How to convert decimal fractions to binary in a more attractive way

We all know how to convert decimal integral numbers to binary (don't we?) by the simple method of dividing succesively by 2 and using the remainders but what happens when we are trying to convert a decimal number which has a fractional part?

First we can see that it is obvious that the integral part of a decimal number will always be represented by an integral binary (with no fractional part) while the fractional part of a decimal number will always be represented by a fractional part of a binary number (with no integral part). An integral number will be integral in any integral base and a fractional number will be fractional in any integral base. This means we can split a decimal number into its integral and fractional parts, convert them separately to binary and add them up again in binary. This means we can forget about the integral part and concentrate on converting the fractional part. Some decimal fractions may convert into binary exactly (like .5625) but others may not (like .5624) and we may get an infinite number of binary digits in the binary fraction.

One way of converting a decimal fraction to binary fraction is to first multiply it by a power of 2 so that it becomes an integral number, then convert to binary and then divide by the same power of 2 (which now just means displacing the binary point to the left).

- Convert .5625 to binary
- Multiply .5625 * 2^10 = 576
- Convert 576 to binary = 1001000000
- Divide 1001000000 / 2^10 = .1001000000
(Same thing, more precision)

- Convert .5624 to binary
- Multiply .5624 * 2^20 = 589719.1424
- Convert 589719 to binary = 10001111111110010111
- Divide 10001111111110010111 / 2^20 = .10001111111110010111 (The more precision you want, the higher the power...

...Binary Number System:
Conversion of Decimal number to Binary number:
Set up the problem. For this example, let's convert the decimal number 15610 to binary.
Write the decimal number as the dividend inside an upside-down "long division" symbol.
Write the base of the destination system (in our case, "2" for binary) as the divisor outside the curve of the division symbol.
Write the integer answer (quotient) under the long division symbol, and write the remainder (0 or 1) to the right of the dividend. Basically, if the dividend is even, the binary remainder will be 0; if the dividend is odd, the binary remainder will be 1.
Continue downwards, dividing each new quotient by two and writing the remainders to the right of each dividend. Stop when the quotient is 0.
Starting with the bottom remainder, read the sequence of remainders upwards to the top. For this example, you should have 10011100. This is the binary equivalent of the decimal number 156. Or, written with base subscripts: 15610 = 100111002
This method can be modified to convert from decimal to any base. The divisor is 2 because the desired destination is base 2. If the desired destination is a different base, replace the 2 in the method with the desired base. For example, if the desired destination is base 8 or 16...

...included in the Literature Cited listing at the back of this
plan.
3.1
Principles of Watershed Protection
•
Forested watersheds generally yield higher quality water than non-forested cover types. Urban,
suburban and agricultural land uses all contribute in some way to lowered water quality.
•
Uncontrolled human activities on water supply watersheds represent a major source of potential
contamination. Efficient and effective water quality protection on both filtered and unfiltered
water supplies requires control over human activities.
•
Watershed cover conditions differ in their regulation of certain nutrients (especially phosphorus
and nitrogen); the best regulation of nutrients is provided by vigorously growing forest that is
fully occupying all watershed sites.
•
Fire protection, police surveillance, water sampling, and other watershed management activities,
including forest management, all depend upon an adequate, well-maintained road system.
•
The proper management and protection of wetland and riparian zones is a critical component of
watershed protection.
3.2
Principles of Watershed Forest Management: General
•
Watershed forests can be managed in a way that provides significant benefits to long-term water
quality protection, while minimizing adverse impacts during management operations.
•
Potential negative tributary water quality effects (including turbidity, nutrients, and...

...Decimalsdecimals
The decimal numeral system (also called
base ten or occasionally denary) has ten
as its base.
It is the numerical base most widely used
by modern civilizations.
Decimals also refer to decimalfractions.
To understand decimal numbers you must
first know about Place Value.
When we write numbers, the position (or
"place") of each number is important.
History ofDecimals
The Arabic numeral system is
considered one of the most significant
developments in mathematics, and
several theories have been made about
them such as The idea that it originated in China.
The idea that it was invented by AlKhwarizmi.
DecimalsFraction
Decimalfractions are commonly
expressed without a denominator.
The integer part, or integral part of
a decimal number is the part to the
left of the decimal separator .
The part from the decimal separator
to the right is the fractional part.
History of DecimalFractions
• According to Joseph Needham,
decimalfractions were first
developed and used by the Chinese
in the 1st century BC, and then
spread to the Middle East and from
there to Europe. The written Chinese
decimalfractions were nonpositional. However, counting rod...

...Fraction (mathematics)
A fraction (from Latin: fractus, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters. A common, vulgar, or simple fraction (examples: \tfrac{1}{2} and 17/3) consists of an integer numerator, displayed above a line (or before a slash), and a non-zero integer denominator, displayed below (or after) that line. Numerators and denominators are also used in fractions that are not common, including compound fractions, complex fractions, and mixed numerals.
The numerator represents a number of equal parts, and the denominator, which cannot be zero, indicates how many of those parts make up a unit or a whole. For example, in the fraction 3/4, the numerator, 3, tells us that the fraction represents 3 equal parts, and the denominator, 4, tells us that 4 parts make up a whole. The picture to the right illustrates \tfrac{3}{4} or 3/4 of a cake.
Fractional numbers can also be written without using explicit numerators or denominators, by using decimals, percent signs, or negative exponents (as in 0.01, 1%, and 10−2 respectively, all of which are equivalent to 1/100). An integer such as the number 7...

...Fractions
The problem here is to add and |
These two fractions do not have the same denominators (lower numbers), so we must first find a common denominator of the two fractions, before adding them together.
For the denominators here, the 8 and 14, a common denominator for both is 56.
With the common denominator, the
becomes a
and the
becomes a
So now our addition problem becomes this...
The problem here is to add and |
Since these two fractions have the same denominators (the numbersunder the fraction bar), we can add them together by simply adding the numerators (the 21 and 36 = 57), while keeping the same denominator (the 56).
Our answer here is:
The fraction is an improper fraction (the numerator is greater than the denominator).
While there is nothing incorrect about this, an improper fraction is typically
simplified further into a mixed number.
The whole number part of the mixed number is found by dividing the 57 by the 56.
In this case we get 1.
The fractional part of the mixed number is found by using the remainder of the division,
which in this case is 1 (57 divided by 56 is 1 remainder 1).
The final answer is: |
The problem here is to add and |
These two fractions do not have the same denominators (lower numbers), so we must first find a common denominator of the two fractions, before...

...of this strategy. However, in order for a resource to have the potential of being a sustained competitive advantage, it must contain the following four attributes: Firstly, it must be valuable, in the sense that it exploits opportunities and/or neutralizes threats in a firm’s environment, secondly, it must be rare among firm’s current and potential competition; thirdly, it must be imperfectly imitable and fourthly, there cannot be any strategically equivalent substitutes for this resource that are valuable but neither rare or imperfectly imitable.(Amit,2001)
The resource-based theory is based on the assumption that firms are fundamentally heterogeneous regarding their resources and internal competencies. This debates with the problem of how firms can exploit their internal resource base and capabilities to obtain sustained competitive advantages. The articles also provides a precise distinction between the intrinsic causal ambiguity associated with a particular strategy and the subjective ambiguity perceived by a challenger. (Dollinger,2010) It also indicates that intrinsic ambiguity is a necessary but insufficient condition for a sustained capability-based advantage. These also demonstrate that combinatorial complexity, a phenomenon that has attracted the recent attention of strategy theorists, and causal ambiguity are distinct barriers to imitation. The former acts as a barrier to explorative/active learning and the latter as one to absorptive or passive...

...A PROPOSAL ON HOW TO MAKE IRKUTSK CITY MOREATTRACTIVE AS A TOURISTIC CITY
A Proposal Submitted to
The Irkutsk department of tourism
March 30, 2012
Prepared by
Tatiana Peskova
Snezhana Polozova
Maria Selezneva
TABLE OF CONTENT
TABLE OF CONTENT 2
EXECUTIVE SUMMARY 3
INTRODUCTION 4
THE PROBLEM 4
THE BACKGROUND 5
PROPOSED SOLUTION 6
RECOMMENDED COURSE OF ACTIONS 7
REFERENCE LIST 9
EXECUTIVE SUMMARY
This paper entitled “A PROPOSAL ON HOW TO MAKE IRKUTSK CITY MOREATTRACTIVE AS A TOURISTIC CITY” is made by three students of Baikal International Business School, Tatiana Peskova, Snezhana Polozova and Maria Selezneva. It examines the problem of the poorly developed system of acceptance and supporting Russian and foreign tourists in Irkutsk; presents research and recommended course of actions on how to solve this problem. This proposal is made to the Irkutsk department of tourism to grant permission on working on one of the projects that can help to develop tourism in Irkutsk.
The actuality of this paper is confirmed by the fact that during the last six years the touristic flow has increased in 2.5 times. The government of Irkutsk region has conducted several actions to improve the touristic service, however, that is still cannot be considered to be at international level, and does not provide the complex solution for this issue. In the...

...How be more confident as a man
Ryan Bornack
Period 4
Becoming a man is the only thing asked of you when you are born. When you come into the world, you’re not afraid. You’re not worried about being judged, or dealing with responsibilities. You’re not worried about how things work out, or how you get through the day. You’re only worried about what’s in front of your face, and how you take it in. Eventually, you grow older and make decisions based on what you have taken in. These decisions grow harder, and when you become an adult, you have the pressure of the world on your shoulders, managing wealth, health, and love. Sometimes men lose their mind dealing with stress, and fall into being an uncomfortable, non-confident individual, which leads to depression, or lack of motivation. Staying confident is a great way to keep your head up, and don’t let emotions get in the way of what you need to get done. Being confident will help you make better choices, and be less conservative with new opportunities that enter your life. There are multiple ways you can go about maintaining confidence, or gaining confidence.
The first thing you can do is acknowledge that you were once unaware of anything that should hinder your attitude. By growing older and becoming more and more aware of any possible problems, you should become more...

{"hostname":"studymode.com","essaysImgCdnUrl":"\/\/images-study.netdna-ssl.com\/pi\/","useDefaultThumbs":true,"defaultThumbImgs":["\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_1.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_2.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_3.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_4.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_5.png"],"thumb_default_size":"160x220","thumb_ac_size":"80x110","isPayOrJoin":false,"essayUpload":false,"site_id":1,"autoComplete":false,"isPremiumCountry":false,"userCountryCode":"US","logPixelPath":"\/\/www.smhpix.com\/pixel.gif","tracking_url":"\/\/www.smhpix.com\/pixel.gif","cookies":{"unlimitedBanner":"off"},"essay":{"essayId":37078579,"categoryName":"Literature","categoryParentId":null,"currentPage":1,"format":"text","pageMeta":{"text":{"startPage":1,"endPage":3,"pageRange":"1-3","totalPages":3}},"access":"premium","title":"How to Convert Decimal Fractions to Binary in a More Attractive Way","additionalIds":[],"additional":[],"loadedPages":{"html":[],"text":[1,2,3]}},"user":null,"canonicalUrl":"http:\/\/www.studymode.com\/essays\/How-To-Convert-Decimal-Fractions-To-1434316.html","pagesPerLoad":50,"userType":"member_guest","ct":10,"ndocs":"1,500,000","pdocs":"6,000","cc":"10_PERCENT_1MO_AND_6MO","signUpUrl":"https:\/\/www.studymode.com\/signup\/","joinUrl":"https:\/\/www.studymode.com\/join","payPlanUrl":"\/checkout\/pay","upgradeUrl":"\/checkout\/upgrade","freeTrialUrl":"https:\/\/www.studymode.com\/signup\/?redirectUrl=https%3A%2F%2Fwww.studymode.com%2Fcheckout%2Fpay%2Ffree-trial\u0026bypassPaymentPage=1","showModal":"get-access","showModalUrl":"https:\/\/www.studymode.com\/signup\/?redirectUrl=https%3A%2F%2Fwww.studymode.com%2Fjoin","joinFreeUrl":"\/essays\/?newuser=1","siteId":1,"facebook":{"clientId":"306058689489023","version":"v2.9","language":"en_US"}}