CONTENTS
INTRODUCTION,
TYPES OF NUMBER SYSTEM,
DECIMAL NUMBER SYSTEM,
BINARY NUMBER SYSTEM,
OCTAL NUMBER SYSTEM,
HEXADECIMAL NUMBER SYSTEM,
CONVERSION METHOD,
• INTRODUCTION:
A set of values used to represent different quantities is known as NUMBER SYSTEM.
For example-
A number can be used to represent the number of student in a class or number of viewers watching a certain TV program etc.
• TYPES OF NUMBER SYSTEM:
Number systems are four types,
1. DECIMAL NUMBER SYSTEM,
2. BINARY NUMBER SYSTEM,
3. OCTAL NUMBER SYSTEM,
4. HEXADECIMAL NUMBER SYSTEM,
DECIMAL NUMBER SYSTEM:
The number system that we used in our day to day life is the decimal number system.
Decimal number system has base 10 as it uses ten digits from 0 to 9.
EXAMPLE-(234)10
BINARY NUMBER SYSTEM:
Binary number system uses two digits 0&1.
Its base is 2.
A combination of binary numbers may be used to represent different quantities like 1001.
Example –
(1001)2,
(100)2,
OCTAL NUMBER SYSTEM:
Octal number system consists of eight digits from 0 to 7.
The base of octal system is 8.
Any digit in this system is always less than 8.
It is shortcut method to represent long binary number.
Example –
(34)8,
(235)8,
• HEXADECIMAL NUMBER SYSTEM:
Hexadecimal number system consist of 16 digits from 0 to 9 and a to f.
Its base is 16.
Each digit of this number system represents a power of 8.
Example-
(6D) 16,
(A3)16,
CONVERSION METHOD:
There are two methods used most frequently to convert a number in a particular base to another base.
Remainder method,
Expansion method,
REMAINDER METHOD:
This method is used to convert a decimal number to its equivalent value in any other base.
The following steps are to be followed by this method:
Divide the number by the base and note the remainder.
Divide the quotient by the base and note the remainder.
Repeat step 2 until the quotient cannot be divided further. That is, the quotient become to smaller than divisor.
The sequence of remainder starting from last generated 1 prefix by undivided quotient is the converted number.
EXPANSION METHOD:
This method can be applied to convert any number in any base to its equivalent in base 10.
During expansion, the base of the number is sequentially raised to start with 0 and is incremented by one for every digit that occurs in the binary number.
THANK YOU!!!!!
this presentation explains the nature of digital and binary data. it introduces the number systems such as decimal, binary, octal and hexadecimal. it also explains the addition and subtraction of binary numbers by following their arithmetical rules. explains the different forms of data and forms of processed data.
there are different number system such as binary, decimal, octal and hexadecimal. binary has 2 digits 0 & 1. decimal has 0 to 9 digits. octal has 0 to 7 digits. and hexadecimal number system has 0 to 9 digits and 10 to 15 are denoted by alphabets. such as A=10, B=11 etc.
CONTENTS
INTRODUCTION,
TYPES OF NUMBER SYSTEM,
DECIMAL NUMBER SYSTEM,
BINARY NUMBER SYSTEM,
OCTAL NUMBER SYSTEM,
HEXADECIMAL NUMBER SYSTEM,
CONVERSION METHOD,
• INTRODUCTION:
A set of values used to represent different quantities is known as NUMBER SYSTEM.
For example-
A number can be used to represent the number of student in a class or number of viewers watching a certain TV program etc.
• TYPES OF NUMBER SYSTEM:
Number systems are four types,
1. DECIMAL NUMBER SYSTEM,
2. BINARY NUMBER SYSTEM,
3. OCTAL NUMBER SYSTEM,
4. HEXADECIMAL NUMBER SYSTEM,
DECIMAL NUMBER SYSTEM:
The number system that we used in our day to day life is the decimal number system.
Decimal number system has base 10 as it uses ten digits from 0 to 9.
EXAMPLE-(234)10
BINARY NUMBER SYSTEM:
Binary number system uses two digits 0&1.
Its base is 2.
A combination of binary numbers may be used to represent different quantities like 1001.
Example –
(1001)2,
(100)2,
OCTAL NUMBER SYSTEM:
Octal number system consists of eight digits from 0 to 7.
The base of octal system is 8.
Any digit in this system is always less than 8.
It is shortcut method to represent long binary number.
Example –
(34)8,
(235)8,
• HEXADECIMAL NUMBER SYSTEM:
Hexadecimal number system consist of 16 digits from 0 to 9 and a to f.
Its base is 16.
Each digit of this number system represents a power of 8.
Example-
(6D) 16,
(A3)16,
CONVERSION METHOD:
There are two methods used most frequently to convert a number in a particular base to another base.
Remainder method,
Expansion method,
REMAINDER METHOD:
This method is used to convert a decimal number to its equivalent value in any other base.
The following steps are to be followed by this method:
Divide the number by the base and note the remainder.
Divide the quotient by the base and note the remainder.
Repeat step 2 until the quotient cannot be divided further. That is, the quotient become to smaller than divisor.
The sequence of remainder starting from last generated 1 prefix by undivided quotient is the converted number.
EXPANSION METHOD:
This method can be applied to convert any number in any base to its equivalent in base 10.
During expansion, the base of the number is sequentially raised to start with 0 and is incremented by one for every digit that occurs in the binary number.
THANK YOU!!!!!
this presentation explains the nature of digital and binary data. it introduces the number systems such as decimal, binary, octal and hexadecimal. it also explains the addition and subtraction of binary numbers by following their arithmetical rules. explains the different forms of data and forms of processed data.
there are different number system such as binary, decimal, octal and hexadecimal. binary has 2 digits 0 & 1. decimal has 0 to 9 digits. octal has 0 to 7 digits. and hexadecimal number system has 0 to 9 digits and 10 to 15 are denoted by alphabets. such as A=10, B=11 etc.
It is a ppt on number system of computer science. It is relative to class 11th CBSE. This can help you to get quickly to through number system and help them to revise when needed.
The 10th Digital Learning Maths for IT sessions - The theme this time being the OCTAL number system which is used widely in computing circles - IP addressing being one.
Some straight forward conversion tasks for you!
Explain the concept of Number System- Binary , Decimal , Octal and Hexadecimal, conversion types, ASCII ,EBCDIC, EXCESS 3 Codes , Binary and Subtraction
Conversion of Number Systems
Number System is a method of representing Numbers on the Number Line with the help of a set of Symbols and rules. These symbols range from 0-9 and are termed as digits. Number System is used to perform mathematical computations ranging from great scientific calculations to calculations like counting the number of Toys for a Kid or Number chocolates remaining in the box. Number Systems comprise of multiple types based on the base value for its digits.
9 in the Maths for I.T Digital Learning sessions - This time the theme is the Hexadecimal number system.
Tasks incorporated include the following;
Hex to Binary
Binary to Hex
and more...
Understandable and user-friendly way to master the Hex way of working.
Number 9 in the Maths for I.T Digital Learning sessions - This time the theme is the Hexadecimal number system.
Tasks incorporated include the following;
Hex to Binary
Binary to Hex
and more...
Understandable and user-friendly way to master the Hex way of working.
It is a ppt on number system of computer science. It is relative to class 11th CBSE. This can help you to get quickly to through number system and help them to revise when needed.
The 10th Digital Learning Maths for IT sessions - The theme this time being the OCTAL number system which is used widely in computing circles - IP addressing being one.
Some straight forward conversion tasks for you!
Explain the concept of Number System- Binary , Decimal , Octal and Hexadecimal, conversion types, ASCII ,EBCDIC, EXCESS 3 Codes , Binary and Subtraction
Conversion of Number Systems
Number System is a method of representing Numbers on the Number Line with the help of a set of Symbols and rules. These symbols range from 0-9 and are termed as digits. Number System is used to perform mathematical computations ranging from great scientific calculations to calculations like counting the number of Toys for a Kid or Number chocolates remaining in the box. Number Systems comprise of multiple types based on the base value for its digits.
9 in the Maths for I.T Digital Learning sessions - This time the theme is the Hexadecimal number system.
Tasks incorporated include the following;
Hex to Binary
Binary to Hex
and more...
Understandable and user-friendly way to master the Hex way of working.
Number 9 in the Maths for I.T Digital Learning sessions - This time the theme is the Hexadecimal number system.
Tasks incorporated include the following;
Hex to Binary
Binary to Hex
and more...
Understandable and user-friendly way to master the Hex way of working.
A number system is a mathematical framework for representing and expressing numbers. It consists of a set of symbols and rules for using those symbols to represent numeric values. The most common number systems include:
Decimal (Base-10): The decimal system uses ten symbols (0-9) to represent numbers. It is the system most widely used in everyday life.
Binary (Base-2): The binary system uses two symbols (0 and 1). It's fundamental in computer science and digital electronics, representing data using on/off or high/low states.
Octal (Base-8): Octal uses eight symbols (0-7). It is occasionally used in computing and programming.
Hexadecimal (Base-16): Hexadecimal uses sixteen symbols (0-9 and A-F). It's prevalent in computer science for representing binary values in a more concise and readable form.
Roman Numerals: Roman numerals are a non-positional system that uses combinations of letters (e.g., I, V, X, L) to represent numbers. They are often found in historical and formal contexts.
Each number system has its own rules for counting and arithmetic operations. The choice of number system depends on the application, with decimal being the most common for everyday use and binary being vital for computer operations. Different systems have their advantages and disadvantages in different contexts.
Number System is a method of representing Numbers on the Number Line with the help of a set of Symbols and rules. These symbols range from 0-9 and are termed as digits. Number System is used to perform mathematical computations ranging from great scientific calculations to calculations like counting the number of Toys for a Kid or Number chocolates remaining in the box. Number Systems comprise of multiple types based on the base value for its digits.
What is the Number Line?
A Number line is a representation of Numbers with a fixed interval in between on a straight line. A Number line contains all the types of numbers like natural numbers, rationals, Integers, etc. Numbers on the number line increase while moving Left to Right and decrease while moving from right to left. Ends of a number line are not defined i.e., numbers on a number line range from infinity on the left side of the zero to infinity on the right side of the zero.
Positive Numbers: Numbers that are represented on the right side of the zero are termed as Positive Numbers. The value of these numbers increases on moving towards the right. Positive numbers are used for Addition between numbers. Example: 1, 2, 3, 4, …
Negative Numbers: Numbers that are represented on the left side of the zero are termed as Negative Numbers. The value of these numbers decreases on moving towards the left. Negative numbers are used for Subtraction between numbers. Example: -1, -2, -3, -4, …
Number and Its Types
A number is a value created by the combination of digits with the help of certain rules. These numbers are used to represent arithmetical quantities. A digit is a symbol from a set 10 symbols ranging from 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Any combination of digits represents a Number. The size of a Number depends on the count of digits that are used for its creation.
For Example: 123, 124, 0.345, -16, 73, 9, etc.
Types of Numbers
Numbers are of various types depending upon the patterns of digits that are used for their creation. Various symbols and rules are also applied on Numbers which classifies them into a variety of different types:
Number and Its Types
1. Natural Numbers: Natural Numbers are the most basic type of Numbers that range from 1 to infinity. These numbers are also called Positive Numbers or Counting Numbers. Natural Numbers are represented by the symbol N.
Example: 1, 2, 3, 4, 5, 6, 7, and so on.
2. Whole Numbers: Whole Numbers are basically the Natural Numbers, but they also include ‘zero’. Whole numbers are represented by the symbol W.
Example: 0, 1, 2, 3, 4, and so on.
3. Integers: Integers are the collection of Whole Numbers plus the negative values of the Natural Numbers. Integers do not include fraction numbers i.e. they can’t be written in a/b form. The range of Integers is from the Infinity at the Negative end and Infinity at the Positive end, including zero. Integers are represented by the symbol Z.
Example: ...,-4, -3, -2, -1, 0, 1, 2, 3, 4,...
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Acem numbersystem
1. NUMBER SYSTEM
Program Name : BBA (FS&B)
Semester : 1st Sem
Course Name: Computer &
Information Systems
Course Code : BBA/II/104
2. What is Number System ?
•A system for representing number of certain
type.
•A number system defines a set of values
used to represent quantity.
• Example:
–There are several systems for representing
the counting numbers.
–These include the usual base “10” or decimal
system : 0,1,2,3,…..10,11,12,..99,100,…
3. Number System
•Decimal is the number system and is used in our day to day life
•Binary is a number system that is used in computers
•Octal is a number system that represents groups of binary
numbers. It is used in digital displays.
•Hexadecimal (Hex) is a number system that represents groups
of binary numbers. Hex is primarily used in computing.
4. Different Number System
•Decimal Number System
-Base 10
• Binary Number System
- Base 2
• Octal Number System
-Base 8
• Hexadecimal Number Sys tem
- Base 16
5. Common Number System
Decimal 10 0, 1, … 9 Yes No
Binary 2 0, 1 No Yes
Octal 8 0, 1, … 7 No No
Hexa- 16 0, 1, … 9, No No
System Base Symbols
Used by
humans?
Used in
computers
?
decimal A, B, … F
6. Counting
Decimal Binary Octal
8 1000 10 8
9 1001 11 9
10 1010 12 A
11 1011 13 B
12 1100 14 C
13 1101 15 D
14 1110 16 E
15 1111 17 F
Hexa- decimal
7. Decimal Number System
• Decimal number system contains ten unique symbols 0,1,2,3,4,5,6,7,8 and 9.
• Since counting in decimal involves ten symbols, we can say that its base or
radix is ten.
• In this system, any number (integer, fraction or mixed) of any magnitude can
be represented by the use of these ten symbols only
• Each symbols in the number is called a “Digit”
• Examples
• 1214
• 1897
• 9875.54
8. Binary Number System
•Binary number system is a positional weighted system.
•It contains two unique symbols 0 and 1.
•Since counting in binary involves two symbols , we can say that its
base or radix is two.
•A binary digit is called a “Bit”
•A binary number consists of a sequence of bits, each of which is
either a 0 or a 1.
•The binary point separates the integer and fraction parts.
•Examples,
1110
0000
1001
0101
9. Octal Number System
•Octal number system is a positional weighted system.
•It contains eight unique symbols 0,1,2,3,4,5,6 and 7.
•Since counting in octal involves eight symbols, we can say that its base or
radix is eight.
•The largest value of a digit in the octal system will be 7.
•That means the octal number higher than 7 will not be 8, instead of that it
will be 10
10. Hexadecimal Number System
•Binary numbers are long. These numbers are fine for
machines but are too lengthy to be handled by human
beings. So there is a need to represent the binary numbers
concisely.
•One number system developed with this objective is the
hexadecimal number system (or Hex)
•It contains sixteen unique symbols
•0,1,2,3,4,5,6,7,8,9,A,B,C,D,E and F.
•Since counting in hex involves sixteen symbols, we can say
that its base or radix is sixteen.
11. BCD or 8421 Numbers
•BCD means Binary Coded Decimal.
•BCD is a system of weiting a numbers that a four-digit binary code to
each digit 0 through 9 in decimal numbers.
•The smallest BCD number is (0000) and the largest is (1001).The next
number to 9 will be 10 which is expressed as (0001 0000) in BCD.
•There are six illegal combinations 1010, 1011,1100, 1101, 1110 and 1111 in
this code i.e. they are not part of the 8421 BCD code