1. Various number system used in digital
computers
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2. Recap:
Number systems
Importance of binary number system
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3. Prerequisite
What are various number systems used in
computers?
Binary number system.
Octal number system.
Hexadecimal number system.
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4. DECIMAL NUMBER
SYSTEM
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5. Decimal number system:
 The number system that we use in our daily life
is called the decimal number system.
 The decimal number system is a base-10
system.
 It uses 10 digits, from 0 to 9.
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6. Decimal number system (contd...) :
 Example – (1234)10 subscript 10 denotes decimal
number.
 The base or radix of a number system is defined
as the number system uses ten digits.
 The weight of each digit of a decimal number
depends on its relative position within the
number.
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7. Weight of each digit of a decimal number:
6498 = 6000 + 400 + 90 + 8
= 6*103 + 4*102 + 9*101 + 8*100
 The weight of the 1st digit of the number from
right hand
side = 1st digit * 100
 The weight of the 2nd digit of the number from
right hand
side = 2nd digit * 101
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8. Weight of each digit of a decimal number
(contd) :
 The weight of the 3rd digit of the number from
right hand
side = 3rd digit * 102
 The weight of the 4th digit of the number from
right hand
side = 4th digit * 103
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9. Weight of each digit of a decimal number
(contd) :
General expression
The weight of the nth digit of the number from right
hand side
= nth digit * 10n-1
= nth digit * (Base)n-1
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10. BINARY NUMBER
SYSTEM
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11. Binary number system:
 Binary number system is used in digital
computers.
 The base (or radix) of binary system is 2.
 It uses only two digits 0 or 1 and these digits are
abbreviated as bits.
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12. Binary number system (contd) :
 Example – (11010)2 = (26)10
 The weight of each digit of a binary number
depends on its relative position within the
number.
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13. Weight of each bit of a binary number:
1101 (binary number) = 1*23 + 1*22 + 0*21 + 1*20
=8+4+0+1
= 13 (decimal number)
 The weight of the 1st bit of the binary number
from right hand side = 1st bit * 20
 The weight of the 2nd bit of the number from right
hand
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side = 2nd bit * 21

14. Weight of each bit of a binary number
(contd) :
 The weight of the 3rd bit of the number from right
hand
side = 3rd bit * 22
 The weight of the 4th bit of the number from right
hand
side = 4th bit * 23
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15. Weight of each bit of a binary number
(contd) :
General expression
The weight of the nth bit of the number from
right hand side
= nth bit * 2n-1
= nth bit * (Base)n-1
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16. Binary equivalent of decimal numbers:
Decimal No. Binary equal Decimal No. Binary equal
0 0 11 1011
1 01 12 1100
2 10 13 1101
3 11 14 1110
4 100 15 1111
5 101 16 10000
6 110 31 11111
7 111 32 100000
8 1000 63 111111
9 1001 64 1000000
10 1010 128 10000000
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17. OCTAL NUMBER
SYSTEM
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18. Octal number system:
 Octal means 8.
 The base of octal number system is 8.
 It uses eight digits 0,1,2,3,4,5,6, and 7.
 The decimal number 8 is represented by 10, 9
by 11, 10 by 12 and so in octal number system.
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19. Octal number system (contd) :
 As 8 = 23, each octal digit is represented by a
group of three binary bits.
 This system was issued to provide a shorthand
way to deal with long strings of 0s and 1s
created in binary.
 Example – (2056)8 = (1070)10
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20. Binary representation of octal digits:
Decimal Octal number
0 0
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 10
10 12
15 17
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21. Conversion of octal to binary:
To convert a binary number to octal.
 Group binary digits in group of three.
 Convert each group to its equivalent octal digit.
 Example – (101110)8= 56
101 110
5 6
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22. Hexadecimal number system
 Hexadecimal means 16(6+10)
 It contains 16 symbols
 Its base is 16.
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23. Hexadecimal number system (contd)
 The first ten digits are represented by digits 0 to
9 and remaining six by the letters A through F.
 Each hexadecimal digit is represented by four
binary bits.
 Example – (A3)16 = (1010 0011)2
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24. EQUIVALENT VALUES OF DIFFERENT SYSTEMS
DECIMAL BINARY OCTAL HEXADECIMAL
0 0000 0 0
1 0001 1 1
2 0010 2 2
3 0011 3 3
4 0100 4 4
5 0101 5 5
6 0110 6 6
7 0111 7 7
8 1000 10 8
9 1001 11 9
10 1010 12 A
11 1011 13 B
12 1100 14 C
13 1101 15 D
14 1110 16 E
15 1111 17 F
16 10000 20 10
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25. Summary:
In this class, you have learnt about
Various number systems used in
digital computer
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26. Frequently Asked Questions
1. What is meant by base of a number system ?
2. What is the value of the base for decimal,
binary, octal and hexadecimal number systems?
3. What are octal and hexadecimal number
systems ?
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27. Quiz
1. The decimal number system is a
a. base 2
b. base 16
c. base 10
Answer: c
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28. Quiz
2. The base of octal number system is
a. 8
b. 16
c. 2
Answer: a
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29. Quiz
3. The first ten digits in hexa decimal system are
represented by digits 0 to 9 and remaining six
by the letters
a. 10 to 16
b. A to F
c. A1 to A6
Answer: b
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