Conversion of Number Bases Decimal to Binary, Octal, and Hexadecimal Computer Studies JSS 2 First Term Lesson Notes Week 10

Lesson Plan for Computer Studies

Subject: Computer Studies
Class: JSS 2
Term: First Term
Week: 10
Age: 12 years
Topic: Conversion of Number Bases
Sub-topic: Decimal to Binary, Octal, and Hexadecimal
Duration: 40 minutes

Behavioral Objectives:

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

1. Convert numbers from decimal to binary and vice versa.
2. Convert numbers from decimal to octal and vice versa.
3. Convert numbers from decimal to hexadecimal.
4. Explain the steps involved in each conversion process.

Keywords:

• Conversion
• Decimal
• Binary
• Octal
• Hexadecimal

Set Induction:

Ask students: “How do computers understand numbers?” Discuss the importance of number systems in computing and how conversions play a crucial role.

Entry Behavior:

Students have a basic understanding of number bases and how they relate to computing.

Learning Resources and Materials:

• Whiteboard and markers
• Handouts with conversion methods
• Calculators

Building Background/Connection to Prior Knowledge:

Review previous lessons on number bases and ensure students are familiar with decimal, binary, octal, and hexadecimal systems.

Embedded Core Skills:

• Analytical thinking
• Problem-solving
• Numeracy skills

Learning Materials:

• “Computer Studies for Junior Secondary Schools” by P. Olanrewaju
• Lagos State Scheme of Work

Instructional Materials:

• Visual aids showing conversion charts
• Worked examples for each conversion type

Content:

1. Introduction to Number Base Conversion:
   • Explain the importance of converting numbers between bases in computing.
2. Conversion from Decimal to Binary:
   • Method: Successive division by 2.
   • Example: Convert decimal 10 to binary.
     • 10 ÷ 2 = 5 (remainder 0)
     • 5 ÷ 2 = 2 (remainder 1)
     • 2 ÷ 2 = 1 (remainder 0)
     • 1 ÷ 2 = 0 (remainder 1)
     • Read remainders from bottom to top: 1010.
3. Conversion from Binary to Decimal:
   • Method: Multiply each digit by its power of 2.
   • Example: Convert binary 1010 to decimal.
     • (1×2³) + (0×2²) + (1×2¹) + (0×2⁰) = 8 + 0 + 2 + 0 = 10.
4. Conversion from Decimal to Octal:
   • Method: Successive division by 8.
   • Example: Convert decimal 65 to octal.
     • 65 ÷ 8 = 8 (remainder 1)
     • 8 ÷ 8 = 1 (remainder 0)
     • 1 ÷ 8 = 0 (remainder 1)
     • Read remainders: 101.
5. Conversion from Octal to Decimal:
   • Method: Multiply each digit by its power of 8.
   • Example: Convert octal 101 to decimal.
     • (1×8²) + (0×8¹) + (1×8⁰) = 64 + 0 + 1 = 65.
6. Conversion from Decimal to Hexadecimal:
   • Method: Successive division by 16.
   • Example: Convert decimal 255 to hexadecimal.
     • 255 ÷ 16 = 15 (remainder 15, which is F)
     • 15 ÷ 16 = 0 (remainder 15, which is F)
     • Result: FF.
7. Conversion from Hexadecimal to Decimal:
   • Method: Multiply each digit by its power of 16.
   • Example: Convert hexadecimal FF to decimal.
     • (F×16¹) + (F×16⁰) = (15×16) + (15×1) = 240 + 15 = 255.

Fill-in-the-Blank Questions (15):

1. To convert decimal to binary, we use __________ division. (a) 2 (b) 8 (c) 10 (d) 16
2. The binary equivalent of decimal 5 is __________. (a) 101 (b) 100 (c) 110 (d) 111
3. The octal system is base __________. (a) 2 (b) 8 (c) 10 (d) 16
4. When converting decimal 64 to octal, the first division gives a quotient of __________. (a) 8 (b) 6 (c) 10 (d) 4
5. The hexadecimal system uses digits from 0 to __________. (a) 9 (b) F (c) 8 (d) A
6. Decimal 15 is represented as __________ in hexadecimal. (a) E (b) F (c) D (d) C
7. The octal equivalent of binary 101 is __________. (a) 2 (b) 3 (c) 5 (d) 4
8. To convert hexadecimal A to decimal, we calculate __________. (a) 10 (b) 11 (c) 12 (d) 9
9. The binary representation of decimal 12 is __________. (a) 1100 (b) 1010 (c) 1110 (d) 1000
10. To convert decimal 32 to binary, the last remainder is __________. (a) 0 (b) 1 (c) 2 (d) 3
11. The number system that uses base 16 is __________. (a) Decimal (b) Binary (c) Octal (d) Hexadecimal
12. The octal number 7 is the same in decimal as __________. (a) 6 (b) 7 (c) 8 (d) 9
13. The conversion of binary 1111 to decimal is __________. (a) 10 (b) 11 (c) 12 (d) 15
14. When converting from octal to decimal, we multiply by __________. (a) 2 (b) 8 (c) 10 (d) 16
15. The decimal number 255 converts to __________ in hexadecimal. (a) FF (b) F0 (c) 0F (d) 10

FAQs (15):

1. What is base conversion?
   Base conversion is the process of changing a number from one base to another.
2. Why do we convert decimal to binary?
   Computers use binary, so we need to convert decimal numbers for computer processing.
3. How do you convert decimal to octal?
   Divide the decimal number by 8 and record the remainders.
4. What does binary 1101 equal in decimal?
   Binary 1101 equals 13 in decimal.
5. What is the octal representation of decimal 9?
   Decimal 9 is represented as 11 in octal.
6. How is hexadecimal used in programming?
   Hexadecimal simplifies binary and is used for color codes in web design.
7. What is the first step in converting decimal to binary?
   Divide the decimal number by 2.
8. Can you convert octal to binary directly?
   Yes, each octal digit can be represented by a 3-digit binary number.
9. How do you convert hexadecimal to decimal?
   Multiply each digit by its power of 16 and sum the results.
10. What is the binary equivalent of octal 10?
    Octal 10 is represented as 1000 in binary.
11. Why is it important to learn number base conversions?
    Understanding conversions is essential for programming and computer science.
12. What does the hexadecimal number B represent in decimal?
    Hexadecimal B represents 11 in decimal.
13. How do you check your conversion is correct?
    Convert the result back to the original base and see if you get the same number.
14. Can all numbers be converted to binary?
    Yes, all numbers can be represented in binary.
15. What is the octal equivalent of decimal 16?
    Decimal 16 is represented as 20 in octal.

Presentation Steps:

1. Revising the Previous Topic: Recap previous discussions on number bases.
2. Introducing the New Topic: Explain the significance of conversions and introduce each method step-by-step.
3. Allowing Pupils to Contribute: Invite students to share any experiences or difficulties they have had with conversions.

Teacher’s Activities:

• Demonstrate each conversion method clearly on the whiteboard.
• Guide students through examples.
• Answer questions and provide clarification as needed.

Learners’ Activities:

• Work in pairs to practice conversions using provided numbers.
• Complete fill-in-the-blank questions and discuss their answers.
• Perform conversion exercises on calculators.

Assessment:

• Evaluate student understanding through fill-in-the-blank and conversion exercises.
• Assign a quiz on conversions for homework.

Evaluation Questions (10):

1. What is the first step in converting decimal to binary?
2. How do you convert octal to decimal?
3. What is the binary equivalent of decimal 8?
4. Give an example of converting hexadecimal to decimal.
5. What does binary 1010 equal in decimal?
6. How is decimal 45 represented in octal?
7. What is the remainder when 16 is divided by 2?
8. How do you know if a conversion is correct?
9. What is the base of the hexadecimal system?
10. Why is binary important in computing?

Conclusion:

Summarize the key points about number base conversions and their importance in computer science. Emphasize practice and application in real-world scenarios. Mark the exercises and provide feedback for improvement.