right-most digit in the number, starting with 0. Here are two examples: Reference: More on numbers systems The conversion of a decimal number to its octal equivalent is done by the repeated division method. You simply divide the base 10 number by 8 and extract the remainders. Here are two examples to illustrate this method: Reference: 24

25 Unit summary In this unit you have learned about: The difference between the analogue world we inhabit and the digital world of the computer. How features of our world can cross the boundary and be represented in the digital world, and then brought back across the boundary to us. 25