AS/A Level (for 2024 Exam) The image you sent is a lesson plan on data representation. It is divided into two sections: Understanding binary numbers Converting integer values from one number base/representation to another The first section explains the difference between binary numbers and decimal numbers, and how to convert between the two bases. The second section explains how to convert an integer value from any number base to any other number base. Students will be able to: Perform binary addition and subtraction using positive and negative binary integers. Show understanding of how overflow can occur. Describe practical applications where Binary Coded Decimal (BCD) and Hexadecimal are used. Show understanding of and be able to represent character data in its internal binary form, depending on the character set used. Additional notes: Students are expected to be familiar with ASCII (American Standard Code for Information Interchange), extended ASCII, and Unicode. Students will not be expected to memorize any particular character codes. Image enhancements: The image could be enhanced by adding visual representations of binary numbers, such as charts or diagrams. Including examples of practical applications where BCD and hexadecimal are used would be helpful. An image showing a table of ASCII or Unicode characters and their corresponding binary representations would also be beneficial.

1. Computer Science
Prepare by: Merbert J. Jeruela, Brainworks-Total International School
Based on 2024-2025 9618 AS/A Level Computer Science Syllabus

2. Chapter 1: Information Representation
1.1: Data Representation
By the end of the lesson students will be able to:

3. 1.1: Data Representation
By the end of the lesson students will be able to:
Chapter 1: Information Representation

4. Key Terms

11. Chapter 1: Information Representation > 1.1 Data Representation > Binary Magnitude > Numbers and Quantities

12. Chapter 1: Information Representation > 1.1 Data Representation > Binary Magnitude
Since binary number can have only two symbols either 0 or 1 for each
position or bit, so it is not possible to add minus or plus symbols in
front of a binary number.
• Sign-Magnitude method
• 1’s Complement method
• 2’s complement method
• The representation of signed binary number is commonly referred
to as sign magnitude.
3 Ways to Represent Magnitude

13. Chapter 1: Information Representation > 1.1 Data Representation > Binary Magnitude > signed magnitude

14. Chapter 1: Information Representation > 1.1 Data Representation > Binary Magnitude > signed magnitude

15. Chapter 1: Information Representation > 1.1 Data Representation > Binary Magnitude > signed magnitude

16. Chapter 1: Information Representation > 1.1 Data Representation > Binary Magnitude > signed magnitude

17. Chapter 1: Information Representation > 1.1 Data Representation > Binary Magnitude > signed magnitude

18. Chapter 1: Information Representation > 1.1 Data Representation > Binary Magnitude > 1’s Complement

19. Chapter 1: Information Representation > 1.1 Data Representation > Binary Magnitude > 2’s Complement

20. Chapter 1: Information Representation > 1.1 Data Representation > Binary Magnitude > 2’s Complement

21. Chapter 1: Information Representation > 1.1 Data Representation > Binary Magnitude > 2’s Complement

22. Chapter 1: Information Representation > 1.1 Data Representation > Binary Magnitude > 2’s Complement

23. Chapter 1: Information Representation > 1.1 Data Representation > Binary Magnitude
1. Using 2’s complement method, show the process to convert (0101
1011)2 into its negative equivalent.
Present your workings in the class.

24. Chapter 1: Information Representation > 1.1 Data Representation > Decimal Prefixes
Key Terms: Decimal prefixes are prefixes to define the magnitude of a
value. Examples are kilo, mega, giga, and tera.
(Based on SI Units)
Prefix Name of Memory Size Equivalent Denary Value
kilo 1 kilobyte (1 KB) 1 000
mega 1 megabyte (1 MB) 1 000 000
giga 1 gigabyte (1 GB) 1 000 000 000
tera 1 terabyte (1 TB) 1 000 000 000 000
peta 1 petabyte (1 PB) 1 000 000 000 000 000

25. Chapter 1: Information Representation > 1.1 Data Representation > Binary Prefixes
Key Terms: Binary prefixes are prefixes to define the magnitude
of a value. Examples are kibi, mebi, gibi, and tebi.
Prefix Name of Memory Size Number of bytes Equivalent denary value (bytes)
kibi 1 kibibyte (1 KiB) 210 1 024
mebi 1 mebibyte (1 MiB) 220 1 048 576
gibi 1 gibibyte (1 GiB) 230 1 073 741 824
tebi 1 tebibyte (1 TiB) 240 1 099 511 627 776
pebi 1 pebibyte (1 PiB) 250 1 125 899 906 842 624
Since memory sizes are measured in terms of powers of 2, the base 10 numbering system is technically
inaccurate, hence another system has been introduced.
(Based on IEE Units)

26. Chapter 1: Information Representation > 1.1 Data Representation > Binary Prefixes
How much a 4 MiB of RAM could store bytes of data?
It could store 4 x 220 bytes of data.

27. Chapter 1: Information Representation > 1.1 Data Representation > Binary Coded Decimal
Key Terms: Binary Coded Decimal (BCD) system uses 4-bit code to
represent each denary digit.
0000 = 0 0101 = 5
0001 = 1 0110 = 6
0010 = 2 0111 = 7
0011 = 3 1000 = 8
0100 = 4 1001 = 9
So,

28. Chapter 1: Information Representation > 1.1 Data Representation > Binary Coded Decimal
Can we consider as a BCD?
1010 = 10
1011 = 11
1100 = 12
1101 = 13
1110 = 14
1111 = 15
No, these are considered forbidden numbers and can not
be used in BCD system. Why though?

29. Chapter 1: Information Representation > 1.1 Data Representation > Binary Coded Decimal
Therefore,
the denary number 3 1 6 5 would be 0011 0001 0110 0101
in BCD format.

30. Chapter 1: Information Representation > 1.1 Data Representation > Binary Coded Decimal
What are the 2 ways to represent BCD in computers?
Check your coursebook (Cambridge Press) at page 13.

31. Chapter 1: Information Representation > 1.1 Data Representation > Binary Coded Decimal
1. Convert these denary numbers into BCD format.
a. 271 b. 5006 c. 7990
2. Convert these BCD numbers into denary numbers.
a. 1001 0011 0111
b. 0111 0111 0110 0010
c. 0010 1111 1010

32. Chapter 1: Information Representation > 1.1 Data Representation > Adding Binary Numbers

33. Chapter 1: Information Representation > 1.1 Data Representation > Adding Binary Numbers

34. Chapter 1: Information Representation > 1.1 Data Representation > Adding Binary Numbers

35. Chapter 1: Information Representation > 1.1 Data Representation > Adding Binary Numbers

36. Chapter 1: Information Representation > 1.1 Data Representation > Adding Binary Numbers

37. Chapter 1: Information Representation > 1.1 Data Representation > Adding Binary Numbers

38. Chapter 1: Information Representation > 1.1 Data Representation > Adding Binary Numbers

39. Chapter 1: Information Representation > 1.1 Data Representation > Adding Binary Numbers
1. Carry out these binary additions and show if the answer matches
its denary equivalent.
a. 00111001 + 00101001
b. 01001011 + 00100011
c. 01011000 + 00101000

40. Chapter 1: Information Representation > 1.1 Data Representation > BCD Addition
Extension Activity:
Look into how to add BCD and give examples.

41. Chapter 1: Information Representation > 1.1 Data Representation > Uses of BCD
Advantages Limitations Uses
Easy conversion between machine-
readable and human-readable
numerals.
Requires extra bits of storage in
computer’s memory.
Used in digital displays such as in
calculators and digital clocks.
To get around the size limitations
imposed on integer arithmetic.
Performing arithmetic can be
cumbersome since no digit can
exceed 9.
Used in currency applications
where floating point representation
are inaccurate.

42. Chapter 1: Information Representation > 1.1 Data Representation > Uses of BCD
Uses
Used in digital displays such as
in calculators and digital clocks.
Used in currency applications
where floating point
representation are inaccurate.
Homework 1: Uses of BCD
• Explain how BCD is used in
digital displays and currency
applications?

43. Chapter 1: Information Representation > 1.1 Data Representation > Uses of Hexadecimal Number System

44. Chapter 1: Information Representation > 1.1 Data Representation > Uses of Hexadecimal Number System

45. Chapter 1: Information Representation > 1.1 Data Representation > Uses of Hexadecimal Number System

46. Chapter 1: Information Representation > 1.1 Data Representation > Uses of Hexadecimal Number System

47. Chapter 1: Information Representation > 1.1 Data Representation > Uses of Hexadecimal Number System

48. Chapter 1: Information Representation > 1.1 Data Representation > Uses of Hexadecimal Number System

49. Chapter 1: Information Representation > 1.1 Data Representation > Uses of Hexadecimal Number System

50. Chapter 1: Information Representation > 1.1 Data Representation > Uses of Hexadecimal Number System

51. Chapter 1: Information Representation > 1.1 Data Representation > Uses of Hexadecimal Number System

52. Chapter 1: Information Representation > 1.1 Data Representation > Uses of Hexadecimal Number System

53. Chapter 1: Information Representation > 1.1 Data Representation > Uses of Hexadecimal Number System

54. Chapter 1: Information Representation > 1.1 Data Representation > Uses of Hexadecimal Number System

55. Chapter 1: Information Representation > 1.1 Data Representation > Uses of Hexadecimal Number System

56. Chapter 1: Information Representation > 1.1 Data Representation > Binary Subtraction
How to subtract
binary numbers?

57. Chapter 1: Information Representation > 1.1 Data Representation > Subracting Binary Numbers
Subtracting Binary Numbers
Rules when subtracting
binary numbers
Binary
subtraction
Borrow Difference
0 - 0
0 - 1
1 - 0
1 - 1
0
1
0
0
0
1
1
0

58. Chapter 1: Information Representation > 1.1 Data Representation > Subtracting Binary Numbers

59. Chapter 1: Information Representation > 1.1 Data Representation > Subtracting Binary Numbers

60. Chapter 1: Information Representation > 1.1 Data Representation > Subtracting Binary Numbers > 2’s Complement
Binary Subtraction Using 2's Complement
Step 1: Find the 1's complement of the subtrahend, which means the second number
of subtraction.
Step 2: Add it with the minuend or the first number.
Step 3: If there is a carryover left then add it with the result obtained from step 2.
Step 4: If there are no carryovers, then the result obtained in step 2 is the difference
of the two numbers using 1's complement binary subtraction.

61. Chapter 1: Information Representation > 1.1 Data Representation > Subtracting Binary Numbers
Let us understand this with an example.
Subtract 1100102 - 1001012 using 1's complement.
Here the binary equivalent of 50 is 1100102 and the binary equivalent of 37 is 1001012.

62. Chapter 1: Information Representation > 1.1 Data Representation > Subtracting Binary Numbers
Let us understand this with an example.
Subtract 1100102 - 1001012 using 1's complement.
Here the binary equivalent of 50 is 1101012 and the binary equivalent of 37 is 1001012.

63. Chapter 1: Information Representation > 1.1 Data Representation > Subtracting Binary Numbers
With a partner, perform the following binary operation using the binary
numbers given below:
1. Borrowing Method:
2. 2’s Complement method:
1 0 0 0 0 1 1 1
0 1 1 1 0 1 0
-
__________________

64. Chapter 1: Information Representation > 1.1 Data Representation > ASCII

65. Chapter 1: Information Representation > 1.1 Data Representation > Extended ASCII

66. Chapter 1: Information Representation > 1.1 Data Representation > Extended ASCII

67. Chapter 1: Information Representation > 1.1 Data Representation > Extended ASCII

68. Chapter 1: Information Representation > 1.1 Data Representation > Extended ASCII

69. Chapter 1: Information Representation > 1.1 Data Representation > UNICODE
Extension Activity:
Look into how a UNICODE look like.

70. Chapter 1: Information Representation > 1.1 Data Representation > UNICODE

71. Chapter 1: Information Representation > 1.1 Data Representation > Similarities and Differences Between ASCII and UNICODE
ASCII vs UNICODE

72. Chapter 1: Information Representation > 1.1: Data Representation
End of Chapter 1.1: Data Representation

73. Chapter 1: Information Representation
1.2: Multimedia
By the end of the lesson students will be able to:

74. 1.2: Multimedia
By the end of the lesson students will be able to:
Chapter 1: Information Representation

75. 1.2.1. Multimedia > Bitmap Images
Chapter 1: Information Representation

76. Bit-map Image
A system that uses pixels to
make up an image.

77. Pixel
Smallest element that
makes up an image

78. File Header
Bitmap image also contains
the File Header which has the
metadata contents of the
bitmap file, including image size,
number of colors, etc.

79. Image Resolution
Number of pixels that make up an
image, for example, an image could
contain 4096 x 3192 pixels (12,738,656
pixels in total).

80. Screen Resolution
• Number of horizontal and vertical pixels that
make up a screen display.
• If screen resolution is smaller than image
resolution, the whole image can not be shown
on the screen.

81. Color Depth
Number of bits used to represent
the colors in a pixel. 8 bit color
depth can represent 28 = 256 colors.

82. Bit Depth
• Number of bits used to represent the
smallest unit in sound or image file.
• The larger the bit depth, the better
the quality.

83. Chapter 1: Information Representation > Recap > Decimal Prefixes
Key Terms: Decimal prefixes are prefixes to define the magnitude of a
value. Examples are kilo, mega, giga, and tera.
(Based on SI Units)
Prefix Name of Memory Size Equivalent Denary Value
kilo 1 kilobyte (1 KB) 1 000
mega 1 megabyte (1 MB) 1 000 000
giga 1 gigabyte (1 GB) 1 000 000 000
tera 1 terabyte (1 TB) 1 000 000 000 000
peta 1 petabyte (1 PB) 1 000 000 000 000 000

84. Chapter 1: Information Representation > Recap> Binary Prefixes
Key Terms: Binary prefixes are prefixes to define the magnitude
of a value. Examples are kibi, mebi, gibi, and tebi.
Prefix Name of Memory Size Number of bytes Equivalent denary value (bytes)
kibi 1 kibibyte (1 KiB) 210 1 024
mebi 1 mebibyte (1 MiB) 220 1 048 576
gibi 1 gibibyte (1 GiB) 230 1 073 741 824
tebi 1 tebibyte (1 TiB) 240 1 099 511 627 776
pebi 1 pebibyte (1 PiB) 250 1 125 899 906 842 624
Since memory sizes are measured in terms of powers of 2, the base 10 numbering system is technically
inaccurate, hence another system has been introduced.
(Based on IEE Units)

85. Chapter 1: Information Representation > Recap> Binary Prefixes
Chapter 1: Information Representation > Recap> bits to bytes to KB to MB to GB to TB

86. Chapter 1: Information Representation > 1.2: Multimedia > Encoding Bitmapped Images
How data for a bitmap image is encoded?
• Data for a bitmapped image is encoded by assigning a solid color to
each pixel, i.e., through bit patterns.
• Bit patterns are generated by considering each row of the grid as a series
of binary color codes which correspond to each pixel’s color.
• These bit patterns are ‘mapped’ onto main memory

87. Chapter 1: Information Representation > 1.2: Multimedia > Encoding Bitmapped Images
How data for a bitmap image is encoded?
Watch the video for further explanation:
Digital Data: Image Encoding
https://www.youtube.com/watch?v=0TeQPizV1kg
While watching:
1. What is an image?
2. What is a bitmap?
3. What is the role of color lookup table?

88. Chapter 1: Information Representation > 1.2: Multimedia > Screen Resolution
Screen Resolution
• Number of pixels which can be viewed horizontally &vertically on the
device’s screen
• Number of pixels = width × height
E.g. 1680 × 1080 pixels

89. Chapter 1: Information Representation > 1.2: Multimedia > Color Depth and File Size
Color Depth
Color depth: number of bits used to represent the color of a single pixel
• An image with n bits has 2n colors per pixel
• E.g. 16-colour bitmap has 4 bits per pixel ∵ 24=1624=16
• Color depth↑: color quality↑ but file size↑
• File Size = Number of Pixels × color depth
• Convert bits to bytes by dividing by 8 if necessary.

90. Chapter 1: Information Representation > 1.2: Multimedia > Calculating File Size

91. Chapter 1: Information Representation > 1.2: Multimedia > Image Resolution
What happens if image resolution is increased?
• If image resolution increases, then image is sharper/more detailed
Watch the video for further explanation:
Image Resolution:
https://www.youtube.com/watch?v=wvb5oNuvBLU
While watching:
1. What is another term for image resolution?
2. To have a smoother circle, you need to have what?
3. What is the pixel density of a 2 X 2 inches2 image size having a 10 x 10 px pixel dimension?

92. Chapter 1: Information Representation
Students present their assigned topics:

93. 1.2.2 Multimedia > Vector Images
Chapter 1: Information Representation

94. 1.2.3 Multimedia > Sound
Chapter 1: Information Representation

95. 1.2.4 Multimedia > Video
Chapter 1: Information Representation

96. 1.3.1 Multimedia > File Compression
Chapter 1: Information Representation

97. 1.3.1 File Compression > File Compression and Applications
Chapter 1: Information Representation

98. 1.3.2 File Compression > General Methods of Compressing Files
Chapter 1: Information Representation

99. Past Paper Question (Paper 1)
• Perform CW8 by answering past paper questions.
Chapter 1: Information Representation