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Higher Computing : COMPUTER SYSTEMS

Higher Computing : COMPUTER SYSTEMS. Part 1 : Data Representation – 6 hours. INT 2. Positive 8-bit binary numbers. Convert binary to decimal Write place headings Write binary number Total headings where 1 present (ignore 0s). Place headings. Data Representation. Binary number.

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Higher Computing : COMPUTER SYSTEMS

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  1. Higher Computing: COMPUTER SYSTEMS Part 1: Data Representation – 6 hours Higher Computing

  2. INT 2 Positive 8-bit binary numbers • Convert binary to decimal • Write place headings • Write binary number • Total headings where 1 present (ignore 0s) Place headings Data Representation Binary number => 64 + 16 + 8 + 4 + 1 = 93 Binary 0101 1101 is Decimal 93 Higher Computing

  3. INT 2 Advantages of Binary Advantages 1 Binary 0 and 1 can be simply used to represent OFF or ON 2 A “degraded” signal can still be detected as representing 1 3 Binary has only 5 rules for addition making calculations simpler. Data Representation Higher Computing

  4. Range up to and including 32-bits The range of positive integer numbers in binary up to 32 bits are detailed in the table below: Data Representation These measurements are used to determine the lower and upper limits of the range numbers possible with a given amount of bits or bytes. Higher Computing

  5. Negative numbers and two’s complement Rules of Binary Addition 0 + 0 = 0 1 + 1 = 0 carry 1 0 + 1 = 1 1 + 1 + 1 = 1 carry 1 1 + 0 = 1 Two’s complement 1 State the positive binary number 2 Invert 0s and 1s 3 Add 1 Example: Represent -9 using two’s complement method. Data Representation = +9 = Inversion = Add binary 1 = Answer! Indicates sign 0 = +, 1 = - => (-128 )+ 64 + 32 + 16 + 4 + 2 + 1 = - 9 Higher Computing

  6. INT 2 Floating point representation Here is a fractional binary number… 1 1 0 1 . 0 0 1 1 0 1 1 1 0 0 1 0 Binary point Rule: Move the point in front of the digits. So the same number could be written as.. Data Representation . 1 1 0 1 0 0 1 1 0 1 1 1 0 0 1 0 x 2 00000100 Mantissa Exponent Higher Computing

  7. Mantissa Exponent Floating point representation And the same number would be stored in memory as… Data Representation • Therefore… • The mantissa stores the actual digits of the number. Increasing the number of bits increases the precision (accuracy) of the number. • The exponent stores the number of places the point has been moved. Increasing the number of bits increases the range of numbers that can be stored. Higher Computing

  8. INT 2 Storage Capacity Memory is organised into groups of bytes and large files sizes are represented as powers of 2. Data Representation These measurements are used in memory (e.g. RAM) and backing storage (e.g. hard disc, DVD etc.) Higher Computing

  9. INT 2 ASCII - American Standard Code for Information Interchange To represent text a unique 7 or 8 bit binary code is used for each character on the keyboard. Note the leftmost bit is always 0, hence only 7-bits used in StandardASCII. The ‘eighth bit’ increases the range of possible characters to 256 and gives Extended ASCII. Data Representation ASCII enables the transfer data from one computer or software package to another e.g. email. It is the simplest form of text with no formatting. A character set is the complete set of characters that are on the keyboard e.g. 1 2 3, a b c, ! ” £, and control characters. A control characteris non-printable e.g. RETURN, TAB, ESCAPE, SPACE etc. They are the first 32 characters in ASCII. Higher Computing

  10. Unicode Unicode is a 16-bit code (2 bytes) that supports 65,536 characters • Advantages • A code for every character based alphabet in the world • Has codes for Chinese, Arabic etc. • Covers all punctuation marks and control characters Data Representation Snapshot of German keyboard Higher Computing

  11. INT 2 Bitmapped graphics Any graphic is made up from a series of pixels (picture elements). Each pixel is an individual dot on the screen. Data Representation Pixel pattern using 8 x 8 grid The BIT MAP of the image In a monochrome graphic, each pixel is represented by either 0 - white OR 1 - black Higher Computing

  12. INT 2 Resolution The quality of the image depends on the number of pixels More pixels means higher resolution and clearer, sharper image. Data Representation Pixel pattern using 8 x 8 grid Pixel pattern using 16 x 16 grid High resolution = many small pixels, larger file size Low resolution = larger pixels, smaller file size Higher Computing

  13. INT 2 Storage Each pixel requires 1 bit of storage. So, the more pixels used, the larger the file size. Example 1 8 x 8 = 64 bits 64 bits / 8 = 8 bytes File size of this graphic is 8 bytes Data Representation Example 2 16 x 16 = 256 bits 256 bits / 8 = 32 bytes File size of this graphic is 32 bytes Higher Computing

  14. Bit-depth and no. of colours up to 24-bits (true colour) Bitmap graphics are made up of pixels (dots) and each dot is stored as bits or bytes in memory. Bit-depth is the number of bits used to represent shades of colours of a pixel. Data Representation The more bits per pixel the more colours can be used - but file size will increase. Higher Computing

  15. Dots per inch (dpi) Dpi is a measure of how many pixels (dots) are in an square inch. Printers and scanners state resolution in dpi. Example The dimensions of an image are 4” x 6”, the resolution is 300 dpi and it is black and white. Calculate the file size. Formula: Pixels / bits = length x breadth x dpi2 Data Representation 4 x 6 x 300 x 300 = 2,160,000 bits => 2160000 / 8 = 270,000 bytes => 270,000 = 263.7 kilobytes File size of this graphic is 263.7 bytes Higher Computing

  16. Pixellated bitmap Bitmapped graphics • Advantages • Individual pixels can be edited • Complexity of image does not affect file size • Can be compressed to JPEG, GIF or TIFF to reduce file size • Disadvantages • Large file size e.g. 3 bytes per pixel • Individual objects cannot be edited • Resolution dependent: low resolution = low quality • Image ‘pixellated’ when resized bigger Data Representation Higher Computing

  17. Need for compression of bitmaps Bitmapped graphics often have a large file size. So... A 1024 x 768 24-bit colour graphic has a file size of 2.25 Megabytes. An image of this size would be slow to transmit across a network or slow to download from the Internet.... Data Representation Bitmaps can be compressed using compression algorithms into JPEG or GIF to reduce file size and enable faster transfer / download across networks. Higher Computing

  18. Need for compression of bitmaps JPEG (Joint Photographics Expert Group) Lossy compression algorithm where some pixel data is removed, but retains 24-bit colour and minimal loss of quality to human eye – ideal for photographs. Data Representation Higher Computing

  19. Need for compression of bitmaps GIF (Graphics Interchange Format) Lossless compression algorithm where colour depth is reduced to 8-bit resulting in 256 colours – ideal for clip art etc but not for photographs. Data Representation Higher Computing

  20. Vectored graphics Vectors are stored as a description of the objects that make up the graphic e.g. start x, start y, line thickness, fill colour etc. • Advantages • Individual objects can be edited • Objects can be grouped and manipulated as one • Are resolution independent i.e. same quality regardless of resolution • Do not lose quality when resized • Small file size as values not stored for every pixel Data Representation • Disadvantages • Cannot be edited at pixel level • File size can be large if many objects / layers Higher Computing

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