Number System
Introduction
Inside a computer system,
data is stored in a format that cannot be easily read by human beings. This is
the reason why input and output interfaces are required. Every computer stores
numbers, letters, and other special characters in a coded form. Before going
into the details of these codes, it is essential to have a basic understanding
of the number system; it also introduces some of the commonly used number
systems by computer professionals and the relationship between them.
Number
systems are basically two types:
i) Non-positional
Number Systems
ii) Positional Number
System
Non-Positional Number System
In early days human
beings counted on fingers. When ten fingers were not adequate, stones, pebbles
or sticks were used to indicate values. This method of counting uses an
additive approach or the non-positional number system. In this system symbols
such as I for 1, II for 2, III for 3, IIII for 4, IIIII for 5 etc. Each symbol
represents the same value regardless of its position in the number and the
symbols are simply added to find out the value of particular number. Since it
is very difficult to perform arithmetic with such a number system, positional
number systems were developed as the centuries passed.
Positional Number System
In a positional number
system, there are only a few symbols called digits, and these symbols represent
different values depending on the position they occupy in the number. The value
of each digit in such a number is determined by three considerations.
i) The digit itself;
ii) The position of the
digit in the number; and
iii) The base of the
number system
Following
are the different number system on the basis of their base value
i) Decimal Number
System
ii) Binary Number
System
iii) Octal Number
System
iv) Hexadecimal Number
System
Decimal Number system
The number system that
we use in our day-to-day life is called the Decimal number system. In this
number system altogether ten symbols or digits (0,1,2,3,4,5,6,7,8,9) used. The
base (subscripted) value of decimal number system is 10 or D.
For
Example: (63)10
or (63)D
Binary Number System
The numbers system
based on only two numbers (0 and 1) which is expressed of 2 is called Binary
Number System. The
base(subscripted) value of Binary
number system is 2 or B
For
Example: (1010)2 or (1010)B
Octal Number System
The number system which
is based on 8 digits i.e. 0,1,2,3,4,5,6,7. The base (subscripted) value of Octal number system is 8 or O.
For example: (54)8 or (54)O
Hexadecimal Number System
The hexadecimal number
system is one with a base of 16. The base of 16 suggests choices of 16
single-character digits or symbols. The first 10 digits are the digits of the
decimal system 0,1,2,3,4,5,6,7,8 and 9. The remaining six digits are denoted by
A,B,C,D,E and F representing the decimal values of 10,11,12,13,14, and 15
respectively. The base(subscripted)
value of Hexadecimal number system is 16 or H
For
Example: (H2)16 or (H2)H
The most important
thing about the number systems is that each system is just a different method
for representing the quantities. Moreover, the quantities do not change, but
the symbols used to represent those quantities are changing in each number
system.
|
Number System |
Radix value |
Set of symbols |
Examples |
|
Decimal |
r=10 |
(0,1,2,3,4,5,6,7,8,9) |
(35)10 |
|
Binary |
r=2 |
(0,1) |
(1001001)2 |
|
Octal |
r=8 |
(0,1,2,3,4,5,6,7) |
(3457)8 |
|
Hexadecimal |
r=16 |
(0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F) |
(234AF2)16 |
Conclusion
The number system is an essential concept in mathematics, computer science, and digital electronics. It is used to represent numbers in different ways and perform various arithmetic operations. Understanding the number system is crucial for students of grade 10 and SEE who want to pursue a career in science, technology, engineering, or mathematics.
FAQs
1) What is the decimal number system?
Ans: The decimal number system is a base-10 number system that uses ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to represent numbers.
2) What is binary number system?
Ans: The binary number system is a base-2 number system that uses only two digits (0 and 1) to represent numbers.
3) How do I convert a decimal number to a binary number?
Ans: To convert a decimal number to a binary number, we need to divide the decimal number by 2 repeatedly until the quotient becomes 0.
4) What is the hexadecimal number system?
Ans: The hexadecimal number system is a base-16 number system that uses 16 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F) to represent numbers.
5) Why is the number system important?
Ans: The number system is important because it is used to represent numbers in different ways and perform various arithmetic operations. It is also used in various fields, such as computer science, digital electronics, and cryptography.
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