Number System is a set of values used to represent different quantities. For example, a
number system can be used to represent the number of
students in a class or number of viewers watching a certain TV program etc. The digital
computer represents all kinds of data and information in
binary numbers. It includes audio, graphics,
video, text and numbers. The total number of digits used in a number system is called its base or radix. The base is written after the
number as subscript such as
51210.
Some important number systems are as follows.
- Decimal number system
- Binary number system
- Octal number system
- Hexadecimal number system
The decimal number system is used in general. However, the computers use
binary number system. The octal and
hexadecimal number
systems
are
used in the computer.
DECIMAL (base 10) - Possible
digits: 0, 1, 2, 3, 4,
5, 6, 7,
8, 9
The Decimal Number System consists of ten digits from 0 to 9. These digits can be used to represent any numeric value. The base of decimal number system is 10. It is the most widely used
number system. The value represented by individual
digit
depends on weight and position of the digit.
Each number in this system consists
of digits which are
located at different positions. The position of first digit towards
left side of the decimal point is 0. The position of second digit towards left side of the decimal point is
1. Similarly, the
position of
first digit towards right side of decimal point is -1. The position
of
second digit towards right side of
decimal
point is -2 and so on.
The value of the number is determined by multiplying the digits with the weight of their position and adding the results. This
method is known as expansion method. The rightmost digit of number has the lowest weight. This digit is called Least Significant Digit (LSD). The leftmost digit of a number has the highest weight. This digit is called Most Significant Digit (MSD). The digit 7 in the number 724 is most significant digit
and 4 is the least significant digit.
BINARY (base 2) - Possible digits: 0, 1
Digital computer represents all kinds of data and information in the binary system. Binary Number System consists of
two
digits 0 and 1. Its base is 2.
Each digit or bit in
binary number system can be 0 or 1.
A combination of
binary numbers may be used to represent
different quantities
like 1001. The positional value
of
each digit in binary number is twice the place
value or
face
value of the digit of its
right side. The weight of each position is a power of 2.
OCTAL (base 8) - Possible digits: 0,
1, 2, 3, 4, 5, 6, 7
Octal Number System consists of eight digits from 0 to 7. The base of octal system is 8. Each digit position in this system
represents a power of 8. Any digit in this system is always less than 8. Octal number system is used as a shorthand
representation of
long binary numbers. The
number 6418 is not valid in
this number system as 8 is not a valid digit.
HEXADECIMAL (base 16) - Possible digits: 0, 1, 2, 3, 4, 5,
6, 7,
8,
9, A, B, C, D,
E, F (Note: In base 10, A = 10, B = 11, C = 12, D = 13, E = 14,
F = 15)
The Hexadecimal Number System consists
of 16 digits from 0 to 9 and A to F. The alphabets A to F represent decimal
numbers from 10 to 15. The base of
this number system is 16. Each digit position in hexadecimal system represents a power of 16. The number 76416 is valid hexadecimal number. It is different
from 76410 which is seven hundred
and sixty four.
This number system provides shortcut method to represent long binary numbers.