MATATAG Grade 7 Additional Material NUmber system.pptx

A. Content Standards
o demonstrate an understanding of the
computer number systems.
o demonstrate an understanding of conversion of
computer number systems.
B. Performance Standards
The learners convert number systems in practical
scenarios.

C. Learning Competencies
o Identify the steps in the conversion of Decimal to Binary.
o apply conversion of computer number systems
Learning Objectives
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.

Lesson:
Computer Number Systems
 Decimal number
 Binary number
Conversion of Computer Number
Systems
 Binary number
Decimal number

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.

A number system is a method of representing numbers using specific rules.
It provides a consistent way to express numerical values.
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.).
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.

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.
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.

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.

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.

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).
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).

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.

Area Vocabulary
 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.
 Then, the numbers are represented using the alphabet from A to F.

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).
Here are the 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).

Conversion:
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
representation.

Example: Convert 4 to Binary:
 Let's convert the decimal number 4 to binary:
 Step 1: Divide 4 by 2. Quotient: 2, Remainder: 0
 Reverse the remainders: 100
Therefore, 4 in binary is 100.

Bit in Binary Number:
A single binary digit is called a bit
Examples:
 100001 is a six-bit binary number.
 10101 is a five-bit binary number.
 101 is a three-bit binary number.

1. How many different digits are used in the binary number system?
2. Can you explain the concept of place value in binary numbers?
3. Why is the binary number system important in computing and
digital technology?
Answer the following questions
1) It uses a base-2 numeral system, which means it only employs two distinct
symbols: 0 (zero) and 1 (one).
2) 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
3) The binary system is used internally by almost all modern computers and
electronic devices because it directly maps to electronic circuits using logic
gates.

Identify what type of number system is the following.
78- ____________
100112 - ____________
F - _______
328 - __________
1110102 - ___________
Decimal
Binary
Hexadecimal
Decimal
Binary

Activity 2: Word Completion – Converting Decimal to Binary
Directions: Supply the missing word to complete the Steps in Conversion of Binary to Decimal.
1. Divide the number by ____________________________________________.
2. Write the quotient and the __________________on its corresponding
___________________.
3. Get the quotient and divide it again by _______________________________.
Write the quotient and remainder in its column.
4. Continue dividing until the quotient results to _________________________.
Always write its quotient and remainder in their column.
5. Copy the remainder from the bottom to _____________________________.
That would be the binary equivalent of the decimal number
2
2

MATATAG Grade 7 Additional Material NUmber system.pptx

MATATAG Grade 7 Additional Material NUmber system.pptx

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