Higher Computing

Mr Arthur

Course Outline

3 Main Units Computer Systems = 40 hours Software Development = 40 hours Artificial Intelligence = 40 hours

Assessment 3 End of Unit Assessments (NABS) Practical Coursework Tasks (/60 or 30%) Written Exam (/140 or 70%)

Computer Systems

5 units in the Computer Systems Section1. Data Representation = 6 hours

2. Computer Structure = 7 hours

3. Peripherals = 5 hours

4. Networking = 9 hours

5. Computer Software = 9 hours

Aims of Lesson 1

1. How are numbers, text and images represented inside the computer system?

2. Discussing the 2 state computer system

3. Converting positive whole numbers to binary and vice versa

4. Playing Binary Bingo

Data Representation

100 billion switches per sq. cm

Data Storage

Numbers, Text, and Images are all stored as a series of 1s and 0s inside the computer system.

These series of 1s and 0s are made up of pulses of electricity from 1 volt to 5 volts

Decimal Counting System

When we represent numbers we use the decimal counting system, for example

123,000

100,000 10,000 1,000 100 10 1

1 2 3 0 0 0 Since the computer is 2 state, the binary counting

system goes up by the power 2, rather than 10 i.e

256 128 64 32 16 8 4 2 1

How Positive Whole Numbers are Stored

34

128 64 32 16 8 4 2 1

0 0 1 0 0 0 1 0

= 32 + 2 134

128 64 32 16 8 4 2 1

1 0 0 0 0 1 1 0

= 128 + 4 + 2

Binary back to Decimal

1011 0011

128 64 32 16 8 4 2 1

1 0 1 1 0 0 1 1

= 128 + 32 + 16 + 2 + 1

=179

Binary to Decimal

1. What is the decimal representation of the following 8 bits using 2s complement

(a) 0001 0110

(b) 1000 1100

(c) 0111 0011

2. What is the 8 bit representation of the following decimal numbers

(a) 174

(b) 121

(c) 71

Binary Bingo

42 81 21 16 121 73 101 75 127

13 209 32 56 175 192 186 176 121

Data Storage

1 or 0 = 1 bit 8 bits = 1 byte 1024 bytes = 1 kilobyte 1024 kilobytes = 1 megabyte 1024 megabytes = 1 gigabyte

Aims of Lesson 2

1. Representation of negative whole numbers

2. The 2s complement system

Representing Negative Numbers

The signed bit method

0000 0001 = 1

0000 0000 = 0

1000 0001 = -1

1000 0010 = -2

1000 0011 = -3

1000 0100 = -4

Representing Negative Numbers

There is a problem with this method??

Using 8 bits you can only store the decimal numbers from

128 64 32 16 8 4 2 1

1 1 1 1 1 1 1 1

= 64 +32+16+8+4+2+1 = -127

128 64 32 16 8 4 2 1

0 1 1 1 1 1 1 1

=64+32+16+8+4+2+1=127

Rather than -255 to 255

2s Complement

What is the 8 bit two’s complement representation of the decimal number -101

101128 64 32 16 8 4 2 10 1 1 0 0 1 0 1Invert numbers1 0 0 1 1 0 1 0

+1-1011 0 0 1 1 0 1 1

Negative Whole Numbers What is the decimal representation of the

following 8 bits using 2s complement 1 0 1 0 1 1 1 1You invert every number0 1 0 1 0 0 0 0Then add 10 1 0 1 0 0 0 1128 64 32 16 8 4 2 164+16+1 -81

2s Complement Questions

1. What is the decimal representation of the following 8 bits using 2s complement

(a) 1000 1011

(b) 1100 1100

(c) 1001 0111

(d) 1110 1100

2. What is the 8 bit two’s complement representation of the following decimal numbers

(a) -45

(b) -121

(c) -176

(d) -71

Aims of Lesson 3

1. So far we have looked at representing positive and negative whole numbers using binary

2. We are now going to look at the representation of non whole numbers using the floating point system

Representing Non Whole Numbers

How do we represent the number 128.75 in binary?

128 + 0.5 + 0.25 = 128.75

128 64 32 16 8 4 2 1 0.5 0.25 0.125 0.0625

1 0 0 0 0 0 0 0 1 1 0 0

Mantissa and Exponent

Mantissa

Exponent

8

8 4 2 1

1 0 0 0

128 64 32 16 8 4 2 1 0.5 0.25 0.125 0.0625

1 0 0 0 0 0 0 0 1 1 0 0

1 0 0 0 0 0 0 0 1 1 0 0

Mantissa

Exponent

6

8 4 2 1

0 1 1 0

1 0 0 1 1 0 0 0 1 0

1 0 0 1 1 0 0 0 1 0

How do we represent the number 38.125 using floating point

32 16 8 4 2 1 0.5 0.25 0.125 0.0625

Representing Non Whole Numbers

Mantissa relates to the precision of the number you can represent i.e 34.44454321

Exponent relates to the range of the number

1111 = 15

1111 1111 = 255

8 4 2 1 0.5 0.25 0.125 0.075 0.0375 0.01875 0.009375

What is the decimal number if the Mantissa is

10010011 and the exponent is 0101

Exponent

8 4 2 1

0 1 0 1

= 5

Mantissa

1 0 0 1 0 0 1 1

Mantissa and Exponent

16 8 4 2 1 0.5 0.25 0.125

16 + 2 + 0.25 + 0.125 =18.375

Aims of Lesson 4

1. So far we have looked at representing positive and negative whole numbers using binary

2. We have also looked at representing non whole numbers using floating point.

3. Today we are going to practice converting storage capacities from bit, byte, kilobyte, megabyte, gigabyte, terabyte

4. Discuss how text is represented in a computer system

Storage Capacities

0 or 1 = 1 bit

8 bits = 1 byte

1024 bytes = 1 Kilobyte

1024 Kilobytes = 1 Megabyte

1024 Megabytes = 1 Gigabyte

1024 Gigabytes = 1 Terabyte

Storage Conversions

I have a 2 Gigabyte IPOD Classic. How many 512Kb songs can I store on the IPOD?

Convert 2Gb to Kb 2 X 1024 = 2048Mb 2048 X 1024 = 2,097,152Kb

512Kb 4096 Songs

Storage Conversion Questions

1. I have a memory card for a Digital Camera with a capacity of 4Gb. How many 460Kb images can I store on the memory card?

2. Mr Haggarty has recently been working as a DJ at weekends. He has bought an external hard disk to back up songs. How many 4Mb songs would he be able to fit on the 80Gb hard disk?

Solutions

4Gb X 1024 = 4096Mb 4096 X 1024 =

4,194,304Kb

460Kb

= 9118 images

80Gb X 1024 = 81920Mb

4Mb

= 20,480 songs

How is Text Represented ASCII

Each key on the keyboard is converted into a binary code using 7 bits

Using 7 bits i.e 2 = 128 characters can be represented

Character Set A list of all the characters

which the computer can process

Control Characters Codes 0 to 31 are non

printable characters

7

Character Binary Decimal

tab 000 1001 9

return 000 1101 13

space 010 0000 32

! 010 0001 33

‘ 010 0010 34

1 011 0001 49

A 100 0001 65

a 110 0001 97

How is Text Represented

Unicode (Universal Code) Each key on the keyboard is converted into a binary code

using 16 bits Using 16 bits i.e 2 = 65,536 characters can be

represented Can represent Latin, Roman, Japanese characters

Advantages More characters can be represented

Disadvantages Takes up more than twice as much space for each

character

16

Aims of Lesson 5

Last Lessons Representing positive

whole numbers as binary Representing negative

whole numbers using 2s complement

Non whole numbers using mantissa and exponent

Storage calculations Looked at how text is

represented using ASCII and Unicode

Today’s Lesson 1. Discuss graphic

representation2. Calculate storage

capacities of colour Bit Map graphics

3. Bit Map v Vector

BIT Map GraphicsSCREEN MEMORY

PIXEL

MEMORY REQUIRED

8 BITS X 8 BITS = 64 BITS

= 8 BYTES

Bit Map = the graphic is made up from a series of pixels

Graphics Resolution

The smaller the size of the pixels, the finer the detail of the image

800 x 600 pixels lower quality than 1024 x 768

As the number of pixels increases so does the storage space required

Pixel Pattern using 8x8 grid

Pixel Pattern using 16x16 grid

Calculating Storage Capacities of Bit Mapped Images

Storage Requirements = total number of pixels * number of bits used for each pixel

This picture of Mr Haggarty has a resolution of 300dpi. The image is 2 inches by 4 inches in 128 colours

300 X 2 = width 600 pixels

300 X 4 = height 1200 pixels

Total pixels = 600 X 1200 = 720,000 pixels

Each pixel = 7 bits i.e. 2 = 128 colours

720,000 X 7 = 5,040,000 bits / 8 = 630,000 bytes

630,000 / 1024 = 615Kb

7

Bit Map V Vector Graphics

Bit Map Graphic Bit map packages paint

pictures by changing the colour of the pixels

Known as “Paint Packages” When shapes overlap, the

one on top rubs out the other

When you save a file the whole screen is saved

The resolution of the image is fixed when you create the image

Vector Graphic Work by drawing objects on

the screen Known as “Draw Packages” When shapes overlap they

remain as separate objects Only the object attributes

are stored taking up much less space

Resolution Independent

Aims of Lesson 6Last Lessons Representing positive whole

numbers as binary Representing negative

whole numbers using 2s complement

Non whole numbers using mantissa and exponent

Storage calculations Looked at how text is

represented using ASCII and Unicode

Discuss graphic representation

Calculate storage capacities of colour Bit Map graphics

Bit Map v Vector

Today’s Lesson 1. Discuss true colour

Today’s Tasks1. Complete Data

Representation Questions2. Read chapter in the book

True Colour Bit Depth (Colour Depth)

The number of bits used to represent colours in the graphic 1 bit = black or white 2 bits = 4 colours 3 bits = 8 colours 8 bits = 256 colours 24 bits = 16,777,216 colours this is true colour

True Colour 24 bits

8 bits for red 8 bits for blue 8 bits for green

Bit Depth = 1 bit

Human eye cannot distinguish between adjacent shades of grey when looking at more than 200 shades between black and white

Bit Depth = 2 bit

Bit DepthsBit Depth = 2 bits

01

10

11

00

Solutions

Question 1 2 inches X 90 = 180 pixels 2 inches X 90 = 180 pixels 180 X 180 = 32,400 pixels

in total 256 colours = 2 power 8 32,400 X 8 = 259,200 bits 259,200/8 = 32,400 bytes 32,400 / 1024 = 31.6Kb

Question 2 5 inches X 200 = 1000

pixels 3 inches X 200 = 600 pixels 1000 X 600 = 600,000

pixels in total 128 colours = 2 power 7 600,000 X 7 = 4,200,000

bits 4,200,000/8 = 525,000

bytes 525,000 / 1024 = 512.7Kb

Aims of Lesson 7Last Lessons Representing positive whole

numbers as binary Representing negative

whole numbers using 2s complement

Non whole numbers using mantissa and exponent

Storage calculations Looked at how text is

represented using ASCII and Unicode

Discuss graphic representation

Calculate storage capacities of colour Bit Map graphics

Bit Map v Vector True Colour

Today’s Lesson 1. Data Compression

Today’s Tasks1. Complete Compression task2. Issue Scholar logins3. Complete Data

Representation Questions Sheet

4. Read chapter in the book

Compression

Data compression means reducing the size of a file in order to save backing storage space.

2 types of compression Lossless compression Lossy compression

Lossless Compression

Lossless means that none of the original data is lost

One method of lossless compression involves counting repeating pixels

COLOUR = 10011000 11100000 e.g. 16 bits

NUMBER OF THE SAME PIXELS = 32

100000

STORAGE REQUIRED = 16 BITS + 6 BITS = 22 BITS

Lossy Compression Lossy compression involves

sacrificing some of the data in order to reduce the file size

Deliberately losing some types of information that our eyes and brains usually ignore

Lossy is only suitable if the loss of data will not cause the file to become useless

JPEG is a file format that uses lossy compression to reduce file sizes

Data Representation – Learning Aims

1. Representation of positive numbers in binary up to 32 bits

2. Conversion from binary to decimal and vice versa3. Representation of negative numbers using 2s

complement4. Representation of non whole numbers using

floating point with mantissa and exponent5. Conversion to and from bit, byte, kilobyte,

megabyte, gigabyte, terabyte

Data Representation – Learning Aims

6. Unicode and its advantages over ASCII

7. Description of the bit map method of graphics representation

8. Description of the relationship between bit depth and the number of colours represented up to 24 bit depth

9. Vector graphics

10. Relationship between bit depth and file size