Chapter 1 - Information Representation.pdf

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

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

1.1: Data Representation

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

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

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

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

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

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.

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

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)

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.

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,

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?

Therefore,
the denary number 3 1 6 5 would be 0011 0001 0110 0101
in BCD format.

What are the 2 ways to represent BCD in computers?
Check your coursebook (Cambridge Press) at page 13.

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

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

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

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

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.

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?

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

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

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

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

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.

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.

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.

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
-
__________________

Chapter 1: Information Representation > 1.1 Data Representation > ASCII

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

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

Chapter 1: Information Representation > 1.1 Data Representation > UNICODE

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

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

1.2: Multimedia

1.2.1. Multimedia > Bitmap Images

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

Pixel
Smallest element that
makes up an image

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.

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).

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.

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

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.

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

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)

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

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

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?

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

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.

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

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?

Students present their assigned topics:

1.2.2 Multimedia > Vector Images

1.2.3 Multimedia > Sound

1.2.4 Multimedia > Video

1.3.1 Multimedia > File Compression

1.3.1 File Compression > File Compression and Applications

1.3.2 File Compression > General Methods of Compressing Files

Past Paper Question (Paper 1)
• Perform CW8 by answering past paper questions.

Chapter 1 - Information Representation.pdf

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Chapter 1 - Information Representation.pdf