The document discusses the binary number system. It begins by defining number systems and the decimal system. It then introduces the binary number system which has a base of 2 and uses only the digits 0 and 1. It shows how to write binary numbers and provides a table to demonstrate counting and place values in the binary system. The document explains two methods for converting between decimal and binary numbers - the division method to convert decimals to binary, and the expansion method to convert binary to decimal. It includes examples and practice problems for students to convert numbers between the two number systems.

1. Q. What is number system?
Answer: It is a system for
representing numeric values or
quantities using different
symbols (digits).

2. Q. What is decimal number
system?
Answer: The decimal number
system has base 10. It uses the
digits 0 to 9.

3. Q. What does base or radix
mean?
Answer: The number of digits
(symbols) a number system
use is called base or radix of
that number system.

4. Today we will learn
BINARY NUMBER SYSTEM

5. Q. What is binary number
system?
Answer: The binary number
system has base 2. It uses the
digits 0 and 1 only.

6. Q. How we write a binary
number?
Answer: The binary number is
written as (1010)2 because its
base is 2.

7. COUNTING IN BINARY NUMBERS
Decimal Binary Decimal Binary
0 0 12 1100
1 1 13 1101
2 10 14 1110
3 11 15 1111
4 100 16 10000
5 101 17 10001
6 110 18 10010
7 111 19 10011
8 1000 20 10100
9 1001 21 10101
10 1010 22 10110
11 1011 23 10111

8. DIVISION METHOD:
i. Divide the number by 2.
ii. Put the reminder on right
side.
iii. Keep dividing the quotient
till we get the quotient less
than 2.
iv. Record reminders from
bottom to top to get the
answer.
CONVERSION OF A DECIMAL NUMBER INTO
BINARY NUMBER
Example: (21)10
Answer: (21)10 = (10101)2

9. Activity
• Convert (31)10 into its binary equivalent.
Answer should be (11111)2

10. Q. What is the place value 2 in
(1259)10?
Answer: The place value of 2 in
(1259)10 is 2×100 = 2×102
= 200.

11. EXPANSION METHOD:
i. Multiply each digit with
its place value.
ii. Add these place values.
iii. The sum is a decimal
number.
CONVERSION OF A BINARY NUMBER INTO
DECIMAL NUMBER
Example: (11101)2
=(1×24
)+ (1×23
)+(1×22
)+(0×21
)+(1×20
)
=(1×16)+ (1×8) +(1×4)+ (0×2)+(1×1)
= 16 + 8 + 4 + 0 + 1
= 29
Answer: (11011)2 = (29)10

12. Activity
• Convert (11011)2 into its decimal
equivalent.
Answer should be (27)10

13. Q. What digits are used in
binary number system?
Answer: The binary number
system uses only 0 and 1.

14. Q. What is the base of binary
number system?
Answer: The base of binary
number system is 2.

15. Q. Which method is used to
convert a decimal number into
binary numbers?
Answer: To convert a decimal
number into binary number
we use Division method.

16. Q. Which method is used to
convert a binary numbers into
decimal number?
Answer: To convert a binary
number into decimal number
we use Expansion method.

17. Home Work
• Convert (63)10 into its binary
equivalent.
• Convert (100110)2 into its decimal
equivalent.

18. • Today we learned binary number
system
• In next lesson we will learn
addition and subtraction in
binary number system