Lesson Notes By Weeks and Term v5 - Grade 9

Lesson Video

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Performance objectives

• Explain data representation (binary, decimal, hexadecimal).
• Convert numbers between decimal and binary.
• Describe encoding methods like ASCII and Unicode.
• Identify basic data security measures.
• Explain data compression (lossy and lossless).

Lesson summary

Communication and information systems are the backbone of modern society. They allow us to share ideas, access information, and connect with each other, regardless of distance. In South Africa, effective communication is especially crucial for addressing social and economic disparities, promoting education, and fostering a sense of national unity. Understanding these systems empowers you to participate fully in the digital world and contribute to a more connected and informed society. This week, we will delve into how information is represented, encoded, and securely transmitted through various digital systems.

Lesson notes

Data Representation: Binary, Decimal, and Hexadecimal Computers use the binary number system (base-2) because they operate using electronic switches that are either ON (represented by 1) or OFF (represented by 0). Humans, on the other hand, commonly use the decimal number system (base-10). Hexadecimal (base-16) is used in computer science as a shorthand representation for binary numbers because it is easier for humans to read and write.

Decimal (Base-10): The number system we use every day, with digits 0-

9. Binary (Base-2): Uses only two digits, 0 and

1. Each position represents a power of 2 (e.g., 2 0 , 2 1 , 2 2 , etc.).

Hexadecimal (Base-16): Uses digits 0-9 and letters A-F (where A=10, B=11, C=12, D=13, E=14, and F=15). Each position represents a power of 16 (e.g., 16 0 , 16 1 , 16 2 , etc.).

Decimal to Binary Conversion: To convert a decimal number to binary, repeatedly divide the decimal number by 2, noting the remainder at each step. The binary number is formed by reading the remainders from bottom to top.

Example: Convert the decimal number 25 to binary. 25 ÷ 2 = 12 remainder 1 12 ÷ 2 = 6 remainder 0 6 ÷ 2 = 3 remainder 0 3 ÷ 2 = 1 remainder 1 1 ÷ 2 = 0 remainder 1 Reading the remainders from bottom to top, we get

1

1

0

0

1. Therefore, 25 in decimal is 11001 in binary.

Binary to Decimal Conversion: To convert a binary number to decimal, multiply each digit by its corresponding power of 2 and then sum the results.

Example: Convert the binary number 10110 to decimal. (1 x 2 4 ) + (0 x 2 3 ) + (1 x 2 2 ) + (1 x 2 1 ) + (0 x 2 0 ) (1 x 16) + (0 x 8) + (1 x 4) + (1 x 2) + (0 x 1) 16 + 0 + 4 + 2 + 0 = 22 Therefore, 10110 in binary is 22 in decimal.

Encoding Methods: ASCII and Unicode ASCII (American Standard Code for Information Interchange): A character encoding standard for electronic communication. ASCII codes represent text in computers, telecommunications equipment, and other devices. It uses 7 bits to represent 128 characters, including uppercase and lowercase letters, numbers, punctuation marks, and control characters.

However, it's limited in representing characters from languages beyond English.

Unicode: A more comprehensive character encoding standard that aims to represent every character from every language in the world. Unicode uses variable-length encoding, often using 16 or 32 bits, allowing it to represent millions of different characters. This is important in South Africa, with its 11 official languages, as it allows computers to accurately display text in all these languages. Data Security Data security is crucial to protect information from unauthorized access, use, disclosure, disruption, modification, or destruction.

Some basic security measures include: Strong Passwords: Use a combination of uppercase and lowercase letters, numbers, and symbols. Avoid using easily guessable information like your name or birthday.

Antivirus Software: Protects your computer from malware (viruses, worms, Trojans).

Firewalls: Act as a barrier between your computer and the internet, blocking unauthorized access.

Secure Websites (HTTPS): Look for the padlock icon in the address bar. HTTPS encrypts the data transmitted between your computer and the website, protecting it from eavesdropping. Be careful about clicking on suspicious links and always be wary of phishing emails.

Data Compression: Lossy and Lossless Data compression reduces the size of a file, making it easier to store and transmit.

There are two main types: Lossless Compression: Reduces file size without losing any data. The original file can be perfectly reconstructed from the compressed file. Examples include ZIP, PNG (for images), and FLAC (for audio). This is vital for documents or software where data integrity is important.

Lossy Compression: Reduces file size by discarding some data that is considered less important. The original file cannot be perfectly reconstructed from the compressed file. Examples include JPEG (for images) and MP3 (for audio). This is often used for multimedia where a slight loss of quality is acceptable in exchange for a significantly smaller file size.

Consider the use case: Would you prefer many low-quality photos, or fewer high-quality photos? This question can inform the choice between lossy and lossless compression. Guided Practice (With Solutions)

Question 1: Convert the decimal number 42 to binary.

Solution: 42 ÷ 2 = 21 remainder 0 21 ÷ 2 = 10 remainder 1 10 ÷ 2 = 5 remainder 0 5 ÷ 2 = 2 remainder 1 2 ÷ 2 = 1 remainder 0 1 ÷ 2 = 0 remainder 1 Reading the remainders from bottom to top, we get

1

0

1

0

1

0. Therefore, 42 in decimal is 101010 in binary.

Question 2: Convert the binary number 11011 to decimal.

Solution: (1 x 2 4 ) + (1 x 2 3 ) + (0 x 2 2 ) + (1 x 2 1 ) + (1 x 2 0 ) (1 x 16) + (1 x 8) + (0 x 4) + (1 x 2) + (1 x 1) 16 + 8 + 0 + 2 + 1 = 27 Therefore, 11011 in binary is 27 in decimal.

Question 3: Explain the difference between ASCII and Unicode.