NUMBER SYSTEM
02. Number system
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Number system: - Number system is a mathematical notation of
expressing or representing numbers.
àIt also provides a unique identity
to each & every number by representing them in the form of digits.
àThere are many number systems that
have been & are still in use like: Arabic, Babylonian, Mayan and Roman.
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Roman number system: - The roman number system uses numerals to
represent each number, e.g. the number 5 is represented as V.
The
most commonly used system is the Arabic which uses the digits from 0to9.
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Radix:
- The total
number of digits used in a number system is called its radix.
àIt is also known as Base.
àThe base is written after the
number as a subscript such as: (123)10.
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The
most popular number systems used in computing are:
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Decimal
number system
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Binary
number system.
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Octal
number system.
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Hexadecimal
number system.
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The
decimal number system is used in general. However, the computers use binary
number system. The octal and hexadecimal number systems are also used in the
computing technology.
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Decimal
number system: - Decimal
number system has base ‘10’ as it uses ten (10) digits i.e. from 0to9. The position of each digit represents a specific power of the base 10, for example, the
decimal number 8910 consists of the digit ‘0’ in the unit’s position, ‘9’ in
the ten’s position, ‘1’ in the hundredth position and ‘8’ in the thousandth
position.
àThe value represented by individual
digit depends on its weight and position. Each number in this system consists
of digits at different positions. The position of digits from right side starts
with 0,1 and so on i.e. that means the position
of second digit from right most side of the digit is 2.
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The
rightmost digit of number has the lowest weight and is said as Least
Significant Digit (LSD).
The leftmost digit
of a number has the highest weight which is known as Most Significant Digit
(MSD). For example, in 724 the digit 7 is the most significant digit and 4 is
the least significant digit.
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Place
value: - Place value
is the value associated with the digit at a particular position. It is also
known as face value.
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Expansion
method: - 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.
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Binary
number system: - Digital
data represents all kinds of information in the binary system. The binary
number system has a base ‘2’ as it constitutes only two(2) digits i.e. 0 and 1. Bit is the short form for Binary digit.
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A
combination of binary numbers can be used to represent different quantities.
The positional value of each digit in binary number is twice the place value or
face value of the digit of its right sides. The weight of each position is a
power of 2.
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Octal
number system: - Octal
number system consists of eight digits i.e. from 0to7; hence the base of octal
number system is ‘8’.Each digit position in this system represents to 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. Examples of valid Octal numbers are 5678, 65438
etc.
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Hexadecimal
number system: - The
Hexadecimal number system has a base of 16. In this system, the ten digits 0to9
and the six letters A to F are used. The hexadecimal digit A is equivalent to
the decimal number 10 and the hexadecimal digit F is equivalent to the decimal
number 15. Each digit position in hexadecimal system represents to a power of
16.
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This
number system provides shortcut method to represent long binary numbers.
NOTE: - Codes in 0’s and 1’s are collectively
known as ‘ASCII’ (American standard code for information interchange).
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Complement:
- Complement
means interchange of bits, i.e. conversion of zeros (0) into ones (1) and
vice-versa. For example; complement of 1001 will be 0110.
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