The document discusses how to convert binary numbers to decimal numbers. It explains that binary numbers are converted to decimal by multiplying each bit by its place value (2n) and summing the results. Examples are provided of converting various binary numbers like 101, 1010, and 10101 to their decimal equivalents of 5, 10, and 21 respectively. The document also gives an example of converting the binary fraction 0.10101 to the decimal 0.65625.

1. Conversions of binary number to decimal
http://improvec.blogspot.in/ 1
9CM105.21

2. Objective
On completion of this period you would be
able to know
How to convert a binary number to
decimal number
http://improvec.blogspot.in/ 2

3. Recap
 Conversion of a decimal number to binary
http://improvec.blogspot.in/ 3

4. Binary Number to Decimal
http://improvec.blogspot.in/ 4

5. Conversion of a binary number to decimal
number
We can convert a binary number to its decimal
value
 By multiplying each binary digit with its position
weight.
 First mark the bit position and then give the
weight of each bit depending on its position.
http://improvec.blogspot.in/ 5

6. Conversion of binary to decimal (contd)
The binary number in spread form = 1 1 0 1
Bit position from right hand side = 4th 3rd 2nd 1st
 The sum of the weights of all bits gives its equivalent
number.
 1x23+1x22+1x21+1x20
 8+4+0+1=(13)10
http://improvec.blogspot.in/ 6

7. Convert the binary number 101 to its
decimal equivalent
The number in the spread form = 1 0 1
Bit position from the right side = 3rd 2nd 1st
http://improvec.blogspot.in/ 7

8. Convert the binary number 101 to its
decimal equivalent (contd)
 The weight of each bit is assigned and added
together to give decimal equivalent.
1 0 1 (binary number) = 1*22 + 0*21 + 1*20
= 4+ 0 + 1
= 5 (decimal number).
http://improvec.blogspot.in/ 8

9. Convert the binary number 1010 to its
decimal equivalent
The number in the spread form = 1 0 1 0
Bit position from the right side = 4th 3rd 2nd 1st
http://improvec.blogspot.in/ 9

10. Convert the binary number 1010 to its
decimal equivalent (contd)
1 0 1 0 (binary number) = 1*23 + 0*22 + 1*21 + + 0*20
=8+0+2+0
= 10 (decimal number).
http://improvec.blogspot.in/ 10

11. Convert the binary number 10101 to its decimal
equivalent
5th 4th 3rd 2nd 1st
1 0 1 0 1
24 23 22 21 20 1*20 = 1
0*21 = 0
1*22 = 4
0*23 = 0
1*24 = 16
SUM = 21
i.e. (10101)2 = 1*20 + 0*21 + 1*22 + 0*23 + 1*24 = 1 + 0 + 4+
0 +16 = 21
(10101)2 = (21)10
http://improvec.blogspot.in/ 11

12. Convert the binary fraction 0.10101 to its
decimal equivalent
0.10101 = 1*2-1 + 0*2-2 + 1*2-3 + 0*2-4 + 1*2-5
= ½ + 0 + 1/8 + 0 + 1/32
= 0.5 + 0 + 0.125 + 0 + 0.03125
= 0.65625
(0.10101)2 = (0.65625)10
http://improvec.blogspot.in/ 12

13. Summary
In this class, you have learnt about
 Conversions of binary number to decimal
http://improvec.blogspot.in/ 13

14. Frequently Asked Questions
1. How to convert a binary number to decimal
number?
2. Convert the binary number 10101 to its
decimal equivalent?
3. Convert the binary fraction 0.10101 to its
decimal equivalent?
http://improvec.blogspot.in/ 14

15. Quiz
1. What is binary equivalent of 10101?
a. 21
b. 23
c.12
Answer: a
http://improvec.blogspot.in/ 15

16. Quiz
2. What is binary equivalent of 1111?
a. 15
b. 16
c. 14
Answer: a
http://improvec.blogspot.in/ 16