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Higher Computing Computer Systems J L Martin 1 Higher Computing Computer Systems

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Higher Computing Computer Systems J L Martin 2 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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Higher Computing Computer Systems J L Martin 3 Assessment 1 written NAB (? 4/2/2010) 1 practical NAB (? 17-25/3/2010) Coursework (? 17-25/2/2010)

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Higher Computing Computer Systems J L Martin 4 Homework Weekly consolidation questions/tasks 1 week to complete substantial HWs Glossary of definitions Mindmaps

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Higher Computing Computer Systems J L Martin 5 Resources Course booklets PowerPoints will be put on network Practice NABs (online) Blank glossary Learning Intentions Mindmap software

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Higher Computing Computer Systems J L Martin 6 Expectations Consistent application throughout is essential Course will be fast paced Written answers require depth, detail and maturity

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Higher Computing Computer Systems J L Martin 7 Course Files P:/ Drive 5&6 Year Progs Computing Department Higher Computing Computer Systems

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Higher Computing Computer Systems J L Martin 8 Data Representation – Technical terms 6 hours

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Higher Computing Computer Systems J L Martin 9 Units of Measurement Decimal number system –0-9 –Powers of 10 1000s100s10sUnits 10 3 10 2 10 1 10 0 12 5281

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Higher Computing Computer Systems J L Martin 10 Units of Measurement Binary number system –0, 1 2121 22929 512 2 42 10 1024 2323 82 11 2048 2424 162 12 4096 2525 322 13 8192 2626 642 14 16384 2727 1282 15 32768 2828 2562 16 65536

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Higher Computing Computer Systems J L Martin 11 Scales Units1 Kilo 1000 (thousand) 10242 10 Mega 1,000,000 (million) 1024x10242 20 Giga 1,000,000,000 (billion) 1024x1024x10 24 2 30 Tera 1,000,000,000,000 (trillion) 1024x1024x 1024x1024 2 40

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Higher Computing Computer Systems J L Martin 12 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 1.Convert 553,476 bits into Kb 2.How many bytes in 91 Mb?

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Higher Computing Computer Systems J L Martin 13 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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Higher Computing Computer Systems J L Martin 14 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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Higher Computing Computer Systems J L Martin 15 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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Higher Computing Computer Systems J L Martin 16 Memory Measured in Mb or Gb E.g. 512Mb upwards

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Higher Computing Computer Systems J L Martin 17 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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Higher Computing Computer Systems J L Martin 18 Resolution Printers measured in dots per inch (dpi) –E.g. Laser printer 2400dpi –Ink jet 750 dpi Monitors measured in pixels –E.g. 1024 x 768 pixels

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Higher Computing Computer Systems J L Martin 19 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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Higher Computing Computer Systems J L Martin 20 Counting in Binary Learn these place values! = 128+32+16+4+1 = 181 2727 2626 2525 2424 23232 2121 2020 1286432168421 10110101

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Higher Computing Computer Systems J L Martin 21 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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Higher Computing Computer Systems J L Martin 22 Why do we use binary? Numbers are long Difficult to read, write and recognise Value is “hidden” from humans

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Higher Computing Computer Systems J L Martin 23 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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Higher Computing Computer Systems J L Martin 24 Bits and Values The number of bits determines the number of values which can be represented

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Higher Computing Computer Systems J L Martin 25 # of bits (n) i.e. Range (Zero to 2 n -1) Number of values (2 n) 10, 10-12 200,01,10,110-34 40000-11110-1516 8 00000000- 11111111 0-255256 16Two bytes0-6553565536 (64k) 24Three bytes0-16,777,21516,777,216 (16 Mb) 32Four bytes0-4,294.967,295 4,294,967,296 (4 Gb) Bits and Values

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Higher Computing Computer Systems J L Martin 26 Data Types Computers need to represent different types of data:- –Text –Numbers (integers and real) –Graphics –Sound –etc

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Higher Computing Computer Systems J L Martin 27 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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Higher Computing Computer Systems J L Martin 28 ASCII Each character is stored in 1 byte Only 7 bits are used (with leading zero) 7 bits = 128 characters (2 7 ) E.g. –A is 01000001 or 65 –0 is 00110000 or 48

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Higher Computing Computer Systems J L Martin 29 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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Higher Computing Computer Systems J L Martin 30 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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Higher Computing Computer Systems J L Martin 31 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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Higher Computing Computer Systems J L Martin 32 Lesson 2 Binary – Decimal Conversion

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Higher Computing Computer Systems J L Martin 33 Homework Homework questions – Data Representation 1 For 17/6/09

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Higher Computing Computer Systems J L Martin 34 Data Representation - Numbers Decimal umbers are converted into binary in order to be stored.

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Higher Computing Computer Systems J L Martin 35 Converting binary to decimal Here is an example of how to convert the binary number 10011010 to a decimal: 1286432168421 1 0 0 11010 = 128 + 16 + 8 + 2 = 154.

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Higher Computing Computer Systems J L Martin 36 Binary to Decimal – 3 steps 1)Draw an appropriately sized table with place values (8,16,24,32) 2)Fill the binary number from right to left 3)Add together the place values which have 1s

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Higher Computing Computer Systems J L Martin 37 Task Convert the following binary numbers to decimal (a) 111101010010 (b) 11011001010101 (c) 1011001011010100 (d) 10010101 (e) 1000001101001111

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Higher Computing Computer Systems J L Martin 38 Task Convert the following binary numbers to decimal (a) 111101010010 - 3922 (b) 11011001010101 - 13909 (c) 1011001011010100 - 45780 (d) 10010101 - 149 (e) 1000001101001111 - 33615

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Higher Computing Computer Systems J L Martin 39 Converting decimal to binary – division method Here is an example of how to convert the decimal number 69 to a binary: 2222222222222222 69 34 17 8 4 2 1 0 R 1 R 0 R 1 R 0 R 1 giving 1000101

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Higher Computing Computer Systems J L Martin 40 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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Higher Computing Computer Systems J L Martin 41 Task Convert the following decimal numbers to binary using the division method –41 –125 –96 –37

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Higher Computing Computer Systems J L Martin 42 Answers 241 220R1 210R0 25 22R1 21R0 20R1 41 = 101001 2125 262R1 231R0 215R1 27 23 21 20 125 = 1111101 296 248R0 224R0 212R0 26 23 21R1 20 237 218R1 29R0 24R1 22R0 21 20R1 96 = 1100000 37 = 100101

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Higher Computing Computer Systems J L Martin 43 Decimal to binary – table method – 5 steps 1)Create table with place values (most significant place should be higher than decimal numebr) 2)Insert a 1 in the highest place which is less than decimal number 3)Subtract place value from number 4)Repeat until zero 5)Fill blank columns with zeros

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Higher Computing Computer Systems J L Martin 44 Table Method 41, 125, 96, 37 1286432168421 101001 1111101 1100000 100101 41-32=9 9-8=1 1-1=0 125-64=61 61-32=29 29-16=13 13-8= 5 5-4=1 1-1=0 96-64=32 32-32=0 37-32=5 5-4=1 1-1=0

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Higher Computing Computer Systems J L Martin 45 Task Convert the following numbers to binary using the table method –28 –53 –101 –84

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Higher Computing Computer Systems J L Martin 46 Answers 28 - 11100 53 - 110101 101 - 1100101 84 - 1010100

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Higher Computing Computer Systems J L Martin 47 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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Higher Computing Computer Systems J L Martin 48 Convert the following decimal numbers to binary using the division method 41 125 96 37

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Higher Computing Computer Systems J L Martin 49 Task 1 Work out the following Number of bits (n) Range of numbers Number of values Show all working!

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Higher Computing Computer Systems J L Martin 50 Task 2 Answer Qs 1-8 from booklet (in jotter or in a word document at computer) Glossary http://web.cs.mun.ca/~michael/c/asci i-table.html

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Higher Computing Computer Systems J L Martin 51 Lesson 3 Binary Arithmetic & Negative Whole Numbers

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Higher Computing Computer Systems J L Martin 52 Basic Binary Arithmetic Try these sums:- a)10+110 b)110 + 1101 c)1011 + 1111 00_000_0 01_101_1 10_110_1 1 __ 10 11 10 ___ 101 11 ___ 110 1

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Higher Computing Computer Systems J L Martin 53 Binary Arithmetic - Answers 10 110 1000 110 1011 10001 1011 1111 11010

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Higher Computing Computer Systems J L Martin 54 Negative Integers Positive numbers are straightforward Difficulty arises when we need to store negative numbers! There are several methods.

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Higher Computing Computer Systems J L Martin 55 Negative Numbers – Sign and Magnitude Simple! Use the most significant bit to store the sign 1 is –ve 0 is +ve Sign bit 6432168421 000010019 10001001-9

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Higher Computing Computer Systems J L Martin 56 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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Higher Computing Computer Systems J L Martin 57 Signed bit - Answer A problem arises at zero This system creates a “negative zero” i.e. 1000 It also causes errors in arithmetic -71111 -61110 -51101 -41100 -31011 -21010 1001 ?1000 00000 10001 20010 30011 40100 50101 60110 70111

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Higher Computing Computer Systems J L Martin 58 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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Higher Computing Computer Systems J L Martin 59 Twos Complement Rule – “Flip the bits and add 1” (remember basic arithmetic) Now test… DecimalBinaryFlip the bits Add 1 3000000111111110011111101 00000011 11111101 00000000 1 Ignore

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Higher Computing Computer Systems J L Martin 60 Twos Complement DecimalBinaryFlip the bits Add 1 20000101001110101111101100 00010100 11101100 00000000 1 Ignore

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Higher Computing Computer Systems J L Martin 61 Reverse the process Twos complement number 1110 1100 We know it’s negative because the most significant bit is a 1 To change to positive – flip the bits and add 1 0001 0011 + 1 = 0001 0100 which is 20 Therefore 1110 1100 is -20

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Higher Computing Computer Systems J L Martin 62 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 – -2 7 to 2 7 -1 – -128 to +127 – 1000 0000 to 0111 1111

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Higher Computing Computer Systems J L Martin 63 Example continued 0111 1111 =+ 127 1000 0000 -128 1286432168421 01111111 1286432168421 10000000

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Higher Computing Computer Systems J L Martin 64 Summary The leftmost bit is used to store whether a number is positive or negative. The rule is “Flip the bits and add 1” Twos complement representation is used to store both positive and negative numbers. Integer -3 -2 0 1 2 3 Binary 11111101 11111110 11111111 00000000 00000001 00000010 00000011

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Higher Computing Computer Systems J L Martin 65 Summary The number of integers which could be stored in one byte ( 8 bits ) is 2 8 = 256 The range of integers which could be stored in one byte ( 8 bits ) is -128 to +127

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Higher Computing Computer Systems J L Martin 66 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 : 1000 000 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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Higher Computing Computer Systems J L Martin 67 Task c)Convert the following decimal numbers to binary using 2’s complement i) -15ii) -20iii) -32iv) -63 d)Using 2’s complement solve :- i)(-6) + (-8)ii)(-11) + (-21)

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Higher Computing Computer Systems J L Martin 68 Answers – c) i)1111 0001 ii)1110 1100 iii)1110 0000 iv)1100 0001

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Higher Computing Computer Systems J L Martin 69 Answers d) d)i)-6 = 0000 0110-8 =0000 1000 1111 10011111 0111 +1 -61111 10101111 1000 -81111 1000 -141111 0010 ii)-11 =0000 1011-21 =0001 0101 1111 01001110 1010 +1 +1 -111111 01011110 1011 -211110 1011 -321110 0000

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Higher Computing Computer Systems J L Martin 70 Lesson 4 Binary Real Numbers and Fractions

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Higher Computing Computer Systems J L Martin 71 Useful Fractional Values to remember 1/20.5 1/40.25 1/80.125 1/160.0625

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Higher Computing Computer Systems J L Martin 72 Binary Fractions A real number is a decimal number like 12345.6789. Binary real numbers are converted to binary fractions Place values to the right are ½, ¼, 1/8, 1/16 etc 8421.1/21/41/8

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Higher Computing Computer Systems J L Martin 73 So… 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. 8421.1/21/41/8 3.511.1 12.751100.11 9.251001.01

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Higher Computing Computer Systems J L Martin 74 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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Higher Computing Computer Systems J L Martin 75 Standard Form Example E.g. In decimal base 10, 1234.56 becomes 1.23456 * 10 3 (the decimal place has been ‘floated’ 3 places to the left) The ‘1.23456’ is called the mantissa. The ‘3’ is called the exponent. Between 1-10

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Higher Computing Computer Systems J L Martin 76 There are three values involved:- mantissa x base exponent Note

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Higher Computing Computer Systems J L Martin 77 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! Storing Large Numbers on Computer 204810245122561286432168421 111111111111

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Higher Computing Computer Systems J L Martin 78 How the point floats… 1 1 1 0 1 1 x 2 1 010001011100000101110 59

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Higher Computing Computer Systems J L Martin 79 How the point floats… 1 1 1 0 1 1 x 2 1 010001011100000 14.75

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Higher Computing Computer Systems J L Martin 80 The Point can float in either direction 0 0 0 0 1 x 2 1 -010-011000 0.0625

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Higher Computing Computer Systems J L Martin 81 Binary is base 2. Example decimal number 25 = binary 11001 11001 becomes.11001 x 2 101 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? Summary

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Higher Computing Computer Systems J L Martin 82 12864321684218421 111111111111 MantissaExponent The largest mantissa which can be stored is 11111111 = 255 The largest exponent which can be stored is 1111 = 15 So we can store.11111111 x 2 1111 Which equals 111111110000000 (float the decimal place 15 places to the right) Which equals decimal 32640! 12 bits revisited

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Higher Computing Computer Systems J L Martin 83 MARE 1.Increasing the size of the storage for numeric data increases the range of numbers that can be stored. 2.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. 3.The range of numbers can be increased by increasing the size of the exponent. 4.MARE

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Higher Computing Computer Systems J L Martin 84 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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Higher Computing Computer Systems J L Martin 85 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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Higher Computing Computer Systems J L Martin 86 Other number systems

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Higher Computing Computer Systems J L Martin 87 Think How might a base 16 number system work?

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Higher Computing Computer Systems J L Martin 88 Hexadecimal 0123456789ABCDEF DecBinHex 000000x 910019x 101010Ax 151111Fx 1270111 11117Fx

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Higher Computing Computer Systems J L Martin 89 Task e)Display the following numbers using floating point notation :- i)1010.110ii)010111.01 iii)100011.1010 e) Display the following numbers using floating point representation i) 11010.101ii) 1011.01 iii) 0111011.101

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Higher Computing Computer Systems J L Martin 90 Tasks Read section on floating point and then answer questions 9-12 on page 10 of booklet

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Higher Computing Computer Systems J L Martin 91 Graphics Bit-Map Graphics

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Higher Computing Computer Systems J L Martin 92 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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Higher Computing Computer Systems J L Martin 93 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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Higher Computing Computer Systems J L Martin 94 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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Higher Computing Computer Systems J L Martin 95 Bit Depth The number of bits used to represent the colour of the pixels is called the bit depth. Bit depthColours 1 2 3 8 16 24 2 4 8 256 65536 16777216

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Higher Computing Computer Systems J L Martin 96 Bit mapped Storage Requirements An image, 5in by 7in is stored at 600 dpi in 65536 colours. How much memory would be required to store this image? Pixels used to store image = 5 x 7 x 600 x 600 = 12600000 65536 colours = 16 bits = 2 bytes Amount of memory = 12600000 x 2 bytes = 25200000 bytes = 24Mb

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Higher Computing Computer Systems J L Martin 97 File sizes Things which affect the size of a bit- mapped graphic are:- 1.Number of colours (bit or colour depth) 2.Number of pixels (resolution)

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Higher Computing Computer Systems J L Martin 98 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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Higher Computing Computer Systems J L Martin 99 Bitmap file extensions BMP JPG GIF TIFF

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Higher Computing Computer Systems J L Martin 100 Vector Graphics

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Higher Computing Computer Systems J L Martin 101 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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Higher Computing Computer Systems J L Martin 102 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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Higher Computing Computer Systems J L Martin 103 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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Higher Computing Computer Systems J L Martin 104 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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Higher Computing Computer Systems J L Martin 105 Object Oriented Data

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Higher Computing Computer Systems J L Martin 106 Synthesised Sound

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Higher Computing Computer Systems J L Martin 107 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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Higher Computing Computer Systems J L Martin 108 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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Higher Computing Computer Systems J L Martin 109 MIDI Software Cakewalk Magix Anvil Studio Instruments Cubase MidiSoft Studio

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Higher Computing Computer Systems J L Martin 110 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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Higher Computing Computer Systems J L Martin 111 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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Higher Computing Computer Systems J L Martin 112 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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Higher Computing Computer Systems J L Martin 113 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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Higher Computing Computer Systems J L Martin 114 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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Higher Computing Computer Systems J L Martin 115 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 (e ven with an expensive sound card) No vocals Fewer effects can be applied to the sound

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