Lesson Notes By Weeks and Term v3 - Junior Secondary 1
Conversion of base 10 numerals to binary numbers
Download the Lessonotes Mobile Nigeria 2025 app for faster lesson access on Android and iPhone.
Conversion of base 10 numerals to binary numbers
Download the Lessonotes Mobile Nigeria 2025 app for faster lesson access on Android and iPhone.
Subject: General Mathematics
Class: Junior Secondary 1
Term: 2nd Term
Week: 2
Theme: Number And Numeration
This page supports the lesson note with a companion video and a short classroom-ready summary.
For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.
Students should be able to convert base 10 numerals to binary numbers
A. Introduction to Number Bases A number base or radix is the number of unique digits, including zero, used to represent numbers in a positional numeral system.
Base 10 (Decimal System): This is the everyday number system commonly used. It uses ten distinct digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). The position of each digit determines its value, which is a power of
1
0. Example: $345_{10} = (3 \times 10^2) + (4 \times 10^1) + (5 \times 10^0)$.
Base 2 (Binary System): This system uses only two distinct digits (0 and 1). It is fundamental to digital computers and electronic devices because these digits can represent the two states of an electronic switch (on/off, true/false, high/low voltage). The position of each digit determines its value, which is a power of
2. Example: $101_2 = (1 \times 2^2) + (0 \times 2^1) + (1 \times 2^0)$. B. Conversion of Base 10 Numerals to Binary Numbers (Base 2) The standard method for converting a base 10 numeral to any other base (including binary) is the repeated division method. For converting to base 2, the base 10 number is repeatedly divided by 2, and the remainders are recorded at each step.
Steps for Conversion: Divide the given base 10 number by
2. Note down the remainder (which will always be either 0 or 1). Take the quotient from the division and divide it by 2 again. Note down the new remainder. Repeat this process until the quotient becomes
0. To obtain the binary number, write down the remainders from the last remainder to the first remainder (bottom-up). Worked
Examples: Example 1: Convert $5_{10}$ to binary. | Division | Quotient | Remainder | | :------- | :------- | :-------- | | $5 \div 2$ | 2 | 1 | | $2 \div 2$ | 1 | 0 | | $1 \div 2$ | 0 | 1 | Reading the remainders from bottom to top: $101_2$.
Therefore, $5_{10} = 101_2$.
Example 2: Convert $13_{10}$ to binary. | Division | Quotient | Remainder | | :------- | :------- | :-------- | | $13 \div 2$ | 6 | 1 | | $6 \div 2$ | 3 | 0 | | $3 \div 2$ | 1 | 1 | | $1 \div 2$ | 0 | 1 | Reading the remainders from bottom to top: $1101_2$.
Therefore, $13_{10} = 1101_2$.
Example 3: Convert $25_{10}$ to binary. | Division | Quotient | Remainder | | :------- | :------- | :-------- | | $25 \div 2$ | 12 | 1 | | $12 \div 2$ | 6 | 0 | | $6 \div 2$ | 3 | 0 | | $3 \div 2$ | 1 | 1 | | $1 \div 2$ | 0 | 1 | Reading the remainders from bottom to top: $11001_2$.
Therefore, $25_{10} = 11001_2$.
Example 4: Convert $42_{10}$ to binary. | Division | Quotient | Remainder | | :------- | :------- | :-------- | | $42 \div 2$ | 21 | 0 | | $21 \div 2$ | 10 | 1 | | $10 \div 2$ | 5 | 0 | | $5 \div 2$ | 2 | 1 | | $2 \div 2$ | 1 | 0 | | $1 \div 2$ | 0 | 1 | Reading the remainders from bottom to top: $101010_2$.
Therefore, $42_{10} = 101010_2$.
Teacher Activities: Introduction (5 minutes): Begin by asking students about numbers they use daily. Introduce the idea that numbers can be written in different ways (bases), just like different languages express the same idea. Introduce Base 10 and Base 2, linking Base 2 to computers and digital devices used in Nigeria (phones, ATMs).
Explanation of Key Concepts (15 minutes): Clearly define Base 10 and Base 2, emphasizing the digits used and place values. Explain the repeated division method for converting Base 10 to Base 2, demonstrating the steps meticulously on the board.
Demonstration with Examples (15 minutes): Work through Example 1 ($5_{10}$) and Example 2 ($13_{10}$) from Section 2 on the board, explaining each step clearly and encouraging questions. Emphasize writing the remainders from bottom to top.
Guided Practice (10 minutes): Provide a simple example for students to attempt individually or in pairs, circulating to check understanding and offer immediate feedback. For instance, "Convert $9_{10}$ to binary." Addressing Misconceptions (5 minutes): Pay attention to common errors, such as reading remainders from top to bottom, or errors in division. Re-explain specific steps as needed. Instruction for Chart Preparation (5 minutes): Guide students on how to prepare a conversion chart from 1-10 base 10 to base 2, explaining its utility.
Student Activities: Active Listening and Participation: Listen attentively to the teacher's explanations and demonstrations.
Note Taking: Copy definitions, steps, and worked examples into their notebooks.
Questioning: Ask clarifying questions when they do not understand a concept or a step in the examples.
Guided Practice: Attempt practice questions given by the teacher, either individually or collaboratively with classmates.
Peer Discussion: Discuss their approaches and solutions with classmates during guided practice.
Chart Creation: Individually prepare the conversion chart for numbers 1-10 (base 10) to base 2 as assigned. Students should attempt these questions in class, with the teacher providing support and feedback.
Question 1: Convert $7_{10}$ to binary.
Solution: | Division | Quotient | Remainder | | :------- | :------- | :-------- | | $7 \div 2$ | 3 | 1 | | $3 \div 2$ | 1 | 1 | | $1 \div 2$ | 0 | 1 | Reading remainders from bottom to top: $111_2$.
Therefore, $7_{10} = 111_2$.
Commentary: This is a straightforward conversion demonstrating the core process.
Question 2: Convert $18_{10}$ to binary.
Solution: | Division | Quotient | Remainder | | :------- | :------- | :-------- | | $18 \div 2$ | 9 | 0 | | $9 \div 2$ | 4 | 1 | | $4 \div 2$ | 2 | 0 | | $2 \div 2$ | 1 | 0 | | $1 \div 2$ | 0 | 1 | Reading remainders from bottom to top: $10010_2$.
Therefore, $18_{10} = 10010_2$.
Commentary: Students should be careful with the zero remainders. The process remains consistent.
Question 3: Convert $31_{10}$ to binary.
Solution: | Division | Quotient | Remainder | | :------- | :------- | :-------- | | $31 \div 2$ | 15 | 1 | | $15 \div 2$ | 7 | 1 | | $7 \div 2$ | 3 | 1 | | $3 \div 2$ | 1 | 1 | | $1 \div 2$ | 0 | 1 | Reading remainders from bottom to top: $11111_2$.
Therefore, $31_{10} = 11111_2$.
Commentary: This example reinforces the process with a larger number, ensuring all steps are followed correctly.
Differentiation: For struggling learners: Visual Aids: Use a large conversion chart displayed prominently.
Step-by-Step Prompts: Provide a written checklist of conversion steps to guide them through each problem.
Simpler Numbers: Start with very small numbers ($1_{10}$ to $10_{10}$) and gradually increase complexity.
Peer Support: Pair struggling learners with high-achieving students for collaborative problem-solving.
Manipulatives: Use physical objects (e.g., counters, stones, bottle caps) to represent quantities before abstract division. For example, to convert 5 to binary, have 5 counters, divide them into groups of 2, and identify remainders.
For high-achieving learners (Extension): Reverse Conversion: Challenge them to convert binary numbers back to base 10 to verify their answers. This reinforces understanding of place values in base
2. Other Bases: Introduce conversion to other bases like base 5 or base 8, using the same repeated division method but with a different divisor.
Binary Arithmetic: Introduce basic binary addition or subtraction.
Research Task: Assign a mini-research project on the history of number systems or the role of binary in modern computing.
Remediation: Re-teaching Core Concepts: Re-explain the concepts of base 10 and base 2, focusing on the meaning of "remainder" in division.
Focused Practice: Provide additional practice sheets with numbers that require only a few steps of division (e.g., numbers up to 20).
Individualized Attention: Work one-on-one or in small groups with learners who are still struggling, addressing their specific areas of difficulty.
Error Analysis: Review their incorrect attempts and help them identify where they went wrong (e.g., incorrect division, misidentifying remainder, reading remainders in the wrong order).
Example 1: Convert $5_{10}$ to binary.
| Division | Quotient | Remainder |
| :------- | :------- | :-------- |
| $5 \div 2$ | 2 | 1 |
| $2 \div 2$ | 1 | 0 |
| $1 \div 2$ | 0 | 1 |
Reading the remainders from bottom to top: $101_2$.
Therefore, $5_{10} = 101_2$.
Example 2: Convert $13_{10}$ to binary.
Digital Devices and Computing: This is the most direct application. Every smartphone, computer, tablet, or smart TV in Nigeria processes information using binary code. When a user types a message or takes a picture, the device converts that information into 0s and 1s for storage and processing. Understanding binary helps students grasp the fundamental language of these devices.
Data Storage and Transmission: Information stored on flash drives, hard drives, or transmitted over the internet (e.g., watching a YouTube video or sending an email from Nigeria) is all in binary format. Learning conversion helps demystify how digital content is encoded and decoded.
Electronic Switches and Logic Gates: Basic electronic circuits, like those found in traffic lights or security systems in Nigerian homes and businesses, use binary logic (on/off states). A switch being "on" could be represented by 1, and "off" by
0. This topic lays a foundation for understanding digital electronics.