Class 9 (Data Representations)
Number Systems
The language we use to communicate with each other is comprised of words
and characters. We understand numbers, characters and words. But this type of
data is not suitable for computers. Computers only understand the numbers.
So, when we enter data, the data is converted into electronic pulse. Each
pulse is identified as code and the code is converted into numeric format by
ASCII. It gives each number, character and symbol a numeric value (number) that
a computer understands.
So to understand the language of computers, one must be
familiar with the number systems.
The Number Systems used in computers are:
- Binary number system
- Octal number system
- Decimal number system
- Hexadecimal number system
Binary number system (Base:2)
It has only two digits '0' and '1' so its base is 2. Accordingly, In this
number system, there are only two types of electronic pulses; absence of
electronic pulse which represents '0'and presence of electronic pulse which
represents '1'. Each digit is called a bit.
A group of four bits (1101) is
called a nibble and group of eight bits (11001010) is called a byte. The
position of each digit in a binary number represents a specific power of the
base (2) of the number system.
Octal number system(Base: 8)
It has eight digits (0, 1, 2, 3, 4, 5, 6, 7) so its base is 8. Each digit
in an octal number represents a specific power of its base (8). As there are
only eight digits, three bits (23=8) of binary number system can convert any
octal number into binary number.
This number system is also used to shorten
long binary numbers. The three binary digits can be represented with a single
octal digit.
Decimal number system(Base:10)
This number system has ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) so its
base is 10. In this number system, the maximum value of a digit is 9 and the
minimum value of a digit is 0. The position of each digit in decimal number
represents a specific power of the base (10) of the number system.
This number
system is widely used in our day to day life. It can represent any numeric
value.
Hexadecimal number system(Base:16)
This number system has 16 digits that ranges from 0 to 9 and A to F. So,
its base is 16. The A to F alphabets represent 10 to 15 decimal numbers.
The
position of each digit in a hexadecimal number represents a specific power of
base (16) of the number system. As there are only sixteen digits, four bits
(24=16) of binary number system can convert any hexadecimal number into binary
number.
It is also known as alphanumeric number system as it uses both numeric digits
and alphabets.
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