Class: Senior Secondary School 2 (SS2 / SSS2)
Term: 3rd Term
Week: 7
Age: 16 years
Duration: 45 minutes
Subject: Basic Electronics
Curriculum Theme: Digital Electronics
Previous Lesson: Number System: Identification and.
Topic: NUMBER SYSTEM
Subject Matter: Meaning of NUMBER SYSTEM (recap definition of number system), simple calculation in binary number (addition and subtraction), conversion from one base to another (binary to octal, hexa to binary, and vice versa).

Specific Objectives

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

Cognitive Domain:

Define number system.
State the rules for binary addition and subtraction.
Explain the methods for converting between binary, octal, and hexadecimal number systems.

Affective Domain:

Appreciate the importance of different number systems in digital electronics.
Show interest in performing calculations and conversions in various number bases.

Psychomotor Domain:

Perform simple addition and subtraction of binary numbers accurately.
Convert numbers from binary to octal and vice versa.
Convert numbers from hexadecimal to binary and vice versa.

Collaborate with peers to solve number system problems.
Participate actively in classroom discussions and problem-solving sessions.

Reference Materials

The following resources were used in planning this lesson:

Senior Secondary Schools Education Curriculum
State Unified Scheme of Work
Basic Electronics for Senior Secondary Schools by various authors

Instructional Materials

The teacher will teach this lesson with the aid of:

Logic modules
Charts showing different number systems and their equivalents
Whiteboard and markers

Rationale for the Lesson

Understanding number systems is important because they form the foundation of digital electronics and computer operations. This lesson enables pupils to grasp how computers process and store information, which is fundamental for further studies in technology.

Prerequisite/Previous Knowledge

Pupils have a basic understanding of counting and different types of numbers (e.g., decimal numbers).

Lesson Content/Board Summary

NUMBER SYSTEM

Meaning of Number System

A number system is a method of representing numbers. It defines a set of symbols (digits) and rules for combining them to represent numerical values. In digital electronics, different number systems like binary, octal, and hexadecimal are used.

Binary Addition

Binary addition follows specific rules based on the base-2 system. The rules are:

0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0 (with a carry of 1 to the next position)
1 + 1 + 1 = 1 (with a carry of 1 to the next position)

Example 1: Add 1011₂ and 110₂

Step 1: Align the numbers by their rightmost digits.

  1011₂
+  110₂
-----

Step 2: Add from right to left.

1 + 0 = 1
1 + 1 = 0 (carry 1)
0 + 1 + (carry 1) = 0 (carry 1)
1 + (carry 1) = 0 (carry 1)

  ¹ ¹
  1 0 1 1₂
+ 0 1 1 0₂
---------
1 0 0 0 1₂

Therefore, 1011₂ + 110₂ = 10001₂

Example 2: Add 111₂ and 101₂

  ¹ ¹ ¹
  1 1 1₂
+ 1 0 1₂
-------
1 1 0 0₂

Therefore, 111₂ + 101₂ = 1100₂

Binary Subtraction

Binary subtraction also follows specific rules:

0 – 0 = 0
1 – 0 = 1
1 – 1 = 0
0 – 1 = 1 (with a borrow of 1 from the next position)

Example 1: Subtract 101₂ from 1101₂

Step 1: Align the numbers.

  1101₂
-  101₂
-----

Step 2: Subtract from right to left.

1 – 1 = 0
0 – 0 = 0
1 – 1 = 0
1 – 0 = 1

  1101₂
- 0101₂
-------
  1000₂

Therefore, 1101₂ – 101₂ = 1000₂

Example 2: Subtract 11₂ from 101₂

  ⁰ ¹⁰ ¹
  1 0 1₂
- 0 1 1₂
-------
  0 1 0₂

Explanation of borrowing:

Rightmost digit: 1 – 1 = 0.
Middle digit: 0 – 1. We need to borrow from the leftmost ‘1’. The ‘1’ becomes ‘0’, and the ‘0’ becomes ’10’ (which is 2 in decimal). So, 10 – 1 = 1.
Leftmost digit: The ‘1’ became ‘0’, so 0 – 0 = 0.

Therefore, 101₂ – 11₂ = 010₂ or 10₂

Conversion from One Base to Another

Binary to Octal Conversion

To convert binary to octal, group the binary digits into sets of three, starting from the right. If the last group on the left has fewer than three digits, add leading zeros to complete the group. Then, convert each group of three binary digits into its octal equivalent.

Binary to Octal Chart:

000₂ = 0₈
001₂ = 1₈
010₂ = 2₈
011₂ = 3₈
100₂ = 4₈
101₂ = 5₈
110₂ = 6₈
111₂ = 7₈

Example: Convert 1101101₂ to Octal

Step 1: Group into three bits from the right.

001 101 101 (added two leading zeros)

Step 2: Convert each group.

001₂ = 1₈
101₂ = 5₈
101₂ = 5₈

Therefore, 1101101₂ = 155₈

Octal to Binary Conversion

To convert octal to binary, replace each octal digit with its three-bit binary equivalent.

Example: Convert 372₈ to Binary

Step 1: Convert each octal digit to 3-bit binary.

3₈ = 011₂
7₈ = 111₂
2₈ = 010₂

Step 2: Combine the binary groups.

011 111 010

Therefore, 372₈ = 011111010₂ or 11111010₂

Hexadecimal to Binary Conversion

To convert hexadecimal to binary, replace each hexadecimal digit with its four-bit binary equivalent.

Hexadecimal to Binary Chart:

0₁₆ = 0000₂
1₁₆ = 0001₂
2₁₆ = 0010₂
3₁₆ = 0011₂
4₁₆ = 0100₂
5₁₆ = 0101₂
6₁₆ = 0110₂
7₁₆ = 0111₂
8₁₆ = 1000₂
9₁₆ = 1001₂
A₁₆ = 1010₂
B₁₆ = 1011₂
C₁₆ = 1100₂
D₁₆ = 1101₂
E₁₆ = 1110₂
F₁₆ = 1111₂

Example: Convert A5C₁₆ to Binary

Step 1: Convert each hexadecimal digit to 4-bit binary.

A₁₆ = 1010₂
5₁₆ = 0101₂
C₁₆ = 1100₂

Step 2: Combine the binary groups.

1010 0101 1100

Therefore, A5C₁₆ = 101001011100₂

Binary to Hexadecimal Conversion

To convert binary to hexadecimal, group the binary digits into sets of four, starting from the right. If the last group on the left has fewer than four digits, add leading zeros. Then, convert each group of four binary digits into its hexadecimal equivalent.

Example: Convert 111010110₂ to Hexadecimal

Step 1: Group into four bits from the right.

0001 1101 0110 (added three leading zeros)

Step 2: Convert each group.

0001₂ = 1₁₆
1101₂ = D₁₆
0110₂ = 6₁₆

Therefore, 111010110₂ = 1D6₁₆

Teaching Methods/Instructional Techniques

Discussion, Lecture, Demonstration, Question and Answer, Visual Aids

Instructional Procedures

Step 1: Introduction

Time: 5 minutes
Teaching Skill: Set Induction
Teacher’s Activity: The teacher greets the pupils and introduces the topic by asking them about the different ways they represent numbers in daily life (e.g., using 0-9 digits). The teacher explains that just as we use the decimal system, computers use other number systems.
Pupils’ Activity: Pupils respond to the teacher’s questions and listen attentively to the introduction.
Learning Point: Pupils are introduced to the concept of number systems and their relevance.

Step 2: Meaning of Number System

Time: 5 minutes
Teaching Skill: Explanation/Definition
Teacher’s Activity: The teacher defines a number system and explains its components, such as base and digits. The teacher highlights the binary, octal, and hexadecimal systems used in electronics.
Pupils’ Activity: Pupils listen, take notes, and ask questions for clarification.
Learning Point: Pupils understand the definition and basic components of a number system.

Step 3: Binary Addition

Time: 8 minutes
Teaching Skill: Demonstration/Problem Solving
Teacher’s Activity: The teacher explains the rules for binary addition and demonstrates two examples on the board, showing step-by-step calculations, including carry-overs. The teacher encourages pupils to follow along.
Pupils’ Activity: Pupils observe the demonstration, copy the examples, and attempt practice problems given by the teacher.
Learning Point: Pupils learn how to perform binary addition.

Step 4: Binary Subtraction

Time: 8 minutes
Teaching Skill: Demonstration/Problem Solving
Teacher’s Activity: The teacher explains the rules for binary subtraction, including the concept of borrowing. The teacher demonstrates two examples on the board, showing step-by-step calculations.
Pupils’ Activity: Pupils pay attention to the borrowing concept, copy the examples, and solve additional problems.
Learning Point: Pupils learn how to perform binary subtraction.

Step 5: Binary to Octal and Octal to Binary Conversion

Time: 7 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher explains the grouping method (3 bits) for converting binary to octal and octal to binary. The teacher uses the chart of equivalents and demonstrates examples for both conversions.
Pupils’ Activity: Pupils observe the conversion steps, note the chart, and practice converting numbers.
Learning Point: Pupils understand and can perform binary-octal conversions.

Step 6: Hexadecimal to Binary and Binary to Hexadecimal Conversion

Time: 7 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher explains the grouping method (4 bits) for converting hexadecimal to binary and binary to hexadecimal. The teacher uses the chart of equivalents and demonstrates examples for both conversions.
Pupils’ Activity: Pupils observe the conversion steps, note the chart, and practice converting numbers.
Learning Point: Pupils understand and can perform hexadecimal-binary conversions.

Step 7: Evaluation/Review

Time: 5 minutes
Teaching Skill: Questioning/Assessment
Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

Define a number system.
Add the binary numbers: 1101₂ + 111₂.
Subtract the binary numbers: 1010₂ – 101₂.
Convert 110101₂ to octal.
Convert 73₈ to binary.
Convert D9₁₆ to binary.
Convert 11101101₂ to hexadecimal.

Pupils’ Activity: Pupils answer orally and in writing.
Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 5 minutes
Teaching Skill: Summarization
Teacher’s Activity: The teacher summarizes the key learning points, emphasizing the importance of number systems in digital electronics. The teacher assigns homework, including more practice problems on binary arithmetic and conversions.
Pupils’ Activity: Pupils listen to the summary, ask final questions, and copy the homework assignment.
Learning Point: Pupils reinforce their understanding and prepare for independent practice.

Lesson Keywords

Number System – A system for representing numbers using a set of symbols and rules.
Binary – A base-2 number system using only digits 0 and 1.
Octal – A base-8 number system using digits 0-7.
Hexadecimal – A base-16 number system using digits 0-9 and letters A-F.
Base – The number of unique digits, including zero, used in a positional numeral system.
Conversion – The process of changing a number from one base to another.

Differentiation

For pupils who grasp the concepts quickly, the teacher can provide more complex conversion problems involving mixed number systems or introduce signed binary numbers. For pupils who need more support, the teacher can provide additional guided practice with simpler examples and visual aids, or pair them with peers for collaborative learning.

Note for teachers using this lesson plan

Ensure pupils have a clear understanding of place values in different number systems before moving to conversions. Encourage consistent practice as proficiency in number systems comes with repeated application. Use the charts provided as visual aids throughout the lesson.