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. 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)
It's part of Computer Organization And Architecture .Data representation is how to data represented in computer by using complements of number , float point ,fix point, so it's
slide is useful
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.
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 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.
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!
It's part of Computer Organization And Architecture .Data representation is how to data represented in computer by using complements of number , float point ,fix point, so it's
slide is useful
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.
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 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.
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!
Spiral model : System analysis and designMitul Desai
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This Slideshare presentation is a partial preview of the full business document. To view and download the full document, please go here:
http://flevy.com/browse/business-document/system-analysis-and-design-program-1926
BENEFITS OF DOCUMENT
1. Detailed presentation on system analysis and design program
DOCUMENT DESCRIPTION
Content:
Introduction
Software Development Life Cycle
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Estimation
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Describing Process Specifications and Structured Decisions
Review
Introduction to Testing
Number systems - Efficiency of number system, Decimal, Binary, Octal, Hexadecimalconversion
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representation of signed numbers, addition and subtraction using 2’s complement and I’s
complement.
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codes, Error correcting code.Deepak john,SJCET-Pala
Digital computers represent data by means of an easily identified symbol called a digit. The data may
contain digits, alphabets or special character, which are converted to bits, understandable by the computer.
In Digital Computer, data and instructions are stored in computer memory using binary code (or
machine code) represented by Binary digIT’s 1 and 0 called BIT’s.
The number system uses well-defined symbols called digits.
Number systems are classified into two types:
o Non-positional number system
o Positional number system
Introduction
Number Systems
Types of Number systems
Inter conversion of number systems
Binary addition ,subtraction, multiplication and
division
Complements of binary number(1’s and 2’s
complement)
Grey code, ASCII, Ex
3,BCD
FYBSC IT Digital Electronics Unit I Chapter I Number System and Binary Arithm...Arti Parab Academics
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Computer data representation (integers, floating-point numbers, text, images,...ArtemKovera
How computers represent different types of data.
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4) Representing integer numbers in computers
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C Programming : Arrays, One Dimensional Arrays, Two Dimensional Arrays, Three Dimensional Arrays, Operations on Arrays like Insertion, Deletion, Searching, Sorting, Merging, Traversing, Matrix Manipulation like Addition, Multiplication etc. : Visit us at : www.rozyph.com
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Nested Loops and Jumping Statements(Loop Control Statements), Goto statement in C, Return Statement in C Exit statement in C, For Loops with Nested Loops, While Loop with Nested Loop, Do-While Loop with Nested Loops, Break Statement, Continue Statement : visit us at : www.rozyph.com
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Control Statement in C, Looping in C, Conditional and Unconditional Statements, For Loop, While Loop, Do-While Loop, C Programming, Examples : Visit us at www.rozyph.com
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This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
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The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
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http://sandymillin.wordpress.com/iateflwebinar2024
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Overview on Edible Vaccine: Pros & Cons with Mechanism
Number system
1. Gagan Deep
Founder & Director
Rozy Computech Services
3rd Gate, Kurukshetra University,
Kurukshetra-136119
rozygag@yahoo.com
rozyph.com
Number System
A part of a chapter of my book “Fundamentals of Computers Vol.-I”
2. NUMBER SYSTEM
Rozy Computech Services, Kurukshetra
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Number systems are very important to
understand because the design and organisation
of a computer is dependent upon the number
system. We have different types of number
system
Non-positional
Positional
3. Non-positional Number system
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In this system, each symbol represent the same
value regardless of its position in the number and
the symbols are simply added to find out the
value of a particular number e.g. we have
symbols such that I for 1, II for 2 ......III for 3 etc.
4. Positional Number system
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Those numbers in which each digit has its
importance, like 234 read as two hundred and
thirty four. Because in this number each digit has
its importance. We read in primary education
about Ikai(One’s), Dahai(Tens) and Sankara
(Hundreds), these are the different positional
values for decimal number system, which is used
in our daily life. The value of each digit in this
number is determined by
The digit itself
The position of the digit in the number.
The base or radix of the number system.
5. Base or Radix
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Now, What do you mean by base? The base of a
number system is defined as the number of different
symbols used to represent numbers in the system.
The decimal system uses ten symbols 0,1,2,3....9.
and its base is ten(10). E.g. a decimal number 234
can be represented as
2x(10)2 + 3x(10)1 + 4(10)0
2x100 +3x10 +4x1
200 + 30 + 4 = 234
Hence Left most digit(2) value is 200 and Right most
digit(4) value is 4. So Left most digit is known as Most
Significant Digit(MSD) and Right most digit is known
as Least Significant Digit(LSD).
6. Number Systems
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The various number systems is essential for
understanding of computers so we begin with the
number systems. The various positional number
systems are
Decimal Number System
Binary Number System
Octal Number System
Hexadecimal Number System
7. Characteristics of Number
System
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Each number system has three characteristics
The value of base determines the total number of different
symbols or digits available in the said number system.
The first digit of every number system is always zero(0).
The maximum value of the last digit of any number system
is always equal to base minus one (1) e.g. In decimal
number system(base 10), the minimum digit value is 0 and
the maximum digit value is 9.
In binary (base 2) are 0 and 1
In octal (base 8) are 0 and 7
In hexadecimal(base 16) are 0 and 15(F)
These Positional Number Systems have two different types
of representation
Integers
Real (Fractional)
8. INTEGER NUMBERS
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The set of whole numbers (including zero) is
called a integer number. Thus, the number having
no fractional part or you can say having no
decimal point is called integer number. These
integers may be positive or negative. Usually, a
positive integers are written without or with a plus
(+) sign before them whereas negative numbers
have a minus(-) sign before them. e.g. 234, 123,
+105, -105 etc.
Here we will discuss only the positive integers for
various conversions from one number system to
another. About sign of number we will discuss
later on, in sign magnitude topic.
9. Decimal Number System
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How a decimal number gives values
As we had discussed about Ikai(one’s), Dahai(Ten’s) and
Sankara (hundred's) with number 234. How it comes
2 x 102 + 3 x 101 + 4 x 100
2x100 + 3x 10 + 4 x 1
200 + 30 + 4
234
Always Remember
Any number’s power 0 = 1 i.e. N0 = 1
Any number’s multiply by 0= 0 i.e Nx0= 0
Any number’s power -n i.e N-n = 1/Nn
Where N,n =1,2,.................N
For conversion the base’s power for LSD is zero(0) & it is
increases one by one toward MSD. Also remember the power
of base for MSD is always total digit minus one.
10. BINARY NUMBER SYSTEM
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Information handled by the computer must be encoded in a
suitable format. Since most present day hardware (i.e.,
electronic and electromechanical equipment employees
digital circuits which have only two stable states namely,
ON and OFF. That is each number, character of text or
instruction is encoded as a string of two symbols, one
symbol to represent each state. The two symbols normally
used are 0 and 1. These are known as bits abbreviation for
binary digits.
Computer use the binary systems in which only two digits
are used i.e. 0 & 1. So it is known as Binary system as Bi
means Two & Bit means a digit, as a binary number 10101
have 5 bits.
In the decimal system we refer to the positional value as
One’s, Ten’s and hundred’s etc. i.e. 100, 101, 102 etc.
Similarly the Positional values in binary system are 20, 21,
22 etc. from right hand side to left hand side.
12. Binary to Decimal Conversion
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Consider a binary number 1101. This is 4 bit number. The
left most bit is known as Most significant bit(MSB) and the
right most bit is known as Least significant bit(LSB).
=1 x 23 + 1 x 22 + 0 x 21 + 1 x 20
=1 x 8 + 1 x 4 + 0 x 2 + 1 x 1
=8 + 4 + 0 + 1 = (13)10
Let us take another example
(1110110)2 to (?)10
=1 x 26 + 1 x 25 + 1 x 24 + 0 x 23 + 1 x 22 + 1 x 21 + 0
x 20
=1 x 64 + 1 x 32 + 1 x 16 + 0 x 8 + 1 x 4 + 1 x 2 + 0 x
1
=64 + 32 + 16 + 0 + 4 + 2 + 0
= (118)10
13. Some Questions for Exercise
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Convert the following binary number into decimal
numbers.
1) (1100)2
2) (1011101)2
3) (11001100)2
4) (110110011)2
14. Decimal to Binary Conversion
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To convert a decimal number into a binary
number, divide the decimal number by 2 and the
successive quotients by 2.
The successive reminders (which can be only 0
or 1), written in the reverse order, form the
equivalent binary number.
Let us two examples of converting from decimal
to binary
1. (13)10
2. (118)10
16. OCTAL NUMBER SYSTEM
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In octal number system, octal means eight(8). So, base or radix
is 8. The digits of the octal number system are 0,1,2,3,4,5,6,7.
The Positional values in Octal system are 80, 81, 82 etc. from
right hand side to left hand side.
Octal to Decimal Conversion
Consider a octal number 56. This is 2 digit number. The left most
bit is known as Most significant digit(MSD) and the right most
digit is known as Least significant digit(LSD).
=5 x 81 + 6 x 80
=5 x 8 + 6 x 1
= 40 + 6 = (46)10
Let us take another example
(3056)8 to (?)10
=3 x 83 + 0 x 82 + 5 x 81 + 6 x 80
=3x512 + 0 x 64 + 5 x 8 + 6 x 1
=1536 + 0 + 40 + 6 = (1582)10
17. Decimal to Octal Conversion
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To convert a decimal number into a octal number,
divide the decimal number by 8 and the successive
quotients by 8. The successive reminders (which can
be only 0 to 7), written in the reverse order, form the
equivalent octal number.
Let us two examples of converting from decimal to
octal
1. (46)10
2. (1582)10
1. (46)10 to (?)8
So (46)10 = (56)8
Similarly do another example
8 46 Reminder
8 5 6 LSD
0 5 MSD
18. HEXADECIMAL NUMBER SYSTEM
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In Hexadecimal number system, Hexadecimal means Sixteen(16). So,
base or radix is 16. The digits of the hexadecimal number system are 0,1,
2,3, 4,5, 6,7, 8,9, A,B, C, D, F whose decimal equivalent are 0, 1,2,3,
4,5,6,7, 8,9,10, 11, 12, 13, 14, 15. The Positional values in Hexadecimal
system are 160, 161, 162 etc. from RHS to LHS.
Hexadecimal(HD) to Decimal Conversion
Consider a HD number A5. This is 2 digit number. The left most bit is
known as Most significant digit(MSB) and the right most digit is known as
Least significant digit(LSD).
=A x 161 + 5 x 160
=A x 16 + 5 x 1
= 10x16 + 5 x 1 (Because A = 10)
= 160 + 5 = (165)10
Let us take another example
(A5C)16 to (?)10
= A x 162 + 5 x 161 + C x 160
=Ax256 + 5 x 16 + C x 1
Because A=10 and C=12
=10x256 + 5x16 + 12x1
= 2560 + 80 + 12 = (2652)10
19. Decimal to Hexadecimal
Conversion
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To convert a decimal number into a HD number, divide
the decimal number by 16 and the successive quotients
by 16. The successive reminders (which can be only 0 to
15 or you can say 0 to F)), written in the reverse order,
form the equivalent HD number.
Let us two examples of converting from decimal to octal
1. (165)10
2. (2652)10
So (2652)10 = (A5C)16
Similarly do another one.
16 2652 Reminder Dec. to HD.equivalent
16 165 12 LSB 12 C
16 10 5 5 5
0 10 MSB 10 A
20. REAL NUMBERS
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A real number consists of an integral part and a
fractional part or you can say that a
real number is number having decimal point. A
real number may be positive or negative. e.g.,
12.23, + 12.24, -0.56 etc.
Here we are discussing only about the
conversions of various real numbers from one
system to another. Later on we will discuss about
how these will represent in computer memory.
21. Decimal Number
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In decimal number what is the positional value of
fraction part, let us discuss
We have a number 12.23 in this 12 is the integral
part and .23 is the fractional part.
=1 x 101 + 2 x100 + 2 x 10-1 + 3 x 10-2
=1 x 10 + 2 x 1 + 2 x (1/101) + 3 x (1/102)
=1x10 + 2 x 1 + 2/10 + 3/100
= 10 + 2 + 0.2 + 0.03 =
(12.23)10
It means after decimal point(fractional part) the
power increases with minus sign from left hand side
to right hand side i.e. 10-1 , 10-2 , 10-3 etc.
22. Binary to Decimal Number
System
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In Binary number system, for positional values after decimal
point(fractional part), the power increases with minus sign from left
hand side to right hand side i.e. 2-1, 2-2 , 2-3 etc.
Let us consider an example (1101.101)2
In this binary number 1101 is the integral part and .101 is the
fractional part.
=1 x 23 + 1 x 22 + 0 x 21 + 1 x20 + 1 x 2-1 + 0 x 2-2 + 1 x 2-3
=1 x 8 + 1 x 4 + 0 x 2 + 1 x 1 + 1 x (1/21) + 0 x (1/22) + 1 x (1/23)
= 8 + 4 + 0 + 1 + 1/2 + 0/4 + 1/8
= 13 + 1/2 + 0 + 1/8
= 13 + 0.5 + 0 + 0.125 =
(13.625)10
One another example is
(101.11)2 = 1x22+ 0 x21+1x20+ 1x2-1+1x2-2
= 4 + 0 + 1 + 1/2 + 1/4
= 5+3/4 or (5.75)
23. Decimal To Binary Conversion
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To find the binary equivalent of a decimal real
number. Divide the number into two parts Integer
and Real(fractional) parts. Integer part will be
converted as in integer number conversion in
above conversions, and in fractional part fraction,
multiply successively by 2. The procedure is just
the reverse of converting decimal whole numbers
to binary, i.e. we multiply by 2 instead of
dividing and keep track of
overflow instead of the remainders.
Let us see two examples of converting (13.625)10
and (118.2)10 to their binary equivalents :
24. (13.625)10
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Integer Part
The integral part 13 is converted as in above examples,
therefore, the binary equivalent of 13 is (1101)2 .
Fractional Part
Integral Part Fractional PartBinary Position
0.625 x 2 = 1.250 1 0.250 1x2-1
(MSB)
0.250 x 2 = 0.500 0 0.500 0 x2-2
0.500 x 2 = 1.000 1 0.000 1 x2-3
(LSB)
Therefore (0.625)10 = (0.101)2
Combine both parts integer and fractional part. therefore
our answer is
(13.625)10 = (1101.101)2
25. Convert (118.2)10 to their binary
equivalents
Rozy Computech Services, Kurukshetra
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Integer Part
The integral part 118 is converted as in above example,
therefore, the binary equivalent of 118 is (1110110)2 .
Fractional Part
Integral Part Fractional Part Binary Position
0.2 x 2 = 0.4 0 0.4 0 x2-1 (MSB)
0.4 x 2 = 0.8 0 0.8 0 x2-2
0.8 x 2 = 1.6 1 0.6 1 x2-3
0.6 x 2 = 1.2 1 0.2 1 x2-4
0.2 x 2 = 0.4 0 0.4 1 x2-5 (LSB)
As you will observe, the binary digits begin to repeat or
recur.
Therefore (0.2)10 = (0.00110)2 = (0.0011)2
Combine both parts integer and fractional part. Therefore our
answer is
26. Octal to Decimal Number
System
Rozy Computech Services, Kurukshetra
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In Binary number system, for positional values after
decimal point(fractional part), the power increases
with minus sign from left hand side to right hand side
i.e. 8-1, 8-2, 8-3 etc.
Let us consider an example (56.45)8
Similarly in this octal number 56 is the integral part
and .45 is the fractional part.
=5 x 81 + 6 x80 + 4 x 8-1 + 5 x 8-2
=5 x 8 + 6 x 1 + 4 x (1/81) + 5 x (1/82)
= 40 + 6 + 4/8 + 5/64
= 46 + 37/64
= 46 + .578 = (46.578)10
27. Decimal To Octal Conversion
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To find the octal equivalent of a decimal real number,
divide the number into two parts Integer and Real
parts. Integer part will be converted as in integer
number conversion in above conversions. and in
fractional part fraction, multiply successively by 8. The
procedure is just the reverse of converting decimal
whole numbers to octal, i.e. we multiply by 8 instead
of dividing and keep track of overflow instead of the
remainders.
Integer Part
Let us see one example of converting (46.35)10 into
octal number
The integral part 46 is converted as in above
example, therefore, the octal equivalent is (56)8 .
28. Rozy Computech Services, Kurukshetra
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Fractional Part
Integral Part Fractional PartOctal
Position
0.35 x 8 = 2.80 2 0.80 2 x8-1
(MSD)
0.80 x 8 = 6.40 6 0.40 6 x8-2
0.40 x 8 = 3.20 3 0.20 3 x8-3
0.20 x 8 = 1.60 1 0.60 1 x8-4
0.60 x 8 = 4.80 4 0.80 4 x8-5
(LSD)
As you will observe, the octal digits begin to repeat
or recur.
Therefore (0.35)10 = (0.26314)8
Combine both parts integer and fractional part.
Therefore our answer is
29. Hexadecimal to Decimal Number
System
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In HD number system, for positional values after
decimal point(fractional part), the power increases
with minus sign from left hand side to right hand side
i.e. 16-1, 16-2, 16-3 etc.
Let us consider an example (A5.45)8
Similarly in this HD number A5 is the integral part and
.45 is the fractional part.
=A x 161 + 5 x160 + 4 x 16-1 + 5 x 16-2
=10 x 16 + 5 x 1 + 4 x (1/161) + 5 x (1/162)
= 160 + 5 + 4/16 + 5/256
= 165 + 69/256
= 165 + 0.2695 = (165.2695)10
30. Decimal To HD Conversion
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To find the HD equivalent of a decimal real number, divide the number into
two parts Integer and Real parts. Integer part will be converted as in
integer number conversion in above conversions, and in fractional part,
multiply successively by 16. The procedure is just the reverse of converting
decimal whole numbers to HD, i.e. we multiply by 16 instead of dividing
and keep track of overflow instead of the remainders.
Let us see one example of converting (2652.35)10 into HD number
Integer Part
The integral part 2652 is converted as in above example, therefore, the HD
equivalent of (2652)10 is (A5C)16 .
Fractional Part (0.35)10
Integral Part Fractional Part HD Position
=0.35 x 16 = 5.60 5 0.60 5 x16-1 (MSD)
=0.60 x 16 = 9.60 9 0.60 9 x16-2
=0.60 x 16 = 9.60 9 0.60 9 x16-3 (LSB)
As you will observe, the HD digits begin to repeat or recur.
Therefore (0.35)10 = (0.599)16
Combine both parts integer and fractional part. therefore our answer is
(2652.35)10 = (A5C.599)16
31. Tables for Octal to binary is
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Here we have taken 3 bit binary code for octal
numbers, because the last digit have 3 bit
code i.e. for 7 we have 111
Octal Decimal Binary
0 0 000
1 1 001
2 2 010
3 3 011
4 4 100
5 5 101
6 6 110
7 7 111
32. Table for Hexadecimal to
Binary
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Here we have
taken 4 bit binary
code for octal
numbers, because
the last digit have
4 bit code i.e. for
F we have 1111
Hexadecimal Decimal Binary
0 0 0000
1 1 0001
2 2 0010
3 3 0011
4 4 0100
5 5 0101
6 6 0110
7 7 0111
8 8 1000
9 9 1001
A 10 1010
B 11 1011
C 12 1100
D 13 1101
E 14 1110
F 15 1111
33. CONVERSION FROM OCTAL OR HEXADECIMAL TO BINARY
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For this we have two methods
Indirect
Direct
Indirect
Step 1 - First convert Octal or Hexadecimal to
decimal
Step 2 – Then Convert decimal to Binary
Direct Method
In this method we have to take each digits equivalent
3 bit binary code in case of Octal number system
and 4 bit binary code in case of hexadecimal code.
34. Example for Octal number system
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(23.67)8 (?)2
Step 1 Take each digit’s equivalent 3 bit binary
number from above table. i.e.
2 010
3 011
6 110
7 111
Step 2 Arrange them in order
(010011.110111)2
35. Example for Hexadecimal number system
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(23.67)16 (?)2
Step 1 Take each digit’s equivalent 4 bit binary
number from above table. i.e.
2 0010
3 0011
6 0110
7 0111
Step 2 Arrange them in order
(00100011.01100111)2
36. Conversion from Binary to Octal or
Hexadecimal
Rozy Computech Services, Kurukshetra
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For this we have two methods
Indirect
Direct
Indirect
Step 1 - First convert binary to decimal
Step 2 – Then Convert decimal to octal or
hexadecimal
Direct
In this method we have to make 3 bit(octal) and 4
bit(HD) groups and put each groups equivalent
Octal or HD digit.
37. Example for Octal number system
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(10011.110111)2 (?)8
Step 1 Make 3 bit groups
Before decimal (Integral part) from RHS to LHS
After Decimal (Fractional part) from LHS to RHS
010 011 . 110 111
In case of left most group we had placed a extra zero to
make 3 bit groups.
010 2
011 3
110 6
111 7
Step 2 Arrange them in order
(23.67)8
(10011.110111)2 = (23.67)8
38. Example for Hexadecimal number
system
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(100011.01100111)2 (?)16
Step 1 Make 4 bit groups
Before decimal (Integral part) from RHS to LHS
After Decimal (Fractional part) from LHS to RHS
0010 0011 . 0110 0111
In case of left most group we had placed two extra zero
to make 4 bit groups.
0010 2
0011 3
0110 6
0111 7
Step 2 Arrange them in order
(23.67)16
(100011.01100111)2 = (23.67)16
39. Always Remember
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Decimal No. System - Base or Radix is 10,
digits are 0,1,2,3,4,5,6,7,8,9
Binary No. System - Base or Radix is 2, digits
are 0,1
Octal No. System - Base or Radix is 8, digits are
0,1,2,3,4,5,6,7
Hexadecimal No. System - Base or Radix is 16,
digits are 0,1,2,3,4,5,6,7,8,9, A, B,C,D,E,F
40. Advantages of Hexadecimal Number
System
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It has already been pointed out that memory system
of a computer, whether core memory or
semiconductor memory, consists of locations, also
known as memory registers. Further each memory
location has an address.
Consider a computer having 64 K bytes of memory.
It implies that this computer can store 64 X 1024 =
65,536 bytes in its memory.
In other words, there are 65,536 memory locations in
its memory and each memory location can store
eight bits (1 byte = 8 bits) of a data or of an
instruction. Since, each of these locations has an
address, the addresses for these locations vary from
00000 to 65,535.
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Now, if one has to refer to the memory location,
addressed 60, he may use binary or hexadecimal
numbers. Now, the binary and hexadecimal
equivalents of 60 are given below.
(60)10 = (00111100)2
(60)10 = (3C)16.
Thus, we may say that memory location is referred
either by 00111100 or by 3C, both meaning the
Same location. Imagine how difficult it will be to refer
to the last location 65,535 in binary system, where
as in hexadecimal system it can be referred to as
FFFF.
Now it is obvious that referring to very large
numbers, these may be addresses of memory
locations or contents of memory locations, becomes
very easy in terms of hexadecimal numbers as
compared to binary numbers.
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In fact, the purpose of introducing the hexadecimal
number system is to shorten the lengthy binary
strings of Os and 1s. This procedure of shortening
the strings of binary digits is referred to as Chunking.
It is for this reason that today anybody working with
microprocessors is using the hex numbers instead of
binary numbers.
However, it must be remembered that whatever
number system one may use, the information stored
in the computer memory is always in terms of binary
digits. It is only for our convenience that we use octal
or hexadecimal numbers.
43. About Me
Rozy Computech Services, Kurukshetra
university, Kurukshetra
I am in the profession of teaching in Computer Science since 1996.
In 1996, established a professional setup “Rozy Computech
Services” for providing Computer Education, computer hardware and
software services. In this span of 20 years , in conjunction with
Rozy’s, I also associated in Teaching with different Institutions like
Assistant Professor(Part-time) in University College, Kurukshetra
University, Kurukshetra Guest Faculty in Directorate of Distance
Education, Kurukshetra University, Visiting Faculty in University
Institute of Engineering & Technology, Kurukshetra University
and a resource person in EDUSAT, Haryana. Besides, I am also
serving as Guide and Mentor in various private educational
institutions.
I also worked on many popular teaching resources like authoring
books and development of learning material for regular and
correspondence students. From the year 1997, In particular I authored
some popular volumes like Fundamentals of computer Vol. I, II &
III, Artificial Intelligence, Database Systems, Software
Engineering, and Object-Oriented Analysis & Design.
I have been actively involved in research mainly leading to Wireless
Networks communication and setup. I intend to make wireless
networks cost effective and to provide more functionality to the users
residing in rural areas.
As per my educational facts, I am Master of Philosophy in Computer
Sc., Master’s in Computer Science & Applications, Master’s in
44. Rozy Computech Services, Kurukshetra
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Thanks!
If you have any query please mail me at
rozygag@yahoo.com
rozyph.com