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Higher Computing Computer Systems

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Topics Data Representation (6 Hours) Computer Structure (7 Hours) Peripherals (5 hours) Networking (9 Hours) Computer Software (9 hours) Also – Multimedia Vector Graphics & Synthesised Sound (6 hours)

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Assessment 1 written NAB (? 4/2/2010) 1 practical NAB (? 17-25/3/2010) Coursework (? 17-25/2/2010)

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Homework Weekly consolidation questions/tasks 1 week to complete substantial HWs Glossary of definitions Mindmaps

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Resources Course booklets PowerPoints will be put on network Practice NABs (online) Blank glossary Learning Intentions Mindmap software

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Expectations Consistent application throughout is essential Course will be fast paced Written answers require depth, detail and maturity

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Course Files P:/ Drive 5&6 Year Progs Computing Department Higher Computing Computer Systems

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**Data Representation – Technical terms**

6 hours

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**Units of Measurement Decimal number system 1000s 100s 10s Units 103**

0-9 Powers of 10 1000s 100s 10s Units 103 102 101 100 1 2 5 8

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**Units of Measurement Binary number system 0, 1 21 2 29 512 22 4 210**

1024 23 8 211 2048 24 16 212 4096 25 32 213 8192 26 64 214 16384 27 128 215 32768 28 256 216 65536

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**Scales Units 1 Kilo 1000 (thousand) 1024 210 Mega 1,000,000 (million)**

1024x1024 220 Giga 1,000,000,000 (billion) 1024x1024x10 24 230 Tera 1,000,000,000,000 (trillion) 1024x1024x 240

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**Converting between Units**

8 bits in a byte 1024 bytes in a Kb 1024 Kb in a Mb 1024 Mb in a Gb 1024 Gb in a Tb Convert 553,476 bits into Kb How many bytes in 91 Mb?

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Answers 553,476 bits /8 69,184.5 bytes /1024 67.56 Kb (rounded to 2 decimal places) 91 Mb * 1024 93,184 Kb * 1024 95,420,416 Bytes

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Processor Clock speed is measured in GigaHertz (GHz) Hertz = 1 cycle (pulse) per second E.g. 2 GHz = approx 2 billion clock beats per second

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Word The word size of a computer is the number of bits which can be moved and processed in a single operation As a rule, it also tends to be the size of the data bus (more later) e.g. 16-bit, 32-bit (Nintendo 64!)

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Memory Measured in Mb or Gb E.g. 512Mb upwards

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**Measured in Gb – e.g. 80Gb hard disk **

Backing Storage Measured in Gb – e.g. 80Gb hard disk Floppy Disk (almost obsolete) – 1.44Mb Etc File sizes – depends on data type Word processed document – Kb Graphic file (uncompressed) – Mb Video file - Gb

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**Printers measured in dots per inch (dpi)**

Resolution Printers measured in dots per inch (dpi) E.g. Laser printer 2400dpi Ink jet 750 dpi Monitors measured in pixels E.g x 768 pixels

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**Computers store and process binary numbers Binary uses two digits 1, 0 **

Data Representation Computers store and process binary numbers Binary uses two digits 1, 0 These can be represented by Electricity on or off Land or pit (on optical disk) This is why a computer is called a two-state machine

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**Learn these place values!**

Counting in Binary Learn these place values! = = 181 27 26 25 24 23 22 21 20 128 64 32 16 8 4 2 1

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Why do we use binary? simplicity, in only having to generate and detect two voltage levels (on/off) good tolerance, because a degraded 1 is still recognisable as a 1. calculations are kept simple as the only combinations are 0+0, 0+1, 1+0 and 1+1

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** Why do we use binary? Numbers are long**

Difficult to read, write and recognise Value is “hidden” from humans

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Why NOT use decimal? Decimal is familiar to humans but… There are too many symbols 0-9 Too many rules for +,-,* and / Would require 10 voltage levels Would require a circuit for every combination of two digits e.g. 2+3, 6+7 etc

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Bits and Values The number of bits determines the number of values which can be represented

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**Bits and Values # of bits (n) i.e. Range (Zero to 2n-1)**

Number of values (2n) 1 0, 1 0-1 2 00,01,10,11 0-3 4 0-15 16 8 0-255 256 Two bytes 65536 (64k) 24 Three bytes 0-16,777,215 16,777,216 (16 Mb) 32 Four bytes 0-4, ,295 4,294,967,296 (4 Gb)

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**Computers need to represent different types of data:-**

Data Types Computers need to represent different types of data:- Text Numbers (integers and real) Graphics Sound etc

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Text ASCII standard American Standard Code for Information Interchange All computers use the same codes to represent the same characters Allows computers to communicate

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**Each character is stored in 1 byte **

ASCII Each character is stored in 1 byte Only 7 bits are used (with leading zero) 7 bits = 128 characters (27) E.g. A is or 65 0 is or 48

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Control Characters First 32 characters in the ASCII character set Non-printing characters Perform some function instead E.g. audible beep, arrow keys NOT Enter, tab, space-bar

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ANSI American National Standards Institute Uses 8 bits to represent 256 characters First 128 same as ASCII Then additional characters such as ©, â, ç and Ä

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Unicode Uses 16 bits Can store up to 65,536 characters Enables characters from every language to be stored E.g. Japanese and Chinese characters

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**Binary – Decimal Conversion**

Lesson 2 Binary – Decimal Conversion

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Homework Homework questions – Data Representation 1 For 17/6/09

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**Data Representation - Numbers**

Decimal umbers are converted into binary in order to be stored.

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**Converting binary to decimal**

Here is an example of how to convert the binary number to a decimal: = = 154.

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**Binary to Decimal – 3 steps**

Draw an appropriately sized table with place values (8,16,24,32) Fill the binary number from right to left Add together the place values which have 1s

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**Task Convert the following binary numbers to decimal (a) 111101010010**

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**Task Convert the following binary numbers to decimal**

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**Converting decimal to binary – division method**

Here is an example of how to convert the decimal number 69 to a binary: 2 69 34 17 8 4 1 R 1 R 0 giving

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**Decimal to binary – 2 steps**

Divide decimal number by 2 until result is zero Starting at the bottom, list the remainders

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Task Convert the following decimal numbers to binary using the division method 41 125 96 37

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Answers 2 41 20 R1 10 R0 5 1 2 125 62 R1 31 R0 15 7 3 1 2 96 48 R0 24 12 6 3 1 R1 2 37 18 R1 9 R0 4 1 41 = 37 = 125 = 96 =

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**Decimal to binary – table method – 5 steps**

Create table with place values (most significant place should be higher than decimal numebr) Insert a 1 in the highest place which is less than decimal number Subtract place value from number Repeat until zero Fill blank columns with zeros

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**Table Method 41, 125, 96, 37 41-32=9 9-8=1 1-1=0 125-64=61 61-32=29**

128 64 32 16 8 4 2 1 41-32=9 9-8=1 1-1=0 125-64=61 61-32=29 29-16=13 13-8= 5 5-4=1 96-64=32 32-32=0 37-32=5 5-4=1 1-1=0

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**Convert the following numbers to binary using the table method**

Task Convert the following numbers to binary using the table method 28 53 101 84

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Answers

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Note! Question - How do you know if a number is binary or decimal (e.g. 101) Answer – you will be told in the question.

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**Convert the following decimal numbers to binary using the division method**

41 125 96 37

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Task 1 Work out the following Number of bits (n) Range of numbers Number of values Show all working!

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Task 2 Answer Qs 1-8 from booklet (in jotter or in a word document at computer) Glossary i-table.html

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**Binary Arithmetic & Negative Whole Numbers**

Lesson 3 Binary Arithmetic & Negative Whole Numbers

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**Basic Binary Arithmetic**

_ 1 _ 1 _ 1 __ 10 11 10 ___ 101 11 ___ 110 1 Try these sums:- 10+110

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**Binary Arithmetic - Answers**

1 1 1

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Negative Integers Positive numbers are straightforward Difficulty arises when we need to store negative numbers! There are several methods.

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**Negative Numbers – Sign and Magnitude**

Simple! Use the most significant bit to store the sign 1 is –ve 0 is +ve Sign bit 64 32 16 8 4 2 1 9 -9

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Task Create a table using signed-bit (4 bits) which shows the range of numbers from -7 to +7 E.g. -7 … 7 values in between{

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**Signed bit - Answer A problem arises at zero**

-7 1111 -6 1110 -5 1101 -4 1100 -3 1011 -2 1010 -1 1001 ? 1000 0000 1 0001 2 0010 3 0011 4 0100 5 0101 6 0110 7 0111 A problem arises at zero This system creates a “negative zero” i.e. 1000 It also causes errors in arithmetic

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**Sign & Magnitude – Errors in Arithmetic**

In decimal, if you add (+3)+(-3), you get zero Try this in signed-bit Verdict – unsuitable Back to the drawing board! 0011 1011 ____ 1110

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**Rule – “Flip the bits and add 1” (remember basic arithmetic)**

Twos Complement Rule – “Flip the bits and add 1” (remember basic arithmetic) Now test… Decimal Binary Flip the bits Add 1 3 1 Ignore 1

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**Twos Complement Decimal Binary Flip the bits Add 1 20 00010100**

1 Ignore 1

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Reverse the process Twos complement number We know it’s negative because the most significant bit is a 1 To change to positive – flip the bits and add 1 = which is 20 Therefore is -20

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**Range of values for Twos Complement**

Most significant bit is reserved for the sign-bit Range is therefore –2(n-1) - 2(n-1)-1 E.g. 8 bits -27 to 27-1 -128 to +127 to

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Example continued =+ 127 -128 128 64 32 16 8 4 2 1 128 64 32 16 8 4 2 1

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Summary Twos complement representation is used to store both positive and negative numbers. Integer -3 -2 -1 1 2 3 Binary The leftmost bit is used to store whether a number is positive or negative. The rule is “Flip the bits and add 1”

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Summary The number of integers which could be stored in one byte ( 8 bits ) is 28 = 256 The range of integers which could be stored in one byte ( 8 bits ) is -128 to +127

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**Advantages of Two’s Complement**

There is only one zero Changing from positive-negative and negative-positive follows the same rule Arithmetic is correct Note : could be -128 usng two’s complement or 128 NOT using two’s complement. Interpret the system from the question or state your assumption!

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Task c) Convert the following decimal numbers to binary using 2’s complement i) -15 ii) -20 iii) -32 iv) -63 d) Using 2’s complement solve :- i) (-6) + (-8) ii) (-11) + (-21)

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Answers – c) i) ii)

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Answers d) d) i) -6 = = ii) -11 = =

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**Binary Real Numbers and Fractions**

Lesson 4 Binary Real Numbers and Fractions

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**Useful Fractional Values to remember**

1/2 0.5 1/4 0.25 1/8 0.125 1/16 0.0625

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**A real number is a decimal number like 12345.6789. **

Binary Fractions A real number is a decimal number like Binary real numbers are converted to binary fractions Place values to the right are ½, ¼, 1/8, 1/16 etc 8 4 2 1 . 1/2 1/4 1/8

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So… 8 4 2 1 . 1/2 1/4 1/8 3.5 12.75 1 . 9.25 1 . Real numbers are not always stored exactly as not every fraction can be made up exactly of 1/2 s, 1/4 s, 1/8 s etc. e.g. 1/3 or 1/5. This leads to round-off error and this can become larger when calculations are made with these inexact values.

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Real Numbers Real numbers are stored in a computer as floating point numbers. Used to store very large or very small numbers on computer Similar to standard form in Maths/Science

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**(the decimal place has been ‘floated’ 3 places to the left)**

Standard Form Example E.g. In decimal base 10, becomes * 103 (the decimal place has been ‘floated’ 3 places to the left) The ‘ ’ is called the mantissa. The ‘3’ is called the exponent. Between 1-10

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**mantissa x base exponent**

Note There are three values involved:- mantissa x base exponent

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**Storing Large Numbers on Computer**

The computer stores all data in binary. A disadvantage of using binary is that storing large numbers takes up a lot of memory space. e.g. Let us consider the largest number which we could store in 12 bits:- = 4095 This is a large amount of storage for a relatively small number! 2048 1024 512 256 128 64 32 16 8 4 2 1

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How the point floats… 59 1 000 101 110 011 010 001 100 x 2

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How the point floats… 14.75 1 100 000 001 011 010 x 2

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**The Point can float in either direction**

0.0625 1 000 -011 -010 -001 x 2

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**decimal number 25 = binary 11001**

Summary Binary is base 2. Example decimal number 25 = binary 11001 11001 becomes x 2101 The decimal point has been ‘floated’ 5 places to the left. Decimal 5 = binary 101 Binary numbers will always use base 2 so we need only store the mantissa (11001) and the exponent (101) Now think back to our 12-bit storage space. Supposing we used 8 bits to store the mantissa and 4 bits to store the exponent. What is the largest number which we can now store?

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**12 bits revisited Mantissa Exponent 128 64 32 16 8 4 2 1**

The largest mantissa which can be stored is = 255 The largest exponent which can be stored is 1111 = 15 So we can store x 21111 Which equals (float the decimal place 15 places to the right) Which equals decimal 32640!

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MARE Increasing the size of the storage for numeric data increases the range of numbers that can be stored. Increasing the size of the mantissa increases the accuracy with which the real number can be stored because it allows more digits to be stored. The range of numbers can be increased by increasing the size of the exponent. MARE

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**Two’s complement Floating Point**

Works the same way as two’s complement – most significant bit is used to store the sign bit. (Don’t get tied up with this!)

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Range or Accuracy? Program designers may have to decide between accuracy and range Accuracy may be favoured in Science, range may be favoured in Astronomy A very common storage allocation is to use four bytes for the mantissa and one byte for the exponent

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Other number systems

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Think How might a base 16 number system work?

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**Hexadecimal 0123456789ABCDEF Dec Bin Hex 0000 0x 9 1001 9x 10 1010 Ax**

0000 0x 9 1001 9x 10 1010 Ax 15 1111 Fx 127 7Fx

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**Task e) Display the following numbers using floating point notation :-**

i) ii) iii) e) Display the following numbers using floating point representation i) ii) iii)

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Tasks Read section on floating point and then answer questions 9-12 on page 10 of booklet

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Graphics Bit-Map Graphics

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Bit-Mapped Graphics For a graphic drawn in a painting package, the computer stores it as a two-dimensional array of pixels The number of pixels that makes up an image is called the resolution.

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**Black and White Graphics**

In a black and white display, each white pixel is represented by a 0. In a black and white display, each black pixel is represented by a 1. Only two values, 1 and 0, need to be stored as there are only two colours to be used.

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Colour Graphics However, when more than two colours are used we need more memory to store the colour value for each pixel. In an 8 colour display, each white pixel is represented by a 000. In an 8 colour display, each black pixel is represented by a 001. In an 8 colour display, each yellow pixel is represented by a 011.

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**Bit Depth Bit depth Colours 1 2 3 8 16 24 2 4 8 256 65536 16777216**

The number of bits used to represent the colour of the pixels is called the bit depth.

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**Bit mapped Storage Requirements**

An image, 5in by 7in is stored at 600 dpi in colours. How much memory would be required to store this image? Pixels used to store image = 5 x 7 x 600 x 600 = 65536 colours = 16 bits = 2 bytes Amount of memory = x 2 bytes = bytes = 24Mb

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File sizes Things which affect the size of a bit- mapped graphic are:- Number of colours (bit or colour depth) Number of pixels (resolution)

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**Advantages & Disadvantages of Bit Mapped Graphics**

The advantage of using bit mapped graphics is that you have more control over the graphic as you are able to go into detail and edit the graphic pixel by pixel. The disadvantage of using bit mapped graphics is that each picture or graphic takes up a lot of memory as the colour of each pixel has to be stored. Another disadvantage of using bit mapped graphics is that if you enlarge a bitmap image it becomes ‘blocky’.

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**Bitmap file extensions**

BMP JPG GIF TIFF

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Vector Graphics

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Vector Graphics In a CAD or drawing package, the computer stores information about an object by its attributes i.e. a description of how it is to be drawn. For a rectangle it might be: start x and y position length, breadth and angle of rotation thickness and colour of the lines colour fill etc.

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**Advantages of Vector Graphics**

The advantage of using vector graphics is that you edit shapes. This allows you to scale the graphic easily. Vector graphics are resolution independent It also means that vector graphics don’t take up a lot of memory.

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**Advantages of Vector Graphics**

The disadvantage of using vector graphics is that you are limited to using only the shapes that the package offers. This can mean that only simple graphics can be created. Vector graphics can also be slow to load or update as all the objects need to be recalculated and drawn from the attributes on file.

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Task Read notes on bit-maps & vector graphics and answer Qs 13 & 14 on Page 10 of booklet Binary test tomorrow – excl graphics. Bring a calculator.

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Object Oriented Data

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Synthesised Sound

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**Synthesised Sound Data (MIDI)**

standard file type for musical files an object orientated method of storing and reproducing sound sounds are generated by using short recordings of the real instruments (samples). these samples are stored in memory of the sound card (called a wave-table). stored digitally but can be converted into text allowing it to be edited by a text editor MIDI files contains a maximum of 16 channels, with each channel playing a different instrument.

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**MIDI – Input hardware and Software**

MIDI editing software (e.g. Anvil) + computer with WIMP interface Computer + MIDI instrument (keyboard/guitar/drum/wind controller)

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MIDI Software Cakewalk Magix Anvil Studio Instruments Cubase MidiSoft Studio

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**Features of MIDI Sequencing Software**

Piano roll display Records played notes on a grid Score Display Displays musical notes Mixing desk Enables channels to be combined and special effects to be applied

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MIDI – Input hardware A MIDI keyboard usually looks just like a standard synthesiser keyboard. The musician plays the notes while the computer software records the notes played, duration of each note and the volume etc.

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Processing To synthesise an instrument the soundcard calls on a sample from the wave-table and manipulates it to produce different notes. For a realistic synthesis, several samples may be used to produce the sound for a single instrument, Soundcards can also apply effects such as echo and reverb. These effects selected by the MIDI events are applied by the sound processor in the sound card.

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MIDI File Format A Midi file starts with a header which contains information such as the tempo of the tune A midi file will contain a sequence of messages such as start of a note channel to use pitch of the note volume to play it at end of a note

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**Advantages of MIDI Smaller file size**

All aspects of the music can be edited (mistakes can be corrected) Effects can be applied to individual instruments There is no interference or background noise from the recording

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Disadvantages of MIDI Dependent on soundcard for quality of sound Realistic piano and percussion sounds have been created, but others, like guitars, still sound synthetic (even with an expensive sound card) No vocals Fewer effects can be applied to the sound

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