Arithmetic in Number Bases, Addition and Subtraction for SS 3

Class: SS 3
Term: First Term
Week: 12
Age: 16 years
Duration: 45 minutes
Subject: Computer Science
Curriculum Theme: OVERVIEW OF NUMBER BASES
Previous Lesson: Number Bases, Review and Base Conversion
Topic: Arithmetic in Number Bases, Addition and Subtraction
Subject Matter: Basic arithmetic in number bases: Addition and subtraction

Specific Objectives

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

Cognitive Domain

• State the rules for addition in different number bases.
• State the rules for subtraction in different number bases.

Affective Domain

• Appreciate the importance of arithmetic operations in number bases within computer science.

Psychomotor Domain

• Perform addition operations on numbers in different bases.
• Perform subtraction operations on numbers in different bases.

Reference Materials

The following resources were used in planning this lesson:

• 2025 Revised 9 Years Basic Education Curriculum
• Relevant State Unified Scheme of Work
• Computer Studies for Senior Secondary Schools, Book 3
• The HeadTeacher Scheme of work

Instructional Materials

The teacher will teach this lesson with the aid of:

• Whiteboard and markers
• Charts showing examples of addition and subtraction in various number bases
• Textbook examples
• Projector (optional) for displaying worked examples

Rationale for the Lesson

Understanding arithmetic in number bases is fundamental in Computer Science, as computers operate using binary. This lesson provides students with the practical skills to perform addition and subtraction in different bases, which is essential for comprehending how computers process data and execute calculations.

Prerequisite/Previous Knowledge

Students should have a basic understanding of number bases, including binary, octal, decimal, and hexadecimal, and how to convert numbers between these bases.

Lesson Content/Board Summary

Arithmetic in Number Bases: Addition and Subtraction

Addition in Number Bases

Addition in any number base follows similar principles to decimal addition, but with a crucial difference in how ‘carrying over’ is handled. When the sum of digits in a column exceeds or equals the base, we divide the sum by the base. The remainder is written down, and the quotient is carried over to the next column.

Procedure for Addition:

1. Add the digits in the rightmost column.
2. If the sum is less than the base, write it down.
3. If the sum is equal to or greater than the base, divide the sum by the base. Write down the remainder and carry the quotient to the next column.
4. Repeat the process for all columns, moving from right to left.

Example 1: Binary Addition

Question: Add (110_2 + 111_2)

Solution:

Step 1: Add the rightmost column (units place).

(0_2 + 1_2 = 1_2)

Step 2: Add the next column.

(1_2 + 1_2 = 2_{10} = 10_2). Write down (0), carry (1).

Step 3: Add the leftmost column, including the carry.

(1_2 + 1_2 + text{carry } 1_2 = 3_{10} = 11_2). Write down (1), carry (1).

Step 4: Write down the final carry.

(1)

Answer: (110_2 + 111_2 = 1101_2)

Example 2: Base 5 Addition

Question: Add (004_5 + 234_5)

Solution:

Step 1: Add the rightmost column (units place).

(4_5 + 4_5 = 8_{10}). Divide by base 5: (8 div 5 = 1) remainder (3). Write down (3), carry (1).

Step 2: Add the next column, including the carry.

(0_5 + 3_5 + text{carry } 1_5 = 4_5). Write down (4).

Step 3: Add the leftmost column.

(0_5 + 2_5 = 2_5). Write down (2).

Answer: (004_5 + 234_5 = 243_5)

Subtraction in Number Bases

Subtraction in number bases also resembles decimal subtraction, but ‘borrowing’ involves converting the borrowed value from the higher place value into the current base. When a digit is too small to subtract from, we borrow from the digit to its left. The borrowed ‘1’ from the next column becomes the value of the base in the current column.

Procedure for Subtraction:

1. Subtract the digits in the rightmost column.
2. If a digit in the minuend (top number) is smaller than the corresponding digit in the subtrahend (bottom number), borrow from the digit to its left.
3. When you borrow ‘1’ from the next column, it becomes the value of the base in the current column. Add this base value to the digit in the minuend before subtracting.
4. Decrement the digit from which you borrowed by ‘1’.
5. Repeat the process for all columns, moving from right to left.

Example 1: Base 4 Subtraction

Question: Subtract (122_4 – 032_4)

Solution:

Step 1: Subtract the rightmost column (units place).

(2_4 – 2_4 = 0_4)

Step 2: Subtract the next column.

(2_4 – 3_4). Since (2 < 3), we borrow from the leftmost digit (1_4). The (1_4) becomes (0_4).

The borrowed (1) becomes (4_{10}) in the current column. So, we have ((4_{10} + 2_4) – 3_4 = 6_{10} – 3_{10} = 3_{10} = 3_4).

Step 3: Subtract the leftmost column.

(0_4 – 0_4 = 0_4)

Answer: (122_4 – 032_4 = 30_4)

Example 2: Binary Subtraction

Question: Subtract (1110_2 – 0101_2)

Solution:

Step 1: Subtract the rightmost column (units place).

(0_2 – 1_2). Since (0 < 1), we borrow from the next digit (1_2). The (1_2) becomes (0_2).

The borrowed (1) becomes (2_{10}) in the current column. So, we have ((2_{10} + 0_2) – 1_2 = 2_{10} – 1_{10} = 1_{10} = 1_2).

Step 2: Subtract the next column.

(0_2 – 0_2 = 0_2)

Step 3: Subtract the next column.

(1_2 – 1_2 = 0_2)

Step 4: Subtract the leftmost column.

(1_2 – 0_2 = 1_2)

Answer: (1110_2 – 0101_2 = 1001_2)

Teaching Methods/Instructional Techniques

Discussion, Explanation, Demonstration, Guided Practice, Problem Solving

Instructional Procedures

Step 1: Introduction

Time: 5 minutes

Teaching Skill: Review/Questioning

Teacher’s Activity: The teacher briefly reviews previous knowledge of number bases and their importance in computing. The teacher asks students to recall different number bases and how to convert between them.

Pupils’ Activity: Students respond to questions about number bases and conversion.

Learning Point: Number base recall

Step 2: Introduction to Addition in Number Bases

Time: 5 minutes

Teaching Skill: Explanation

Teacher’s Activity: The teacher explains the general concept of addition in number bases, highlighting the ‘carry over’ rule and how it differs from decimal addition. The teacher introduces the first set of examples from the Board Summary.

Pupils’ Activity: Students listen attentively and ask clarifying questions.

Learning Point: Addition concept introduction

Step 3: Demonstration of Binary Addition

Time: 7 minutes

Teaching Skill: Demonstration

Teacher’s Activity: The teacher demonstrates the addition of (110_2 + 111_2) step-by-step on the whiteboard, explaining each carry operation clearly.

Pupils’ Activity: Students observe the demonstration and follow the steps, noting the carry operations.

Learning Point: Binary addition demonstration

Step 4: Guided Practice for Base 5 Addition

Time: 7 minutes

Teaching Skill: Guided Practice

Teacher’s Activity: The teacher guides students through the addition of (004_5 + 234_5), encouraging them to participate in each step, especially the carrying process.

Pupils’ Activity: Students participate in solving the problem, performing calculations and explaining their steps.

Learning Point: Base 5 addition practice

Step 5: Introduction to Subtraction in Number Bases

Time: 5 minutes

Teaching Skill: Explanation

Teacher’s Activity: The teacher explains the general concept of subtraction in number bases, emphasizing the ‘borrowing’ rule and how the borrowed value relates to the base.

Pupils’ Activity: Students listen and prepare for subtraction examples.

Learning Point: Subtraction concept introduction

Step 6: Demonstration of Base 4 Subtraction

Time: 7 minutes

Teaching Skill: Demonstration

Teacher’s Activity: The teacher demonstrates the subtraction of (122_4 – 032_4) step-by-step on the whiteboard, clearly showing how borrowing works in base 4.

Pupils’ Activity: Students observe the demonstration, paying attention to the borrowing process.

Learning Point: Base 4 subtraction demonstration

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. Add (101_2 + 011_2).
2. Subtract (1011_2 – 100_2).
3. Explain the ‘carry over’ rule in base 8 addition.
4. Explain the ‘borrowing’ rule in base 6 subtraction.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Arithmetic operations assessment

Step 8: Note-Taking

Time: 4 minutes

Teaching Skill: Guided Writing

Teacher’s Activity: The teacher guides pupils/students to copy the essential Board Summary notes on addition and subtraction in number bases into their notebooks.

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

Learning Point: Board notes recording

Step 9: Conclusion

Time: 2 minutes

Teaching Skill: Summarization

Teacher’s Activity: The teacher briefly summarizes the key points of the lesson, reiterating the importance of understanding arithmetic in different number bases for computer science. The teacher encourages students to practice more problems.

Pupils’ Activity: Students listen and ask any final questions.

Learning Point: Lesson summary and reinforcement

Continuous Assessment/Further Study

Type: Homework

Instruction: Solve the following arithmetic problems in the specified number bases:

1. Add (1011_2 + 1101_2)
2. Subtract (11011_2 – 1010_2)
3. Add (34_5 + 23_5)
4. Subtract (41_5 – 13_5)
5. Add (76_8 + 15_8)

Lesson Keywords

• Number Bases – Different systems for representing numbers (e.g., binary, decimal).
• Binary – Base-2 number system, using digits 0 and 1.
• Octal – Base-8 number system, using digits 0-7.
• Decimal – Base-10 number system, using digits 0-9.
• Hexadecimal – Base-16 number system, using digits 0-9 and A-F.
• Addition – The process of combining numbers to find their sum.
• Subtraction – The process of taking one number away from another.
• Carry Over – A digit transferred to the next higher place value during addition.
• Borrowing – Taking value from a higher place value to facilitate subtraction in a lower place value.

Differentiation

For students who grasp the concepts quickly, provide more complex problems involving larger numbers or different bases (e.g., base 16). For students who are struggling, offer additional guided practice with simpler binary or base 5 problems, providing one-on-one support or peer tutoring.

Suggested Lesson Videos

For further understanding, search YouTube for:

• “Addition and subtraction in number bases computer science”
• “Binary arithmetic for SS3”
• “Number base operations explained”

Teacher Guide for Using This Lesson Plan

Before the lesson, ensure you have clear, step-by-step examples prepared for both addition and subtraction in various number bases, especially binary and base 5/4 as specified. Begin by quickly reviewing the concept of number bases to activate prior knowledge. During the demonstration and guided practice, encourage students to explain their reasoning for carrying and borrowing. Pay close attention to common errors, such as forgetting to convert the borrowed value to the base or incorrectly handling carries. Allow sufficient time for students to copy the Board Summary notes after the main teaching points have been covered and evaluated. Provide immediate feedback during practice sessions to correct misconceptions. For weaker learners, simplify the numbers in the examples. For faster learners, challenge them with problems that require converting numbers to a common base before performing arithmetic.