Grade 7 ICT : Computer Number Systems PPT-MATATAG Curriculum
- 1. Computer Number Systems Grade 7 – ICT – Quarter 1- Lesson 5
- 2. Content Computer Number Systems ● binary ● octal ● decimal ● hexadecimal Conversion of Computer Number Systems ● binary ● octal ● decimal ● hexadecimal
- 3. Content Standards The learners will demonstrate an understanding of the computer number systems. demonstrate an understanding of conversion of computer number systems.
- 4. Performance Standards The learners convert number systems in practical scenarios.
- 5. Learning Competencies: differentiate the various computer number systems apply conversion of computer number systems
- 6. Learning Objectives: At the end of the lesson, the learners shall be able to: 1. Explain the basics of number systems and their significance in computing. 2. Identify the steps in the conversion of Decimal to Binary. 3. Convert Decimal to Binary 4. Identify steps in the conversion of binary to decimal. 5. Convert Binary to Decimal. 6. Identify steps in the conversion of Decimal to Octal. 7. Convert Decimal to Octal. 8. Identify steps in the conversion of Octal to Decimal. 9. Convert Octal to Decimal
- 7. In the world of computers, numbers are represented using different systems. The most common system is the binary system, which uses only the digits 0 and 1 to represent all numbers and data. Each digit in a binary number is called a bit. Another important system is the hexadecimal system, which uses the digits 0-9 and letters A-F to represent numbers. Computers also use the octal system, which uses digits 0-7.
- 8. What is a number system? •A number system is a method of representing numbers using specific rules. It provides a consistent way to express numerical values. In mathematics, we use various number systems to represent and manipulate numbers.
- 9. Here are the four most common types: 1. Decimal Number System (Base-10): The decimal system uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Each position to the left of the decimal point represents powers of 10 (units, tens, hundreds, thousands, etc.).
- 10. Here are the four most common types: 2. Binary Number System (Base-2): The binary system uses only two digits: 0 and 1. It is widely used in computer science and digital electronics.
- 11. Here are the four most common types: 3. Octal Number System (Base-8): The octal system uses eight digits: 0, 1, 2, 3, 4, 5, 6, and 7. It is less common but still used in some contexts.
- 12. Here are the four most common types: 4. Hexadecimal Number System (Base-16): The hexadecimal system uses sixteen digits: 0–9 and A– F (where A represents 10, B represents 11, and so on). It is commonly used in computer programming and memory addressing.
- 13. The number system plays a crucial role in mathematics and our daily lives. 1. Representation of Quantities: ✧ A number system provides a way to represent quantities. Whether it’s counting objects, measuring distances, or calculating time, numbers allow us to express these concepts precisely. ✧ For example, when you count the number of apples in a basket or measure the length of a room, you’re using the number system.
- 14. The number system plays a crucial role in mathematics and our daily lives. 2. Foundation for Mathematical Concepts: ✧ All mathematical concepts and formulas are based on the number system. Whether you’re solving equations, working with geometry, or analyzing data, numbers are fundamental. ✧ From basic arithmetic operations (addition, subtraction, multiplication, division) to advanced calculus and algebra, numbers underpin mathematical reasoning.
- 15. 3. Types of Numbers: ✧ The number system encompasses various types of numbers: 1. Counting Numbers: These start with 1 and continue indefinitely (1, 2, 3, 2. Whole Numbers: Include all counting numbers along with zero (0, 1, 2, …). 3. Integers: Positive and negative whole numbers, including zero (-3, -2, -1, 0, 1, 2, 3, …). 4. Rational Numbers: Expressible as fractions (e.g., 3/4, -2/5). 5. Irrational Numbers: Cannot be expressed as fractions (e.g., 2, π). √
- 16. 3. Types of Numbers : ✧ The number system encompasses various types of numbers: 6. Real Numbers: Encompass both rational and irrational numbers. 7. Even Numbers: Divisible by 2 (e.g., 2, 4, 6, …). 8. Odd Numbers: Not divisible by 2 (e.g., 3, 5, 7, …). 9. Prime Numbers: Divisible only by 1 and themselves (e.g., 5, 7, 13). 10. Composite Numbers: Have multiple factors (e.g., 10, 15, 28).
- 17. 4. Digital Systems and Data Representation: ✧ Understanding number systems is essential for digital systems (like computers) because they process data using binary representation (base-2). ✧ Computers use bits (0s and 1s) to represent information, and this binary system relies on the principles of the number system. The number system is not only a mathematical tool but also a fundamental aspect of our everyday interactions with the world. It allows us to quantify, calculate, and communicate effectively.
- 18. Definitio n of Terms • Number system - is a mathematical way of representing a set of values using digits or symbols. • Decimal - is a number that consists of a whole part and a fractional part separated by a decimal point. • Binary - is a number expressed in the base-2 numeral system, in this system, we use only two symbols: typically, "0" (zero) and "1" (one). • Octal - is a type of numeral system that uses a base of eight, in this system, the digits range from 0 to 7. • Hexadecimal - is a base-16 numeral system. Unlike our everyday decimal system (base 10), which uses ten symbols (0-9), hexadecimal employs sixteen symbols. These symbols represent values from 0 to 15.
- 19. Binary number system The binary number system is a fundamental concept in computer science and digital electronics. It uses a base- 2 numeral system, which means it only employs two distinct symbols: 0 (zero) and 1 (one).
- 20. Key points about binary numbers : In binary, each digit is called a bit. The binary system is used internally by almost all modern computers and electronic devices because it directly maps to electronic circuits using logic gates. Unlike our everyday decimal system (base 10), which uses ten symbols (0-9), binary uses only two symbols (0 and 1)
- 21. Conversions To convert a decimal number to binary, follow these steps: Divide the decimal number by 2. Use the integer quotient obtained as the dividend for the next step. Continue dividing until the quotient becomes 0 Write down the remainders in reverse order to get the binary
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