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.
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
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
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