The document outlines a lesson plan covering number systems. It includes converting between decimal, binary, octal, and hexadecimal number systems. The key concepts covered are the different number systems used in computing, including binary, octal, hexadecimal, and their bases. Conversion between these systems involves multiplying digits by place values to get the value in another base. The skills practiced are computational thinking and step-wise thinking. Values reinforced include awareness of computer technology development and patience.

1. ACADEMIC YEAR PLAN
Lesson
No.
Chapter
Name Concepts Skills Values Reinforced
2
Number
System
Number System
Convert decimal number to binary,
hexa-decimal and octal number
Awareness about the
development in computer
technology
Decimal
Number systems
Convert octal, hexa-decimal number
to binary number system
Patience and preservence in the
pursuit of self goals
Binary Number
System
Convert hexa-decimal number to
octal number
Hexa-decimal
Number System Computational thinking
Octa-decimal
Number System Step wise thinking

2. Number System
Number System is a way to represent the numbers in the computer architecture.
There are four different types of the number system, such as:
 Binary number system (base 2)
 Octal number system (base 8)
 Decimal number system (base 10)
 Hexadecimal number system (base 16).

3. What is Binary number system?
The binary number system, also called the base-2 number system, is a method of
representing numbers that counts by using combinations of only two numerals: zero (0) and one
(1). Computers use the binary number system to manipulate and store all of their data
including numbers, words, videos, graphics, and music.
 A single binary digit is called a “Bit”. A binary number consists of several bits. Examples are:
 101 is a three-bit binary number
 1101 is a four-bit binary number
 10101 is a five-bit binary number
 100001 is a six-bit binary number
What is Bit in Binary number system?

4. Conversion of decimal number system into
binary number system
Following are the steps that need to be followed while converting decimal number
system into binary number system.
Step1: Divide the given number by 2.
Step 2: Write down the remainder and divide the quotient again by 2. The steps are
repeated till the quotient becomes zero.
Ex: (25)10 = ( ? )2
Ans:(11001)2
2 25
2 12 1
2 6 0
2 3 0
1 1
1

5. What is Bite in Binary number system?
The basic unit of information in computer storage and processing.
A bite consists of eight adjacent binary digits (bits) each of which consists of a 0 or 1. the
storage of bits making up a bite is processed as a unit by a computer.
Example : 10110111 is a bite and can represent data like a text, image or sound in a
computer.

6. Conversion of binary number system into
decimal number system
 Multiply each digit with its positional value, which is in terms of powers of 2, starting from
the extreme right digit.
 Increase the power one by one, keeping the base fixed at 2.
 Add all the products to get the decimal number.
Let’s understand with examples.
Example 1: (1001)2 = (?)10 Example 1: (1010)2 = (?)10
1 * 20 = 1 0 * 20 = 0
0 * 21 = 0 1 * 21 = 2
0 * 22 = 0 0 * 22 = 0
1 * 23 = 8 1 * 23 = 8
9 10
(1001)2 = (9)10 (1010)2 = (10)10

7. Octal Number System
The octal number system consists of 8 digits, i.e., 0 to 7. Hence, the base of octal number system is 8.
Some examples of octal number system are 527 and 45.
Conversion of Octal Number System into Decimal Number System
Step 1: Multiply each digit with its positional value, which is in terms of power of 8, starting from the
extreme right digit.
Step 2: Increase the power one by one, keeping the base fixed at 8.
Step 3: Add all the products to get the decimal number.
Let’s understand with an example.
(345)8 = (?)10
(345)8
5 * 80 = 5
4 * 81 = 32
3 * 82 = 192
229
(345)8 = (229)10

8. Hexadecimal Number System
The hexadecimal number system consists of 16 digits, i.e., 0 to 9 digits and letters A to F, where 10
represents A, 11 represents B, 12 represents C, 13 represents D 14 represents E, and 15 represents F.
Thus, the base of hexadecimal number system is 16. Some examples of hexadecimal number system
are 54A, 64A and 4D2.
Conversion of Hexadecimal Number system into Decimal Number System
Step 1: Multiply each digit with its positional value, which is in terms of power of 16, starting from
the extreme right digit.
Step 2: Increase the power 1 by 1 keeping the base fixed at 16.
Step 3: add all the products to get the decimal number.
let us understand with an example:
( 4D2)16 = (?)10
(4D2)16
2 * 160 = 2
D * 161 = 208
4 * 162 = 1024
1236

9. Binary Numbers Table

10. How to calculate the binary number
system?
For example, the number to be operated is 1235.
 This indicates,
 1235 = 1 × 1000 + 2 × 100 + 3 × 10 + 5 × 1
 Given,
Thousands Hundreds Tens One / Unit
1 2 3 5
1000 = 10
3
= 10 × 10 × 10
100 = 10
2
= 10 × 10
10 = 10
1
= 10
1 = 10
0
(any value to the
exponent zero is one)

11. Binary Arithmetic Operations
Like we perform the arithmetic operations in numerals, in the same way, we can
perform addition, subtraction, multiplication and division operations on Binary
numbers. Let us learn them one by one.
Binary Addition:
Adding two binary numbers will give us a binary number itself. It is the simplest
method.
For example: Add 11012 and 10012.
Solution:

12. Binary Subtraction
Subtracting two binary numbers will give us a binary number itself. It is also a
straightforward method.
Example: Subtract 11012, and 10102.
Solution:

13. Binary Multiplication
The multiplication process is the same for the binary numbers as it is for numerals. Let
us understand it with example.
Example: Multiply 11012 and 10102.
Solution:

14. Binary Division
The binary division is similar to the decimal number division method. We will learn with
an example here.
Example: Divide 10102 by 102
Solution: