Number System
6.1 Concept of number system
These
numbers belong to different number systems, which have different symbols and
rules. A number system is a writing system with specific symbols and rules for
expressing numbers and doing different calculations. For example, when we count
things, we use the decimal number system, which has 10 symbols, from 0 to 9.
That means we can make any number we want using the 10 symbols. The decimal
number system is easy to use and understand. So, it is the most commonly used number
system in our daily life.
Various number
systems are currently in use. A number system is differentiated by its base or
radix. The base is defined as the total number of digits available in the
number system. There are mainly four types of number systems:
Ø
Decimal number system
Ø
Binary number system
Ø
Octal number system
Ø Hexadecimal
number system
Decimal
number system
The decimal number system is
the common number system we use in our lives. It has a base of 10 since it uses
digits ranging from 0 to 9.
Binary
number system
The binary number system uses
only two digits: 0 and 1. Thus, it is a base-2 number system. It is used by
computers. For example, (110111)2 is a binary number.
Octal
number system
The octal number
system is the base-8 number system that uses 8 digits (0 to 7). Some examples
of octal numbers are (207)8, (5706)8, (601022)8, etc.
Hexadecimal
number system
The hexadecimal number system is the base-16 number system that uses 16 symbols, i.e., 10 digits:0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 6 letters: A, B, C, D, E, F. The letters from A to F represent the values 10 to 15 respectively. Some examples of octal numbers are (8F5)16, (AC4)16, (B52)16, (ACD)16, etc.
|
Hexadecimal
|
0
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
A
|
B
|
C
|
D
|
E
|
F
|
|
Decimal
|
0
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
13
|
14
|
15
|
|
Number
system |
Base
|
Symbols
/ Digits Used |
|
Binary
|
2
|
0,
1 |
|
Octal |
8 |
0, 1, 2, 3, 4, 5, 6, 7 |
|
Decimal |
10 |
0, 1, 2, 3, 4, 5, 6, 7,
8, 9 |
|
Hexadecimal |
16 |
0, 1, 2, 3, 4, 5, 6, 7,
8, 9 and A, B, C, D, E, F |
a. What is a number system? List the different types of
number system.
Ans: Number System is the System used to represent or express
numbers. The different types of number system are as follows:
·
Decimal number system (Base-
10)
·
Binary number system (Base- 2)
·
Octal number system (Base- 8)
·
Hexadecimal number system (Base- 16)
b. What is binary number system?
Ans: The number system that uses two different digits i.e 0
and 1 is known as binary number system.
c. What is hexadecimal number system? List its digits.
Ans: The number system that uses 16 different digits to represent
number is known as hexadecimal number system. It’s digits are 0, 1, 2, 3, 4, 5,
6, 7, 8, 9, A, B, C, D, E, and F
d. What is octal number system? List its digits.
Ans: The
number system that uses 8 different digits to represent number is known as
octal number system. It’s digits are 0, 1, 2, 3, 4, 5, 6 and 7.
e. What are BIT and Byte.
Ans: BIT is
defined as the smallest unit of data in a computer. Byte is defined
as a group of binary digits or bits (usually eight) operated on as a unit.
Binary
addition
Binary
numbers can be added in the same way as we add decimal numbers. The rules for
adding binary numbers are
Binary
subtraction
Binary
numbers can be subtracted in the same way as we subtract decimal numbers. The
rules for subtracting binary numbers are:
Decimal
to Hexadecimal number system conversion
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