Lesson Notes By Weeks and Term v3 - Senior Secondary 3
Data Representation
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Data Representation
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Subject: Computer & IT
Class: Senior Secondary 3
Term: 3rd Term
Week: 3
Theme: Coding Systems In Computer
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Define data representation List methods of data representati on Represent data in different character sets
lowercase English alphabets, digits 0-9, common punctuation marks, and control characters (like carriage return, line feed).
Extended ASCII (ASCII-8): Uses 8 bits (one byte) to represent each character, allowing for 2^8 = 256 unique characters (from 0 to 255). The additional 128 characters are used for special symbols, foreign language characters, and graphical characters, but these vary across different "code pages" or extensions.
Usage: Predominantly used in personal computers, internet communication, and text files.
Examples of ASCII Codes: 'A' = Decimal 65 = Binary 01000001 'a' = Decimal 97 = Binary 01100001 '0' = Decimal 48 = Binary 00110000 ' ' (space) = Decimal 32 = Binary 00100000 '!' = Decimal 33 = Binary 00100001 Example 1: Representing the character 'C' in ASCII
1. Locate 'C' in an ASCII table.
2. The decimal value for 'C' is 67.
3. Convert 67 to its 8-bit binary equivalent: 67 / 2 = 33 remainder 1 33 / 2 = 16 remainder 1 16 / 2 = 8 remainder 0 8 / 2 = 4 remainder 0 4 / 2 = 2 remainder 0 2 / 2 = 1 remainder 0 1 / 2 = 0 remainder 1 Reading the remainders from bottom up: 1000011 Pad with a leading zero for 8 bits: 01000011 2.3.
2. EBCDIC (Extended Binary Coded Decimal Interchange Code)
Definition: EBCDIC is an 8-bit character encoding set developed by IB
M. It is primarily used on IBM mainframe computers and midrange systems.
Structure: Uses 8 bits per character, allowing for 2^8 = 256 unique characters. The arrangement of characters (and their corresponding codes) is different from ASCI
I. Usage: Still prevalent in legacy systems, especially in banking, insurance, and government sectors that rely on IBM mainframes.
Examples of EBCDIC Codes: 'A' = Decimal 193 = Binary 11000001 'a' = Decimal 129 = Binary 10000001 '0' = Decimal 240 = Binary 11110000 ' ' (space) = Decimal 64 = Binary 01000000 '!' = Decimal 90 = Binary 01011010 Example 2: Representing the character 'C' in EBCDIC
1. Locate 'C' in an EBCDIC table.
2. The decimal value for 'C' is 195.
3. Convert 195 to its 8-bit binary equivalent: 195 / 2 = 97 remainder 1 97 / 2 = 48 remainder 1 48 / 2 = 24 remainder 0 24 / 2 = 12 remainder 0 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 up: 11000011 2.3.
3. Unicode (Brief Mention)
Definition: Unicode is a universal character encoding standard designed to represent text in all of the world's writing systems. It supersedes ASCII and EBCDIC by providing a much larger set of characters.
Structure: Uses variable-width encoding (e.g., UTF-8, UTF-16, UTF-32), allowing for millions of unique characters.
Usage: Dominant character set for modern computing, web pages, and international software due to its ability to support multiple languages, emojis, and a vast array of symbols. This section provides a detailed explanation of data representation and the specific character sets aligned with the performance objectives. 2.
1. Definition of Data Representation Data representation refers to the methods and techniques used to encode information (data) into a format that a computer can store, process, and transmit. Computers operate using binary digits (bits), which are represented as 0s and 1s.
Therefore, all data – whether it's text, numbers, images, audio, or video – must be converted into this binary format for the computer to understand and manipulate it. The process involves assigning unique binary codes to different pieces of information.
Why Data Representation is Necessary: Computer Comprehension: Computers only understand electrical signals, represented as ON (1) or OFF (0). All human-readable data must be translated into this machine-readable binary form.
Storage: Data needs to be stored efficiently on hardware devices (hard drives, flash drives, etc.) in a consistent, machine-interpretable format.
Processing: For a computer's Central Processing Unit (CPU) to perform operations (arithmetic, logic, comparison), data must be in a standardized binary format.
Transmission: When data is sent over networks (internet, local area network), it is transmitted as a stream of binary digits. 2.
2. Methods of Data Representation Different types of data require different methods of representation. While the focus of this lesson is on character sets, a brief overview of other methods is useful for context.
Numeric Data Representation: Binary (Base-2): Uses two digits, 0 and
1. This is the native language of computers.
Octal (Base-8): Uses digits 0-
7. Often used as a shorthand for binary (groups of 3 bits).
Decimal (Base-10): Uses digits 0-
9. This is the number system humans commonly use.
Hexadecimal (Base-16): Uses digits 0-9 and letters A-F. Often used as a shorthand for binary (groups of 4 bits) in computing for memory addresses and colour codes. Textual Data Representation (Character Sets): This method assigns a unique binary code to each character (letters, numbers, symbols, punctuation marks). These sets of codes are known as character sets or character encoding schemes. The most prominent ones are ASCII, EBCDIC, and Unicode.
Image Data Representation: Images are typically represented as a grid of tiny dots called pixels. Each pixel is assigned a numerical value (or set of values) representing its colour and intensity.
Bitmap/Raster Images: Stored pixel by pixel (e.g., JPEG, PNG).
Vector Images: Stored as mathematical descriptions of shapes and lines, not pixels (e.g., SVG).
Audio Data Representation: Sound waves are analog. To represent them digitally, they are sampled at regular intervals, and the amplitude of each sample is converted into a binary number (digitization). The number of samples per second (sampling rate) and the number of bits per sample (bit depth) determine the quality.
Video Data Representation: Video is essentially a sequence of still images (frames) played back rapidly, combined with synchronized audio. Each frame is an image, and the audio is represented as described above. Concepts like frame rate, resolution, and codecs (compression/decompression algorithms) are crucial here. 2.
3. Representing Data in Different Character Sets This section focuses on the two primary character sets relevant to the objectives: ASCII and EBCDIC. 2.3.
1. ASCII (American Standard Code for Information Interchange)
Definition: ASCII is a character encoding standard that uses numeric values to represent English letters, numbers, punctuation marks, and control characters. It was one of the earliest and most widely adopted character sets.
Structure: Standard ASCII (ASCII-7): Uses 7 bits to represent each character. This allows for 2^7 = 128 unique characters (from 0 to 127). It includes uppercase and lowercase English alphabets, digits 0-9, common punctuation marks, and control characters (like carriage return, line feed).
Extended ASCII (ASCII-8): Uses 8 bits (one byte) to represent each character, allowing for 2^8 = 256 unique characters (from 0 to 255). The additional 128 characters are used for special symbols, foreign language characters, and graphical characters, but these vary across different "code pages" or extensions.
Usage: Predominantly used in personal computers, internet communication, and text files.
Examples of ASCII Codes: 'A' = Decimal 65 = Binary 01000001 * 'a' = 3.
1. Teacher Activities Introduction (10 minutes): Begin by asking students how computers understand what they type on the keyboard. Introduce the concept of data representation as the "language" computers understand. Briefly state the lesson objectives.
Explanation of Key Concepts (20 minutes): Define data representation clearly, emphasizing the binary nature of computers. Discuss the general methods of data representation (numeric, text, image, audio, video) with brief examples for context, but stress that the focus will be on textual data. Introduce character sets, specifically ASCII and EBCDIC, explaining their purpose and historical context. In-depth Character Set Explanation and Demonstration (30 minutes): Explain ASCII (7-bit vs. 8-bit) with examples from a standard ASCII table (display on board or projector if available). Demonstrate step-by-step conversion of a character (e.g., 'D') from decimal ASCII to 8-bit binary. Explain EBCDIC, its IBM origins, and its distinct character mappings. Provide examples from an EBCDIC table. Demonstrate step-by-step conversion of the same character 'D' from decimal EBCDIC to 8-bit binary, highlighting the difference from ASCI
I. Briefly introduce Unicode as a modern, expanded standard.
Guided Practice (15 minutes): Engage students in converting simple characters or short words using ASCII and EBCDI
C. Provide immediate feedback and correct misconceptions.
Activity-based Learning (20 minutes): Divide students into small groups (3-4 students). Provide each group with a short word (e.g., a Nigerian name like "YEMI" or "ABUJA"). Instruct groups to represent the word in 8-bit ASCII binary using provided ASCII tables (or by recalling values taught). Circulate among groups, providing support and ensuring understanding.
Wrap-up and Review (5 minutes): Summarize key definitions (data representation, ASCII, EBCDIC). Answer any lingering questions. Assign independent practice. 3.
2. Student Activities Participate in introductory discussion on how computers understand data. Listen attentively to explanations of data representation methods and character sets. Take notes on definitions, characteristics, and examples of ASCII and EBCDIC. Actively engage in step-by-step demonstrations, asking clarifying questions. Participate in guided practice by solving character conversions on their individual whiteboards or notebooks. Collaborate in groups to complete the assigned word representation task using ASCII. Present group findings to the class (optional, depending on time). Ask questions during Q&A sessions. Complete independent practice questions.
Question 1: Define data representation in the context of computer systems.
Solution: Data representation is the method by which information (data) is encoded into a format (specifically binary digits or bits) that a computer can understand, process, store, and transmit. It involves assigning unique binary codes to different types of data such as text, numbers, images, audio, and video.
Commentary: This question directly assesses the first performance objective. A good answer will highlight the conversion to binary and the purpose (processing, storage, transmission).
Question 2: List three common methods of data representation, focusing on different data types.
Solution: Numeric Data Representation: Using number systems like binary, decimal, or hexadecimal.
Textual Data Representation: Using character sets like ASCII, EBCDIC, or Unicode.
Image Data Representation: Using pixels and colour codes (e.g., RGB). (Other valid options include Audio Data Representation using sampling and digitization, or Video Data Representation using frames and codecs.)
Commentary: This question assesses the second performance objective, ensuring students can recall various methods.
Question 3: Using an 8-bit representation, convert the character 'F' into its binary form for both ASCII and EBCDI
C. Solution: For ASCII: Look up 'F' in an ASCII table. The decimal value for 'F' is
7
0. Convert 70 to 8-bit binary: 70 / 2 = 35 R 0 35 / 2 = 17 R 1 17 / 2 = 8 R 1 8 / 2 = 4 R 0 4 / 2 = 2 R 0 2 / 2 = 1 R 0 1 / 2 = 0 R 1 Reading remainders upwards: 1000110 Pad to 8 bits: 01000110 For EBCDIC: Look up 'F' in an EBCDIC table. The decimal value for 'F' is
1
9
8. Convert 198 to 8-bit binary: 198 / 2 = 99 R 0 99 / 2 = 49 R 1 49 / 2 = 24 R 1 24 / 2 = 12 R 0 12 / 2 = 6 R 0 6 / 2 = 3 R 0 3 / 2 = 1 R 1 1 / 2 = 0 R 1 Reading remainders upwards: 11000110
Commentary: This question directly addresses the third performance objective and requires a clear understanding of the conversion process for different character sets. It highlights the difference in binary representation for the same character between ASCII and EBCDI
C. Question 4: Represent the word "IT" in 8-bit ASCII binary code.
Solution: For 'I': ASCII decimal is 73. 73 / 2 = 36 R 1 36 / 2 = 18 R 0 18 / 2 = 9 R 0 9 / 2 = 4 R 1 4 / 2 = 2 R 0 2 / 2 = 1 R 0 1 / 2 = 0 R 1 Binary for 'I': 01001001 For 'T': ASCII decimal is 84. 84 / 2 = 42 R 0 42 / 2 = 21 R 0 21 / 2 = 10 R 1 10 / 2 = 5 R 0 5 / 2 = 2 R 1 2 / 2 = 1 R 0 1 / 2 = 0 R 1 Binary for 'T': 01010100 Therefore, "IT" in 8-bit ASCII binary is 01001001
0
1
0
1
0
1
0
0. Commentary: This extends the representation to a simple word, reinforcing the character-by-character conversion.
JAMB CBT Examinations: When students take JAMB's Computer-Based Test (CBT), every character typed for their name, registration number, or answers is represented digitally using character sets. Understanding this helps appreciate the underlying technology that processes their input accurately. Errors in data representation could lead to incorrect registration or misinterpretation of answers.
Mobile Banking and USSD Codes: In Nigeria, mobile banking and USSD (Unstructured Supplementary Service Data) shortcodes are widely used. When a user dials a code like `737#` or types a transaction amount, these numbers and symbols are converted into binary using character sets (and other numeric representations) before being transmitted to the bank's server for processing. This ensures the correct instruction or amount is communicated. Data Entry in Government Agencies and Businesses: From population census data to voter registration and company records, vast amounts of textual information (names, addresses, occupations) are entered into computer systems. These systems rely on character encoding standards (like ASCII or more commonly Unicode for wider language support) to store and retrieve data consistently, preventing data corruption and ensuring accurate record-keeping for citizens and businesses alike.