This document provides an overview of different number systems, including positional and non-positional systems. It describes the binary, decimal, octal, and hexadecimal systems, explaining their bases and symbols. Methods are presented for converting between these systems, such as using binary as an intermediary. Conversions include changing number values, as well as fractional representations. The objective is to understand number systems and perform conversions between binary, octal, decimal, and hexadecimal formats.
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Number System
Decimal Number System
Binary Number System
Why Binary?
Octal Number System
Hexadecimal Number System
Relationship between Hexadecimal, Octal, Decimal, and Binary
Number Conversions
A power point presentation on number system which briefly explains the conversion of decimal to binary, binary to decimal, binary to octal, octal to decimal. Ping me at Twitter (https://twitter.com/rishabh_kanth), to Download this Presentation.
To Download this click on the link below:-
http://www29.zippyshare.com/v/42478054/file.html
Number System
Decimal Number System
Binary Number System
Why Binary?
Octal Number System
Hexadecimal Number System
Relationship between Hexadecimal, Octal, Decimal, and Binary
Number Conversions
A power point presentation on number system which briefly explains the conversion of decimal to binary, binary to decimal, binary to octal, octal to decimal. Ping me at Twitter (https://twitter.com/rishabh_kanth), to Download this Presentation.
In this ppt , you will learn about the evolution of number systems, decimal, binary and hexadecimal and why hexadecima is the most important form of number systems when working with microcontroller programming.
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!
Every computer stores numbers, letters and other specially characters In coded form. There are two types of number system-
Non-Positional Number system
Positional Number System
A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. It can be seen as the context that allows the symbols "11" to be interpreted as the binary symbol for three, the decimal symbol for eleven, or a symbol for other numbers in different bases.
Contents:
1.What is number system?
2.Conversions of number from one radix to another
3.Complements (1's, 2's, 9's, 10's)
4.Binary Arithmetic ( Addition, subtraction, multiplication, division)
A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.
In this ppt , you will learn about the evolution of number systems, decimal, binary and hexadecimal and why hexadecima is the most important form of number systems when working with microcontroller programming.
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!
Every computer stores numbers, letters and other specially characters In coded form. There are two types of number system-
Non-Positional Number system
Positional Number System
A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. It can be seen as the context that allows the symbols "11" to be interpreted as the binary symbol for three, the decimal symbol for eleven, or a symbol for other numbers in different bases.
Contents:
1.What is number system?
2.Conversions of number from one radix to another
3.Complements (1's, 2's, 9's, 10's)
4.Binary Arithmetic ( Addition, subtraction, multiplication, division)
A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.
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we have made this like computer application course material which is so functionable and any one can use it to develop your technological concept skill.
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Introduction to Information Technology Lecture 2MikeCrea
Number Systems
Types of number systems
Number bases
Range of possible numbers
Conversion between number bases
Common powers
Arithmetic in different number bases
Shifting a number
Chapter 2.1 introduction to number systemISMT College
Binary Number System, Decimal Number System, Octal Number System, Hexadecimal Number System, Conversion, Binary Arithmetic, Signed Binary Number Representation, 1's complement, 2's complement, 9's complement, 10's complement
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2. Objective
1. Understand the concept of number systems.
2. Distinguish between non-positional and positional
number systems.
3. Describe the decimal, binary, OCTAL and HEXADECIMAL
system.
4. Convert a number in binary, octal or hexadecimal to a
number in the decimal system.
5. Convert a number in the decimal system to a number in
binary, octal and hexadecimal.
6. Convert a number in binary to octal and vice versa.
7. Convert a number in binary to hexadecimal and vice versa.
3. Introduction
A Number System (or system of numeration) is a writing
system for expressing numbers, that is a mathematical
notation for representing numbers of a given set,
using digits or other symbols in a consistent manner.
Ideally, a numeral system will Represent a useful set of
numbers (e.g. all integers, or rational numbers) Give
every number represented a unique representation (or at
least a standard representation)
Reflect the algebraic and arithmetic structure of the
numbers.
4.
5. Types of Number System
I. Positional Number
II. Non-Positional Number
Positional Number-
In a Positional Number System there are only a few symbols called
represent different values, depending on the position they occupy in a
number. The value of each digit in such a number is determined by three
considerations
a. The digit itself
b. The position of the digit in the number
c. The base of the number system(where
base is defined as the total number of
digits available in the number system)
Non-positional Number-
In This system we have symbols such as I for 1,II for 2,III for 3 etc.
Each symbols represents the same value regardless of its position in a
number and to find the value of a number.
7. The Binary System(base 2)
The word binary is derived from the Latin root
bini (or two by two). In this system the base b
= 2 and we use only two symbols
S ={1,0}
The symbols in this system are often
referred to as binary digits or bits (binary
digit).
8. The Decimal System(base 10)
The word decimal is derived from the Latin
root decem (ten). In this system the base b =
10 and we use ten symbols
s={0,1,2,3,4,5,6,7,8,9}
Example:-
9. The Octal System(base 8)
The word octal is derived from the Latin root octo
(eight). In this system the base b = 8 and we use
eight symbols to represent a number. The set of
symbols is
S={0,1,2,3,4,5,6,7}
The base of the octal number system is eight,
so each position of the octal number
represents a successive power of eight. From
right to left
10. The Hexadecimal System(base 16)
The word hexadecimal is derived from the Greek
root hex (six) and the Latin root decem (ten). In
this system the base b = 16 and we use sixteen
symbols to represent a number. The set of
symbols is
S={0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F}
Note that the symbols A, B, C, D, E, F are
equivalent to 10, 11, 12, 13, 14, and 15 respectively.
The symbols in this system are often referred to as
hexadecimal digits.
11. Common Number Systems
System Base Symbols
Used by
humans?
Used in
computer
s?
Decimal 10 0, 1, … 9 Yes No
Binary 2 0, 1 No Yes
Octal 8 0, 1, … 7 No No
Hexa-
decimal
16 0, 1, … 9,
A, B, …
F
No No
16. Binary to Decimal
Technique
Multiply each bit by 2n, where n is the “weight” of the bit
The weight is the position of the bit, starting from 0 on
the right
Add the results
17. Example
1010112 => 1 x 20 = 1
1 x 21 = 2
0 x 22 = 0
1 x 23 = 8
0 x 24 = 0
1 x 25 = 32
4310
18. Octal to Decimal
Technique
Multiply each bit by 8n, where n is the “weight” of the bit
The weight is the position of the bit, starting from 0 on
the right
Add the results
20. Hexadecimal to Decimal
Technique
Multiply each bit by 16n, where n is the “weight” of the
bit
The weight is the position of the bit, starting from 0 on
the right
Add the results
21. Example
ABC16=>
C x 160 = 12x1 = 12
B x 161 = 11x16 = 176
A x 162 = 10x256= 2560
274810
22. Decimal to Binary
Technique
Divide by two, keep track of the remainder
First remainder is bit 0 (LSB, least-significant bit)
Second remainder is bit 1
Etc.