1. Denary to Binary Numbers & Binary to Denary
Chapter 4 Data Representation

2. Units Bit – 1 bit Nibble – 4 bits Byte – 8 bits
Kilobyte – 1024 bytes or 1024x8 bits
Megabyte – 1024 kilobytes
Gigabyte – 1024 megabytes
Terabyte – 1024 gigabytes
Petabyte - a unit of information equal to one thousand million million (1015) or, strictly, 250 bytes.

3. What is a denary number?
These numbers we use in our everyday lives are called ‘denary’ numbers, it is also referred to as “Base-10”, which uses the power of 10: 1000, 100, 10, 1.

4. Binary
Base of 2
128 64 32 16 8 4 2 1
When given a number to convert to binary you need a sequence of 0’s and 1’s.
To be able to convert deniary numbers to binary you have to firstly pick the first lowest number under the decimal number given.
Then how many digits backwards are you going to use to add together to make the number.
e.g. 42
First lowest number under this from the table above is 32 so this is where I will start:
= this will get 42
1x32 =32
0x16=0
1x8=8
0x4=0
1x2=2
0x1=0
Add all these together will get 42.

5. Binary Another example 228 128 64 32 16 8 4 2 1
What combinations of the numbers before will make 228?
128 64 32 16 8 4 2 1
Answer: Binary =228 (denary)

6. 4-bit binary numbers 13 = 9 = 14 = 11 = 7 = 5 = 8 = 8 4 2 1
Convert the following denary numbers into 4-bit binary, also referred to as Base-2.
13 =
9 =
14 =
11 =
7 =
5 =
8 =
G:\ICT\Miss Elliott\Year \Chapter 3 - Data Representation\worksheet6 – Denary to Binary

7. Binary to denary numbers
Now convert back from binary to denary
1100
0011 8 4 2 1 x X
8 +
4 +
0 +
0 =16 8 4 2 1 x X
0 +
2 +
1 =3
What would happen if the denary number was 23?
Can you write this as 4-bit binary?

8. Binary to denary numbers
Convert the following 4-bit binary numbers into whole denary numbers:
0001 =
0 =
1111 =
1100 =
0011 =
G:\ICT\Miss Elliott\Year \Chapter 3 - Data Representation\worksheet6 – Denary to Binary

9. 8-bit binary numbers =byte
128 64 32 16 8 4 2 1
Convert the following denary numbers into 8-bit binary, also referred to as Base-2.
220 =
300 =
132 =
144 =
G:\ICT\Miss Elliott\Year \Chapter 3 - Data Representation\worksheet6 – Denary to Binary

10. Overflow What is binary overflow?
Watch the video and write a summary in word of what it is.

11. HEX to Denary Denary 5 0 Binary 0011 0010 Hex 3 2
BASE of 16
For HEX to be worked out remember:
3 2
X x
16 1
= 50

12. 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F

13. TASK: worksheet – Binary to Hex
Studentshare\ICT\Miss Elliott\Yr 10\Theory2\Chapter 3 Data representation\ Worksheet 9 EXTENSION 1 on the sheet EXTENSION 2 worksheet 10

14. Starter

16. TASK: worksheet– Binary to Hex
Studentshare\ICT\Miss Elliott\Yr 10\Theory2\Chapter 3 Data representation\ Worksheet 9 EXTENSION 1 on the sheet EXTENSION 2 worksheet 10

17. Hex to Denary to Binary 7A FE 9F 2B
EXTENSION: 8C 3D EF A9 F1 A0

18. Bits and Bytes
G:\ICT\Miss Elliott\Year \Chapter 3 - Data Representation\worksheet 11
EXTENSION

19. Binary Addition
0 + 0 = =1 0+1=1 1+1=10

20. Starter

21. Binary Addition – worksheet 12
G:\ICT\Miss Elliott\Year \Chapter 3 - Data Representation\worksheet 12 Extension: Convert additions to denary

22. Binary Addition
EXTENSION: Can you convert the following Denary values to Hex?

23. Starter
overflow + + + + + +

24. TASK - extension
TASK - extension
Workbook page: 79-80

25. Recap - starter What is binary? 0’s and 1’s switches on and off
What is HEX? Base 16
What is denary? Base 10 normal whole number
What is over flow? Adds up to more than 255
Extension:
Or type in binary quiz bitesize this link is the first link

26. Revision
Binary - 22
HEX – 2A
Denary - 15

27. Recap Q’s – worksheet 14 - REVISION G:\ICT\Miss Elliott\Year \Chapter 3 - Data Representation
What would the denary number 199 be in binary?
What would the denary number 55 be in binary?
What would the denary number 222 be in binary?
What would be as a denary number?
What would be as a denary number?
What would be as a binary number?
What is an overflow error?

28. Starter Recap 0+0=0 1+0=1 0+1=1 1+1=10 1+1+1=11 01010111 11101110

29. Shifting binary numbers

30. DIV MOD
DIV?
MOD?
e.g. 7/2
DIV = 3
MOD = 1

31. Starter

32. ASCII – American Standard Code for Information Interchange

33. Activity – Worksheet 13 – ASCII Table
G:\ICT\Miss Elliott\Year \Chapter 3 - Data Representation
EXTENSION: Create your own ASCII message

34. TASK - extension
TASK - extension
Workbook page: 81

35. Complete the table up to letter y starting at r
G:\ICT\Miss Elliott\Year \Chapter 3 - Data Representation\worksheet 15 – ASCII Table (2)

36. Starter: Worksheet 15 page 2 Uni Code
Complete the uni code.

37. Representing Images
Pixels can be used to represent images. A pixel is short for picture element and is a single point in an image.

38. Representing Images
Images are displayed as a set of pixels which form together to make an image. Visual Display Units (VDUs / monitors) display images using pixels. A true high definition monitor will have 1920 pixels in width and 1080 pixels in height. This works out at a total of approximately 2 million pixels (2,073,600).

39. Higher quality Image
The higher the resolution (more pixels), the better quality an image will be. This is because there are more pixels which appear smaller and can’t be seen and so the ‘blocky’ pixelated effect is not noticed by the human eye. More pixels can also be used to create the image.

40. Bitmaps A bitmap is an image formed from pixels. Bitmap size
The size in pixels of a bitmap is calculated by multiplying the width of the image in pixels by the height of the image in pixels:
Bitmap size in pixels = Width x Height
The size in pixels is often referred to as the resolution of the image.

41. Bitmaps
G:\ICT\Miss Elliott\Year \Chapter 3 - Data Representation\Worksheet 16 – Bitmap Size
Left off of e-book at colour depth next

42. Starter – Bitmap Images
What is a Bitmap Image made up of?
How many pixels is this image made up of:
Remember it’s the whole grid
Reduce the pixels of this image what could it be changed too?
What is resolution?

43. Bitmap Images
Bitmaps are usually the most common file type for images. Bitmap images are made up of tiny dots called pixels.
Each colour of each pixel is represented in binary. The number of colours available in an image is related to the number of bits the code has?
What is binary made up of?
Black and white images only use two colours meaning they need 1 bit to represent each pixel, 0 for white and 1 for black. 1

44. Worksheet 17

45. Colour Depth and Resolution
Colour depth is the number of bits used for each pixel.
The resolution is the density of pixels in an image, how many pixels are within a certain are. It is normally measure in dots per inch (DPI)
The higher the resolution the more pixels in a certain area, so the better the quality of image.
Increasing the colour depth or resolution means the there are more bits in the image. This improves the quality of the image but also the file size.

46. Bitmap file size
The formula to calculate the minimum bitmap file size is:
Minimum Bitmap File Size (bits) = Width x Height x Colour Depth
Or Size (b) = W x H x D

47. Bitmap File Size Worksheet
G:\ICT\Miss Elliott\Year \Chapter 3 - Data Representation\worksheet 18

48. Metadata
Metadata is the information stored in an image file which helps the computer recreate the image on the screen from the binary data in each pixel.
Metadata usually includes the images file format, height, width, colour depth and resolution. It may contain extra info such as time, date
Without metadata devises would not be able to display the image on the screen.

49. Bitmap Images
Page 82 in your books

50. Storing sound Sound is sampled and stored digitally.
Sound is recorded by a microphone as an analogue signal. Analogue signals are pieces of continually changing data.
Analogue signals need to be converted into digital data so that computers can read and store sound files. This is done by analogue to digital converters.

51. Sound
Sampling intervals are the gaps between each of the points where the analogue recording is sampled.
Sampling frequency is how many samples you take in a second.
Bit rate is the number of bits used per second.
Increasing the sampling frequency means the analogue recording is sampled more often. Increasing the sample size means the digital file picks up quieter sounds.

52. Storing Sound
Page 83 in your books

53. Starter – Bitmap Images
What is a Bitmap Image made up of?
Pixels & bits
What is resolution?
How many pixels within the image, quality of the image
What signal is sound recorded in? what does it need to be converted into?
Recorded as analogue
Converted into Digital
What is Sampling frequency?
Numbers of samples per sound/recording

54. Compression Data compression is when you make file sizes smaller.
Take up less storage
Streaming/downloading is quicker
Allows loading to be quicker
service restrictions of file sizes

55. Image compression Lossy Compression (JPG) Lossless Compression (PNG)
The main thing to remember is that image compression reduces the file size
There are two types of compression:
Lossy Compression (JPG)
Lossless Compression (PNG)
Please remember these!

56. Lossy Compression (JPG)
Removes data permanently
Tries to reconstruct an image without the missing data
Much smaller file sizes but some loss of quality
Introduce image compression and explain that JPG files are automatically compressed, but this compression is only achieved by removing some of the original image data permanently. It is surprising just how much image data you can remove without noticing any degradation of quality! The compressed image on the right has been overly compressed and shows the ‘colour banding’ effect that comes of this. This is caused because the compression algorithm used to discard data looks for shades of a similar colour and groups them all as being the same colour so you see harsh bands of 10 different blues rather than a gentle gradient of millions of shades. Noticeable faults in JPG images are known as compression artefacts.
380 KB
21 KB

57. Lossy Compression
JPG files are automatically compressed, but this compression is only achieved by removing some of the original image data permanently. It is surprising just how much image data you can remove without noticing any degradation of quality!
The compressed image on the right has been overly compressed and shows the ‘colour banding’ effect that comes of this. This is caused because the compression algorithm used to discard data looks for shades of a similar colour and groups them all as being the same colour so you see harsh bands of 10 different blues rather than a gentle gradient of millions of shades. Noticeable faults in JPG images are known as compression artefacts.

58. Lossless compression (PNG)
Finds areas of the same colour and records them as 15 blue pixels rather than blue pixel, blue pixel, blue pixel etc.
, , , becomes (4 lots of – )
Lossless compression works by finding patterns in bit values and records the number of times they repeat instead of recording multiple instance of the same bit value. This method retains all of the information required to reconstruct the image and is known as Run Length Encoding (RLE). It will compress an image file, but not by as much as lossy methods.
Demonstrate to students that lossless compression works by finding patterns in bit values and records the number of times they repeat instead of recording multiple instance of the same bit value. This method retains all of the information required to reconstruct the image and is known as Run Length Encoding (RLE). It will compress an image file, but not by as much as lossy methods. Ask students to complete Task 5 from Worksheet 3 Images.

59. PROS & CONS Pros Cons e.g. file type Lossy (JPG) Reduced file size
More files can be stored
Take up less bandwidth
Lots of softwares can read lossy files
Can loose data
Cant be used on text files
Worse quality than original file
MP3 (audio)
AAC (audio)
JPEG (image)
Lossless (PNG)
Data is removed temporarily so there is no reduction in quality
Can be decompressed
Can be used on text files
Slight reduction in file size
PNG (image)
FLAC (image)

60. Compression Page 84 in your books Pros Cons e.g. file type Lossy (JPG)
Reduced file size
More files can be stored
Take up less bandwidth
Lots of softwares can read lossy files
Can loose data
Cant be used on text files
Worse quality than original file
MP3 (audio)
AAC (audio)
JPEG (image)
Lossless (PNG)
Data is removed temporarily so there is no reduction in quality
Can be decompressed
Can be used on text files
Slight reduction in file size
PNG (image)
FLAC (image)

61. Starter – Complete Mixed Questions
Page 85 in your books

62. Revision for Topic Test on Thursday
Homework: PP is on Show my homework.
Revision guide if you wish to take one revise pages: 66-76
Page 76 gives topic Questions

63. Logic Gates
Logic gate takes binary information and gives an output based on the boolean operator.
What is a boolean operator?
Logic gates are special ciruits built into computer chips.
They receive binary data, apply boolean operator and then output the binary result.
Each type of logic gate is shown by different symbols.
Each logic gate has its own corresponding truth table.
Truth table show all of the possible inputs and outputs of 1s and 0s.

64. NOT gate Not gate takes a single input and gives a single output.
The output is always opposite value to the input.
If 1 is input, it outputs 0. If 0 is the input, 1 is the output.
TRUTH TABLE
Input
Output
Input
Output 1

65. AND gate AND gate takes two inputs and gives a single output.
If 1 and 1 is the inputs, it output 1, otherwise the output is 0.
TRUTH TABLE
Input A
Input A
Input B
Output 1
Output
Input B

66. OR gate OR gate takes two inputs and gives a single output.
If 1 or more inputs are 1 then the output 1, otherwise the output is 0.
TRUTH TABLE
Input A
Input A
Input B
Output 1
Output
Input B

67. Worksheet 17 – Logic Gate
G:\ICT\Miss Elliott\Year \Chapter 3 - Data Representation

68. Page 74