Application to computer programming for SS 1

Class: SS 1
Term: First Term
Week: 9
Age: 15 years
Duration: 60 minutes
Subject: General Mathematics
Curriculum Theme: Number and Numeration
Focal competence: Developing competency in students on the basic computer language codes
Key competencies/values: Communication; ICT and Digital Competencies; Digital Competencies
Skills:

• Coding skill

Previous Lesson: Trigonometry, Trigonometric Ratios and Special Angles
Topic: Number Base System (2)
Subject Matter: Application to computer programming

Specific Objectives

By the end of the lesson, pupils/students should be able to:

Cognitive Domain

• Explain why binary and hexadecimal numbers are used in computer programming.
• Relate positional value in number bases to conversion procedures.

Psychomotor Domain

• Display basic computer programming skills by using binary numbers for simple coding.
• Demonstrate how to check number base conversions by expanding digits according to place value.

Affective Domain

• Appreciate the importance of number base systems in modern technology and computing.

Reference Materials

The following resources were used in planning this lesson:

• 2025 New Revised Senior Secondary Education Curriculum (SSEC)
• Relevant State Unified Scheme of Work
• A suitable Mathematics textbook for SS 1
• The HeadTeacher Scheme of work For The New Revised Senior Secondary Education Curriculum (SSEC)

Instructional Materials

The teacher will teach this lesson with the aid of:

• Whiteboard and markers
• Projector or large screen for video clips
• Video clips on how binary numbers are used for coding
• Video clips of how hexadecimal numbers are used in programming
• Charts showing binary and hexadecimal representations

Rationale for the Lesson

This lesson is important because it connects abstract mathematical concepts of number base systems to their practical applications in computer programming. Understanding binary and hexadecimal is fundamental for students interested in technology and provides a real-world context for their mathematical learning, enhancing their digital literacy.

Prerequisite/Previous Knowledge

Students should have a basic understanding of different number base systems, including binary (base 2) and hexadecimal (base 16), and how to convert numbers between these bases and base 10.

Lesson Content/Board Summary

Application to Computer Programming

Understanding Number Base Systems in Computing

A number base system is a mathematical method for representing quantities using a fixed set of digits and place values based on powers of the base. In computing, different number bases are fundamental for how data is stored, processed, and represented.

1. Binary (Base 2): This system uses only two digits, 0 and 1. It is the native language of computers because it directly corresponds to electrical states (e.g., on/off, high/low voltage) within electronic circuits.
2. Hexadecimal (Base 16): This system uses sixteen distinct symbols: 0-9 and A-F (where A represents 10, B represents 11, and so on, up to F for 15). It is often used as a more human-readable shorthand for long binary sequences.

Binary Numbers (Base 2) in Computer Coding

Binary numbers are the foundation of computer programming and data representation. Every instruction, character, image, or sound in a computer is ultimately stored and processed as a sequence of 1s and 0s.

1. Representing Data: Each 0 or 1 is called a bit (binary digit). A group of 8 bits forms a byte, which can represent a single character (like a letter or symbol) or a small number.
2. Simple Coding: In basic computer programming, sequences of binary digits can represent specific commands or states. For example, in a simple digital logic circuit, ‘1’ might mean “activate” and ‘0’ might mean “deactivate”. More complex patterns form instructions for the computer’s processor.
3. Example: The ASCII (American Standard Code for Information Interchange) code for the uppercase letter ‘A’ is (01000001_2). When a programmer types ‘A’ in a program, the computer internally processes this binary sequence.

Hexadecimal Numbers (Base 16) in Programming

While computers operate in binary, working directly with long strings of 1s and 0s can be cumbersome and error-prone for human programmers. Hexadecimal provides a more compact and readable way to represent binary data.

1. Shorthand for Binary: Each hexadecimal digit corresponds to exactly four binary digits (bits). This makes it easy to convert between binary and hexadecimal without losing information, as (16 = 2^4).
2. Applications in Programming:
   1. Memory Addresses: Computer memory locations are often represented in hexadecimal format because it is shorter and easier to manage than long binary addresses.
   2. Colour Codes: In web development and graphics, colours are frequently specified using hexadecimal codes (e.g., #FF0000 for pure red, #00FF00 for pure green, #0000FF for pure blue).
   3. Debugging: Programmers often view raw data, machine code, or error codes in hexadecimal during the process of finding and fixing errors in software.
3. Hexadecimal Digits and their Decimal Equivalents:
   1. 0-9: Represent their usual decimal values.
   2. A: Represents 10
   3. B: Represents 11
   4. C: Represents 12
   5. D: Represents 13
   6. E: Represents 14
   7. F: Represents 15

Positional Value and Conversion Principles

Understanding positional value is crucial for working with any number base, including binary and hexadecimal. The value of each digit in a number depends on its position within the number.

1. Place Value: In any number base, each position to the left of the decimal point (or radix point) represents an increasing power of the base, starting from (base^0). For example, in (101_2), the leftmost ‘1’ is in the (2^2) position, the ‘0’ is in the (2^1) position, and the rightmost ‘1’ is in the (2^0) position.
2. Expansion Method for Conversion and Checking: To convert a number from any base to base 10 (decimal), we expand it by multiplying each digit by its corresponding place value (power of the base) and summing the results. This method also serves as a reliable way to check the correctness of conversions between bases.
   1. Binary to Decimal Example:
      To convert (1011_2) to base 10:
      (1011_2 = (1 times 2^3) + (0 times 2^2) + (1 times 2^1) + (1 times 2^0))
      (= (1 times 8) + (0 times 4) + (1 times 2) + (1 times 1))
      (= 8 + 0 + 2 + 1 = 11_{10})
   2. Hexadecimal to Decimal Example:
      To convert (2A_{16}) to base 10:
      (2A_{16} = (2 times 16^1) + (A times 16^0))
      (= (2 times 16) + (10 times 1)) (Since A = 10 in decimal)
      (= 32 + 10 = 42_{10})

Teaching Methods/Instructional Techniques

Explanation, Discussion, Demonstration, Guided Practice, Question and Answer, Video Presentation

Instructional Procedures

Step 1: Introduction

Time: 5 minutes

Teaching Skill: Recalling/Linking

Teacher’s Activity: The teacher briefly reviews previous lessons on number base systems and asks students to recall what binary and hexadecimal numbers are. The teacher then introduces the lesson by stating that these number systems are not just abstract mathematical concepts but have vital applications, especially in computers.

Pupils’ Activity: Pupils recall definitions of binary and hexadecimal numbers and listen attentively to the introduction of the lesson’s relevance.

Learning Point: Number base system recall

Step 2: Explanation of Number Base Systems in Computing

Time: 10 minutes

Teaching Skill: Explanation/Conceptualisation

Teacher’s Activity: The teacher explains what a number base system is, highlighting the concepts of fixed digits and place values based on powers of the base. The teacher then explains why binary (base 2) and hexadecimal (base 16) are particularly important in computing, linking binary to the on/off states of electronics.

Pupils’ Activity: Pupils listen, ask questions, and take notes on the fundamental role of number base systems in computing.

Learning Point: Role of number bases

Step 3: Binary Numbers (Base 2) in Coding

Time: 10 minutes

Teaching Skill: Explanation/Illustration

Teacher’s Activity: The teacher explains how binary numbers (0s and 1s) are used for basic computer programming coding. The teacher provides simple examples of how sequences of 1s and 0s can represent data or instructions, such as ASCII codes for characters.

Pupils’ Activity: Pupils observe the examples, ask clarifying questions, and understand the concept of binary coding.

Learning Point: Binary coding principles

Step 4: Guided Practice with Binary Coding

Time: 10 minutes

Teaching Skill: Guided Practice/Demonstration

Teacher’s Activity: The teacher guides students to practice basic computer programming coding using 0 and 1 (binary). This could involve simple exercises like converting small decimal numbers to binary or interpreting short binary sequences as simple commands (e.g., 01 for ‘on’, 00 for ‘off’).

Pupils’ Activity: Pupils participate in the guided practice, attempting to code simple instructions using binary numbers and asking for assistance when needed.

Learning Point: Practical binary coding

Step 5: Hexadecimal Numbers (Base 16) in Programming

Time: 5 minutes

Teaching Skill: Explanation/Application

Teacher’s Activity: The teacher explains what hexadecimal numbers are and why they are used in programming, particularly as a shorthand for binary. The teacher mentions applications like memory addresses and colour codes.

Pupils’ Activity: Pupils listen and understand the purpose and applications of hexadecimal numbers in programming.

Learning Point: Hexadecimal applications

Step 6: Video Clips on Binary and Hexadecimal in Programming

Time: 5 minutes

Teaching Skill: Visual Learning/Demonstration

Teacher’s Activity: The teacher guides students to watch video clips demonstrating how binary numbers are used for coding and how hexadecimal numbers are used in programming. This makes the concepts more concrete and visual.

Pupils’ Activity: Pupils watch the video clips, observe the real-world applications, and discuss their observations.

Learning Point: Visualising number base applications

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

1. Why do computers primarily use binary numbers?
2. Give an example of how binary numbers are used in simple coding.
3. What is hexadecimal, and why is it useful in computer programming?
4. Convert (1101_2) to base 10, showing your working.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Application of number bases

Step 8: Note-Taking

Time: 10 minutes

Teaching Skill: Guided Writing

Teacher’s Activity: The teacher guides pupils/students to copy the essential Board Summary notes on the application of number base systems to computer programming into their notebooks.

Pupils’ Activity: Pupils/students copy the notes carefully into their notebooks.

Learning Point: Recording lesson content

Step 9: Conclusion

Time: 5 minutes

Teaching Skill: Consolidation

Teacher’s Activity: The teacher summarises the key points of the lesson, reiterating that binary and hexadecimal are not just mathematical curiosities but fundamental tools in the world of computing and programming. The teacher encourages students to explore more about computer programming.

Pupils’ Activity: Pupils listen to the summary and reflect on the lesson’s importance.

Learning Point: Reinforcing lesson concepts

Continuous Assessment/Further Study

Type: Homework/Practice Exercise

Instruction: Answer the following questions in your notebook:

1. Explain the concept of positional value in a number base system and how it relates to conversion procedures.
2. Convert the binary number (1110_2) to its decimal equivalent. Show your expansion method.
3. Convert the hexadecimal number (3F_{16}) to its decimal equivalent. Show your expansion method.
4. Research and write down two more real-world applications of hexadecimal numbers in technology, apart from those discussed in class.

Lesson Keywords

• Binary – A number system using only two digits, 0 and 1, fundamental to computers.
• Hexadecimal – A number system using 16 symbols (0-9 and A-F), often used as a shorthand for binary in computing.
• Coding – The process of writing instructions for a computer using a programming language.
• Bit – A binary digit, either 0 or 1.
• Byte – A unit of digital information typically consisting of 8 bits.
• Positional Value – The value of a digit based on its position within a number.

Differentiation

Support for struggling learners: Provide simplified examples of binary coding and offer extra guidance during the guided practice. Use visual aids and charts to reinforce the connection between binary/hexadecimal and decimal. Focus on understanding the concept of 0s and 1s as on/off states.

Extension for advanced learners: Challenge them to research how different data types (e.g., integers, floating-point numbers, characters) are represented in binary. Encourage them to explore simple online binary-to-text converters or hexadecimal colour pickers to deepen their understanding of practical applications.

Suggested Lesson Videos

For further understanding, search on YouTube for:

• “Binary numbers in computer programming for beginners”
• “How hexadecimal is used in computing”
• “Number base systems and their applications”