The document discusses different numeration systems used in various cultures and time periods around the world. It begins by explaining that the appropriate numbering system depends on the application. It then provides details on tally systems, the Hindu-Arabic numeral system, and various place-value systems including binary, decimal, and other bases. It also discusses the evolution of the concept of real numbers to include integers, rational numbers, and irrational numbers.
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 slide, the following topics are discussed. Radix number system, Binary number system, Octal, Hexadecimal, Octal to Binary, Binary to Octal, Hexadecimal to binary, Binary to Hexadecimal, BCD codes, Gray codes, one's complement, two's complement, signed magnitude number system, fixed point representation, floating point representation and their conversion.
Number Systems — Decimal, Binary, Octal, and Hexadecimal
Base 10 (Decimal) — Represent any number using 10 digits [0–9]
Base 2 (Binary) — Represent any number using 2 digits [0–1]
Base 8 (Octal) — Represent any number using 8 digits [0–7]
Base 16(Hexadecimal) — Represent any number using 10 digits and 6 characters [0–9, A, B, C, D, E, F]
Computer data representation (integers, floating-point numbers, text, images,...ArtemKovera
How computers represent different types of data.
1) Why learning how computers represent data is important
2) Binary, Octal, and Hexadecimal number systems.
3) A few words about computer memory organization
4) Representing integer numbers in computers
(two's-complement and other encodings)
5) Representing floating-point numbers
(single-precision, double-precision, quadruple-precision)
6) Binary-Coded Decimal (BCD) Representation
7) Introduction to representing text in computers (ASCII, Unicode encodings: UTF-8, UTF-16, etc)
8) Introduction to representing images in computers
9) Introduction to representing sound in computers
10) Books on Artificial Intelligence
This is meant for age group 11 to 14 years.
For Class VIII CBSE.
Some viewers have requested me to send the file through mail.
So I allowed everybody to download.My request is whenever you are using plz acknowledge me.
Pratima Nayak ,Teacher,Kendriya Vidyalaya,Fort William,Kolkata
pnpratima@gmail.com
Based on Text book
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 slide, the following topics are discussed. Radix number system, Binary number system, Octal, Hexadecimal, Octal to Binary, Binary to Octal, Hexadecimal to binary, Binary to Hexadecimal, BCD codes, Gray codes, one's complement, two's complement, signed magnitude number system, fixed point representation, floating point representation and their conversion.
Number Systems — Decimal, Binary, Octal, and Hexadecimal
Base 10 (Decimal) — Represent any number using 10 digits [0–9]
Base 2 (Binary) — Represent any number using 2 digits [0–1]
Base 8 (Octal) — Represent any number using 8 digits [0–7]
Base 16(Hexadecimal) — Represent any number using 10 digits and 6 characters [0–9, A, B, C, D, E, F]
Computer data representation (integers, floating-point numbers, text, images,...ArtemKovera
How computers represent different types of data.
1) Why learning how computers represent data is important
2) Binary, Octal, and Hexadecimal number systems.
3) A few words about computer memory organization
4) Representing integer numbers in computers
(two's-complement and other encodings)
5) Representing floating-point numbers
(single-precision, double-precision, quadruple-precision)
6) Binary-Coded Decimal (BCD) Representation
7) Introduction to representing text in computers (ASCII, Unicode encodings: UTF-8, UTF-16, etc)
8) Introduction to representing images in computers
9) Introduction to representing sound in computers
10) Books on Artificial Intelligence
This is meant for age group 11 to 14 years.
For Class VIII CBSE.
Some viewers have requested me to send the file through mail.
So I allowed everybody to download.My request is whenever you are using plz acknowledge me.
Pratima Nayak ,Teacher,Kendriya Vidyalaya,Fort William,Kolkata
pnpratima@gmail.com
Based on Text book
This ppt slide is all about number system. here we learn-
To represent numbers
To know about different system
How number system works
The study of numbers is not only related to computers. We apply numbers everyday, and knowing how numbers work, will give us an insight of how computers manipulate and store numbers.
Mathematics for Primary School Teachers. Unit 2: NumerationSaide OER Africa
Mathematics for Primary School Teachers has been digitally published by Saide, with the Wits School of Education. It is a revised version of a course originally written for the Bureau for In-service Teacher Development (Bited) at the then Johannesburg College of Education (now Wits School of Education).
The course is for primary school teachers (Foundation and Intermediate Phase) and consists of six content units on the topics of geometry, numeration, operations, fractions, statistics and measurement. Though they do not cover the entire curriculum, the six units cover content from all five mathematics content areas represented in the curriculum.
The Mesopotamian culture is often called Babylonian, after the lar.docxoreo10
The Mesopotamian culture is often called Babylonian, after the large metropolis of that name. We could “babble on”1 and on about their many fine achievements in architecture, irrigation, and commerce, but it is their mathematics that is truly remarkable, dwarfing that of other contemporary civilizations. One might not be impressed by their use of a vertical mark for “one” and a horizontal mark for “ten” – ten being a common unit in the mathematics of many societies, including Egypt, China, Rome, and our own society today. On the other hand, they were the first to employ a “positional” system which, except for minor changes, survives to this day!
1The authors would like to apologize for the easy pun, but we couldn’t resist.
Let’s remind ourselves how our current number system works. It does not suffice to say that it is based on grouping by tens. The Egyptians did this – yet we have left them in the dust by taking a giant step forward to the “position system.” We require only ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Nevertheless, we can handle numbers of any size without the need to define a new symbol. This is because the value of a number is determined not just by the symbol. We must note the positionof the symbol as well. The two 3’s in the number 373 represent different quantities. You would rather have three hundred dollars than three dollars, right? To summarize, our number system employs a mere ten symbols, whose values depend on their position in the number. Moving one digit to the left multiplies its place value by ten, while moving to the right (not surprisingly) divides its place value by ten.
Observe, by the way, that this is true on both sides of the decimal point! In the number 3.1416, the 1 near the 6 is worth only one hundredth of the 1 near the 3. There is no number in the entire universe that is too large or too small for our clever (ten-digit!) number system (of Hindu-Arabic origin, by the way). We call our system the decimal system, because ten is the base.
The Babylonians used instead the sexagesimal system because they chose 60 as their base. While we are not sure why, we are fairly certain they did not have 60 fingers. One theory (which is very popular) is that 60 has a multitude of factors, that is, many numbers go into 60. Put another way, $60 can be divided without coin among 2, 3, 4, 5, 6, 10, 12, 15, 20, or 30 people. We shall follow the common practice of using commas to separate groups. Thus (3, 50)60 shall mean 3 sixties and 50 ones for a total of 230. What does (2, 3, 50)60 mean? Well in our position system, 357 means 3 hundreds, 5 tens, and 7 ones, right? Each column is ten times more valuable than its neighbor. In the same way, each column to the left in the Babylonian system is sixty times bigger! In the number (2, 3, 50)60, the 2 represents 2 3600’s – because 60 × 60 = 3600. The next column to the left would represent 60 × 3600 or 216000.
The Babylonians only used two symbols: a vertical mark for 1 and ...
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
Safalta Digital marketing institute in Noida, provide complete applications that encompass a huge range of virtual advertising and marketing additives, which includes search engine optimization, virtual communication advertising, pay-per-click on marketing, content material advertising, internet analytics, and greater. These university courses are designed for students who possess a comprehensive understanding of virtual marketing strategies and attributes.Safalta Digital Marketing Institute in Noida is a first choice for young individuals or students who are looking to start their careers in the field of digital advertising. The institute gives specialized courses designed and certification.
for beginners, providing thorough training in areas such as SEO, digital communication marketing, and PPC training in Noida. After finishing the program, students receive the certifications recognised by top different universitie, setting a strong foundation for a successful career in digital marketing.
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
Advantages and Disadvantages of CMS from an SEO Perspective
Number Systems
1. ““The appropriate numbering systemThe appropriate numbering system
to represent a value depends on theto represent a value depends on the
application. There are advantagesapplication. There are advantages
and disadvantages to each numberingand disadvantages to each numbering
system”system”
2. Numeration SystemNumeration System
Past and Present ..Past and Present ..
The symbols for writing numbers are called
numerals and the methods for calculating are
called algorithms. Taken together, any
particular system of numerals and algorithms is
called a numeration system.
The earliest means of recording numbers
consisted of a set of tallies – marks on stone,
stones in a bag, notches in a stick – one-for-one
each item being counted.
Example: Often such a stick was split in half with
one half going to the debtor and the other half to
the creditor.
3. It is still common practice today to keep count
by making tallies or marks with the minor but
useful refinement of marking off tallies in group
of five. Thus,
IIII IIII IIII IIII III
is much easier to read as twenty-three than
IIIIIIIIIIIIIIIIIIIIIIII
But such system for recording numbers were
much too simplistic for large numbers and for
calculating.
Numbers actually originated in the history of
the Hindus of India. They have changed greatly
over the centuries, passing first to the Arabs of
the Middle East and finally to Europe in the
Middle Ages.
4. As early as 3400 B.C., the Egyptians developed
a system for recording numbers on stone
tablets using hieroglyphics.
Used number systems other than base 10, like
the duodecimal (base 12) in which they counted
fingers-joints instead of fingers.
Divided their days into twenty-four periods,
which is, in turn, why we have twenty-four
hours in a day.
The Egyptians had symbols for one and the first
few powers of ten, and then combined symbols
to represent other numbers.
The Ancient Egyptians ..
5. The
Ancient
Babylonians ..
Famous for their astrological observations and
calculations
Used a sexagesimal (base 60) numbering system
Made use of six and ten as sub-bases.
First to develop the concept of cipher position
or place value, in representing larger numbers
8. Even the Chinese ..
One 一 (Y )ī
Two 二 (Èr)
Three 三
(S n)ā
Four 四 (Sì)
Five 五
(W )ǔ
Six 六 (Liù)
Seven 七 (Q )ī
Eight 八 (B )ā
Nine 九 (Ji )ǔ
Ten 十 (Shí)
Hundred 百 (B iǎ )
Thousand 千 (Qi n)ā
10 Thousands 万
(Wàn)
Million 百万
100 Millions 亿 (Yì)
Billion 万亿
9. The Aztecs, Eskimos
and Indian Merchants ..
Aztecs - Developed vigesimal (base 20) systems
because they counted using both fingers and
toes.
The Ainu of Japan and the Eskimos of
Greenland are the two people who make use of
vigesimal systems to the present day.
Relatively easy to understand is quinary (base 5)
which uses five digits: 0,1,2,3,4. This system is
particularly interesting, in that a quinary finger
counting scheme is still in use today by Indian
merchants near Bombay. This allows them to
perform calculations on one hand while serving
their customers with the other.
10. The Greeks
and
the Hebrews ..
Used letters for numbers.
Every letter in the Greek or Hebrew alphabet
corresponded to a different number.
For example, in Greek, the letter Alpha
corresponded to 1 and the letter Theta
corresponded to 9.
12. The Romans ..
Devised a system that was an important
improvement over hash marks
Roman Numeral System
Also used letters to represent numbers
DISADVANTAGES: Very difficult to apply in
large numbers; there is no provision for
representing the number zero or negative
numbers which are very important concepts in
mathematics.
13. The Arabs..
Transmitted to us the Hindu Numeral System
The use of Arabic Numerals in Europe is attributed
to the Italian mathematician Fibonacci.
In 1202, he published a book called Liber Acci,
which taught Arabic Numerals and Algebra and
strongly advocated the use of Arabic numerals in
society.
The use of the Hindu-Arabic numerals is now the
prevalent number system throughout the world.
With the development of the printing press in the
16th
century, the numerals have become
standardized, and this only increased with the
development of computers.
14. Decimal
Numeration
System ..
Used on daily basis and has 10 digits
Latin decem “ten”
Symbols used to represent these digits arrived
in Europe around the 13th
century from the
Arabs.
Said to be base 10 or radix 10 where the term
radix comes from the Latin word meaning
“root”
15. Decimals also refer to decimal fractions, either
separately or in contrast to vulgar fractions
It has been also adopted almost universally =
due to the fact that we happen to have 10
fingers
A place value system – the value of a particular
digit depends both on the digit itself and on its
position within the number
16. Almost any other base would be as good as or
better than base 10. This is because, for many
arithmetic operations, the use of a base that is
wholly divisible by many numbers especially the
smaller values , conveys certain advantages.
Some mathematician would ideally prefer a
system with a prime number as a base: for
example, seven or eleven
Nature of ten fingers, place value system, good
choice for interfacing with non-engineers
ADVANTAGES:
DISADVANTAGES:
17. Mathematical terminology and concept use is
identical to the base that is use for counting
everyday numbers
Values for currency, demography, economics,
for quantitative backup in science, etc.
APPLICATIONS
18. The decimal numeration system
uses ten ciphers, and place-
weights that are multiples of ten.
What if we made a numerationWhat if we made a numeration
system with the same strategysystem with the same strategy
of weighted places, except withof weighted places, except with
fewer or more ciphers?fewer or more ciphers?
19. The binary numeration system
is such a system ..
Instead of ten different cipher symbols, with
each weight constant being ten times the one
before it, we only have two cipher symbols, and
each weight constant is twice as much as the
one before it.
The two allowable cipher symbols for the
binary system numeration are “1” and “0”, and
these ciphers are arranged right=to=left in
doubling values of weight.
Binary is referred to as “base 2” numeration.
Each cipher position in binary is called bit
20. Why use
Binary
System ?
The primary reason that the binary numeration
system is used in modern electronic computers
is because of the ease of representing two
cipher states electronically.
Binary numeration also lends itself well to the
storage and retrieval of numerical information:
on magnetic tape, optical disks, or a variety of
other media types.
22. Natural
Numbers ..
At first, “number” meant something you could
count, like how many sheep a farmer owns.
These are called the natural numbers, or
sometimes the counting numbers.
1,2,3,4,5…
The use of three dots at the end of the list is a
common mathematical notation to indicate
that the list keeps going forever.
23. Whole
Numbers ..
At some point, the idea of “zero” came to be
considered as a number. If the farmer does not
have any sheep, then the number of sheep that
the farmer owns is zero. We call the set of
natural numbers plus the number zero the
whole numbers.
0,1,2,3,4,5…
24. About
ZERO ..
After more than a, 500 years of potentially
inaccurate calculations, the Babylonians finally
began the special sign for zero.
Many historians believe that this sign, which
first around 300 BC, was one of the most
significant inventions in the history of
mathematics.
However, the Babylonians only used their
symbol as place holder and they didn’t have the
concept of zero as an actual value.
The concept of zero first appeared in India
around 600 AD.
25. Integers ..
Even more abstract than zero is the idea of
negative numbers. If, in addition to not having
any sheep, the farmer owes someone 3 sheep,
you could say that the number of sheep that
the farmer owns is negative 3. It took longer
for the idea of negative numbers to be
accepted, but eventually they came to be seen
as something we could call “numbers.” The
expanded set of numbers that we get by
including negative versions of the counting
numbers is called the integers.
Whole numbers plus negative numbers
26. About
Negative
Numbers ..
First appeared in India around 600 AD
In 18th
century, the great Swiss mathematician
Leonhard Euler believed that negative numbers
were greater than infinity, and it was common
practice to ignore any negative results
returned by equations on the assumptions that
they were meaningless
27. Rational
Numbers ..
While it is unlikely that a farmer owns a
fractional number of sheep, many other things
in real life are measured in fractions, like a half-
cup of sugar. If we add fractions to the set of
integers, we get the set of rational numbers.
All numbers of the form , where a and b are
integers (but b cannot be zero)
Rational numbers include what we usually call
fractions
Notice that the word “rational” contains the
word “ratio,” which should remind you of
fractions.
28. Irrational
Numbers ..
Now it might seem as though the set of
rational numbers would cover every possible
case, but that is not so. There are numbers
that cannot be expressed as a fraction, and
these numbers are called irrational because they
are not rational.
Cannot be expressed as a ratio of integers.
As decimals they never repeat or terminate
(rationals always do one or the other)
30. An Ordered Set ..
The real numbers have the property that they
are ordered, which means that given any two
different numbers we can always say that one
is greater or less than the other. A more
formal way of saying this is:
For any two real numbers a and b, one and
only one of the following three statements is
true:
1. a is less than b, (expressed as a < b)
2. a is equal to b, (expressed as a = b)
3. a is greater than b, (expressed as a > b)
31. The
Number
Line ..
Every real number corresponds to a distance
on the number line, starting at the center
(zero).
Negative numbers represent distances to the
left of zero, and positive numbers are distances
to the right.
The arrows on the end indicate that it keeps
going forever in both directions.
32. Absolute Value ..
When we want to talk about how “large” a
number is without regard as to whether it is
positive or negative, we use the absolute value
function. The absolute value of a number is the
distance from that number to the origin (zero)
on the number line. That distance is always
given as a non-negative number.
In short:
If a number is positive (or zero), the absolute
value function does nothing to it
If a number is negative, the absolute value
function makes it positive
33. Group 3
Aimee Demontaño
Maila Verdadero
Chara Nina Marie
Enriquez
Victoria Pasilan
Eunice Hangad
Marbie Alpos
Leslie Bernolo /emh
/lr