text:
Adventist Youth Honors Answer Book/Vocational/House Painting, Exterior

2. Tell how to prepare the outside of a house for painting by doing such items as preparation for new and old work, paint removal, priming, puttying, finishing, etc.
Preparing the house for repainting, if done properly, almost always takes longer than the painting itself. It is also the most crucial step in the entire job, as it is the foundation upon which the rest of the work relies.

Inspection & Repair
Begin by making a careful inspection of the entire house. Look for cracked or rotted boards. Severely cracked or rotten boards will need to be replaced, and this may require that you get a building permit (check with local authorities). You cannot simply caulk over rotten wood, as this does nothing to stop the process of decomposition. Soon after you caulk and paint over rotted wood, you will find that even more has rotted, and you will have an even bigger job to do.

Check around the edges of the roof for flashing. All the fascia should be covered with metal flashing to protect the wood from weather. Doors and windows should also have drip edging to direct the water away from the openings and to the outside of the house's siding.

Remove any shutters from the house before painting. Shutters can be repaired (if necessary) and both sides painted while the painter is on ground level (use a drop cloth). They are rehung after the rest of the house has been painted. This allows the careful painter to paint behind the shutters. Though that area may not be visible to onlookers, it still requires the protection from the weather provided by paint, and it cannot be properly painted while the shutters are in place. The same can be said of the back side of the shutters themselves.

Cleaning
Once repairs have been made, the surfaces to be painted should be thoroughly cleaned. A pressure washer can do this effectively. Painting over dirt or algae growths is always a bad idea, as when the dirt flakes away, the paint will go with it and the house will be exposed to the elements. Do not rely on paint to cover the dirt and expect the paint to hold the dirt in place. It must be removed.

Ladders and Scaffolding
Scaffolding is superior to ladders for painting because it allows you to work on a larger area for a long time before you have to move it to another area. However, scaffolding is considerably more expensive than a couple of ladders, so this option may not be viable for you.

When setting up a ladder, be sure the feet are on level ground. If placing it on a hillside, place something solid under the lower foot to raise it up. Test the stability of the ladder before climbing higher than a step or two.

Most people fall from ladders because they are reaching out too far. Do not make that mistake, as a fall from a ladder can cause serious injury, or even death. Keep your weight centered over the ladder, and do not attempt to reach over too far. Getting down and moving the ladder frequently is far easier than spending a few days in the hospital, and the painting will get done quicker that way too.

Scraping and Sanding
After the exterior has been cleaned, it is time to begin removing the old paint. Paint that is well-adhered to the surface need not be removed, but all flaking paint must be. Paint should be scraped off with a scraper. In places where some paint is scraped off but other paint is well-adhered, the intersection between painted and unpainted should be sanded to make a smooth transition. Edges in the paint will cause the paint to drip there.

Caulking
In places where the wood has been lightly cracked, it is appropriate to fill in the cracks with caulking. Be sure to select a caulk that can be painted (not all of them can be - some repel paint). Smooth the caulk with a putty knife, allow it to dry, and then sand it down. Also caulk around windows, doors, electrical entrances, vents, water faucets, etc. How do professionals apply caulk?

Professionals follow a systematic approach to ensure a clean and effective caulking job. Here are the general steps they take:

1. Preparation 2. Selecting the right caulk 3. Cutting the caulk tube 4. Applying the caulk 5. Smoothing the caulk 6. Cleaning up

Masking
Apply masking tape to the glass near the edges of the panes. Alternately, you can go back and scrape paint from the glass after the paint dries, though it is generally better to mask it off in the first place. Be sure to remove the masking tape when the paint has dried (and before you take down the ladder or the scaffolding!)

Priming
Bare wood should have a coat of primer before the paint is applied. Primer is applied the same way paint is, so you can follow the instructions given below.

Painting
After all that has been done, you are finally ready to paint. Maybe. If the temperature is below, do not begin painting. Also resist the urge if there is rain in the forecast. A light shower can quickly ruin a paint job. If the wood is damp, do not use oil-based paints, as the moisture will cause the paint to blister. Buy paint in large containers ( buckets are preferred) so that you can paint an entire section from one batch of paint (for color consistency). Paint for the trim (which should be painted last) can be bought in smaller containers.

Always open the paint container on a surface that will not be marred by a paint circle whose diameter matches that of the can (formed when paint drips down the sides and meets the ground). Use a dropcloth if necessary. You don't want to leave little paint circles on the driveway, porch, sidewalk, or lawn. Place the can in a place where you can easily reach it, but where you will not accidentally kick it over as you step back to admire your work. Admiration comes to an abrupt end when the can tips over.

Pry the lid from the can with a common screw driver or with a tool designed for this purpose. Place the lid next to the can so you are not likely to step on it and track paint everywhere. Shoe prints look even worse than the paint circles.

If the paint was mechanically shaken at the paint store within a day or so of being opened, all you will need to do is stir it briefly. If it has been sitting for a while, you will need to stir it more thoroughly. Failure to properly stir the paint may cause the color to change as the can is used. Stir the paint frequently while you are painting, as the paint components may separate as it sits (this is why you should stir it in the first place too).

Some painters like to punch a hole in the rim of the can so that paint can drip out of the rim and into the can. This hole will be completely covered by the lid when it is replaced, and can be made with an awl or with a nail.

When replacing the lid, be sure to wipe all the paint from the rim of the can. Place the lid on the rim, and then lightly tap around the edges to seal it. If the rim was insufficiently cleaned, paint will splatter all over the place, so it is important to do that job carefully.

If using a brush, dip the tip of the brush into the paint no more than a third the length of the bristles. Wipe the paint from one side of the brush onto the inner side of the can's rim. Then raise it to the surface to be painted and brush it on with a smooth horizontal motion.

Don't completely empty the brush before refilling it with paint. It takes a lot longer to paint a house with a brush that is empty most of the time.

4. Tell how to prepare and paint metal properly.
All rust and flaking paint should be removed before applying new paint. Heavy flakes can be removed with a wire brush, or with a wire brush attachment for an electric drill. Once the heavy flakes and rust have been removed, go over the surface with sandpaper.

Next, determine what type of solvent is used for cleaning the paint. This will depend on the type of paint chosen, and could be turpentine, mineral spirits, paint thinner, or some other solvent. Dampen a clean rag with the solvent and clean the metal with it. Once the solvent dries, the surface is ready for primer. You may use either one or two coats of primer. Follow the directions on the can to determine the amount of time needed between coats. The time between coats of primer may differ from the time between the final coat of primer and the first coat of paint.

Mineral Spirits
Mineral Spirits is a petroleum distillate commonly used as a paint thinner and mild solvent. Outside of the United States and Canada, it is referred to as white spirit. Painters use mineral spirits as an alternative to turpentine, one that is both less flammable and less toxic. Because of interactions with pigments, painters require a higher grade of mineral spirits than many industrial users, including the complete absence of residual sulphur.

It is used as a degreasing solvent and as a solvent in aerosols, paints, wood preservatives, lacquers, varnishes, and asphalt products. In western Europe about 60% of the total mineral spirits consumption is used in paints, lacquers and varnishes. Mineral spirits is the most widely used solvent in the paint industry. In households, white spirit is commonly used to clean paint brushes after decorating. Its paint thinning properties enable brushes to be properly cleaned (by preventing the paint from hardening and ruining the bristles) and therefore enabling them to be re-used.

Turpentine
Turpentine (also called spirit of turpentine, oil of turpentine, wood turpentine, gum turpentine) is a fluid obtained by the distillation of resin obtained from trees, mainly pine trees. As a solvent, turpentine is used for thinning oil-based paints and for producing varnishes.

Mineral Turpentine
Mineral turpentine, also known as turpentine substitute, turps substitute, or just turps is an inexpensive petroleum-based replacement for the vegetable-based turpentine. It is commonly used as a paint thinner for thinning oil-based paint and cleaning brushes, and as an organic solvent in other applications.

Acetone
Acetone can be used for thinning and cleaning fiberglass resins and epoxies. It is a strong solvent for most plastics and synthetic fibers, so it should not be used when it could come into contact with these materials.

It is ideal for thinning fiberglass resin, cleaning fiberglass tools and dissolving two-part epoxies and superglue before hardening. A heavy-duty degreaser, it is useful in the preparation of metal prior to painting; it also thins polyester resins, vinyl and adhesives. It easily removes residues from glass and porcelain.

Brush
Load the brush directly from the paint container as described previously. Be sure to force some paint between clapboards with the brush. Wipe the paint onto the surface, and then brush it out with two to four strokes. Latex should not be overbrushed, as this will leave brush marks in the finished surface. Reload the brush with paint as soon as the paint begins to lighten. It takes much longer to paint a surface with an empty brush than with a full one.

You should be able to tell whether you need to use horizontal or vertical strokes by considering the surface you are working on. On clapboards or horizontal siding, work the brush from side to side. Shingles should be painted with vertical strokes.

Roller
A roller should not be used on siding or clapboards. It should be reserved for flat surfaces such as masonry walls. Pour some paint from the container into the roller tray, filling it so that the paint covers about half the ramp. Place the roller at the top of the ramp, and roll it into the reservoir. At the end of the reservoir, lift the roller and carry it back to the top of the ramp. Then roll it down again. If you roll it back up, you will succeed in wetting the part of the roller that is already wet, and no paint will be loaded into the dry portion of the roller.

Then roll the paint onto the wall with broad up-and-down strokes. First you will apply the paint, then roll it out to a smooth finish. You can paint the edges and corners with a brush if necessary. When the roller is empty, reload it. An extension handle is a handy time saver that will allow you to paint a large vertical section of the wall.

Sprayer
Before using any spray equipment, carefully read and follow the instructions. Sprayers invariably cover more area than anticipated by the novice, so be careful to mask off a very large area adjacent to the surface to be painted. Use tarps and drop cloths for this, covering grass, shrubbery, and concrete. Move cars away from the house before starting. Mask all the glass on windows, not just the parts near the muntins and mullions (i.e., the pane separators). Cover roof shingles too.

Spray the paint on using several thin coats, allowing the paint to dry between each application. Houses are big, so you should be able to move on to another area while the coat dries. If you spray it on too thick, it will drip and look quite unprofessional. Clean spray equipment thoroughly when finished.

7. Paint the outside of a house with at least four rooms (if possible, make this a group project for a special-needs person in the church or community).
Ask your pastor if he knows of a person whose house needs to be painted. Because he makes regular visits to members in need, he should be aware of anyone who could use your assistance.

You will be supplying the labor for free, but the primer, paint, tape, and caulk may need to be purchased. There are several options available for this:
 * Ask the manager of a paint store to sponsor your project.
 * Ask your church board for money to cover the cost of materials.
 * Hold a fundraiser so you will have money to buy materials.
 * Ask the person whose house you are painting to pay for the materials.

In reality, you could use all four of these approaches. The paint store may agree to give a discount on the paint (or provide it free of charge). You could hold a fundraiser to cover part or all of the rest, or the church board could cover it, or the person who benefits could. There may also be other ways to pay for the materials too - use your imagination!

Be sure to do a good job. Be careful not to slop paint all over the shrubbery, windows, driveway, etc. People will be watching to see what kind of job you do - especially those who helped pay for the materials. Don't let them down.


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Talk:Blended Learning in K-12

Orphans
I found some orphaned pages belonging to this book: Please either integrate these pages into this book or mark them for deletion by typing somewhere on each page. Thanks! --hagindaz 02:46, 14 July 2006 (UTC)
 * Blended Learning in K-12/Blending online and face to face instructors and learners
 * Blended Learning in K-12/Types of Blended Learning/Classroom Websites Course Management Systems
 * Blended Learning in K-12/Self-paced and live
 * Blended Learning in K-12/Work and Learning

These materials are standing the test of time.
Even in 2011 I find these observations to be great and relevant. Good work.

Jim Kelly

(k-12math.info)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Talk:Blended Learning in K-12


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Electrodynamics/Kirchoff's Laws

Two laws by Kirchoff are commonly used in circuit analysis. The first is known as Kirchoff's current law, and the second one is Kirchoff's voltage law.

Kirchoff's Current Law

Kirchoff's Current Law states that the sum of the currents entering a node (the point where two or more circuit elements meet) is equal to zero, with the understanding that current flowing out of a node represents a negative number. An equivalent statement of the law is that or the sum of all currents leaving the node equals the sum of all currents entering the node. This law is in fact a statement of the conservation of charge in a circuit.

Kirchoff's Second Law

Kirchoff's Voltage Law states that the sum of the voltages\potential differences in a loop or mesh equals zero. This law is a statement of the conservation of energy, because 1 volt represents the energy associated with one unit of charge passing through that point.

title: Electrodynamics/Kirchoff's Laws


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Lisp Programming/Overview

An overview, eh? So, very quickly, here are the nuts and bolts; (defun ! (x)         ; Defines a factorial function denoted by the exclamation mark symbol.    (if (> x 0) (* x (! (- x 1))) 1)) tail-end recursion... creating a factorial function.

(setf this '(hello world opps goodbye)) (car this) => hello (cdr this) => (world opps goodbye) (cadr this) => world (cdar this) => probably an error

lists, what lisp is named for, and a few functions that get at lisp.

if you must, you can also do: (setf ... same... (first this) => hello ... (second this) => world but you can't compose it (ex have doing car cdr be cadr)

and yay, macros... (defmacro when (cond &body body)   (if (cond) (progn ,@body))) by this time, we're kind of getting in over our heads, but hey!

(defun do-nothing (anargument :key akeywordargument :opt anoptionalargument :rest everythingelseinalist))

I couldn't figure out a way to incorporate all four types of function arguments into one (you can't, and it's generally a bad idea to combine more than 2 of them.)

There's also the CLOS (common lisp object system) and a whole lot of other stuff that you probably should know about, but if you want to really, you better work through a good tutorial.

So hey, that's kind of a rough gist of Lisp. Have fun lisping!

title: Lisp Programming/Overview


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Talk:Lisp Programming/Overview

there wasn't anything here... it isn't pretty, but I guess it kind of works... -jakv

Huh?

This overview would only be understandable to someone already familiar with LISP. It isn't a very good overview either. Lisp is a functional language. The first code example defines a function for the factorial symbol '!' (as in 5! = 5*4*3*2*1 = 120) which takes a variable 'x' as an argument.207.34.115.78 (talk) 15:45, 21 October 2010 (UTC)

title: Talk:Lisp Programming/Overview


text: Category:Book:Operations Strategy

title: Category:Book:Operations Strategy


text: Category:Book:Optics

title: Category:Book:Optics


text: Category:Book:OC Photography Program

title: Category:Book:OC Photography Program


text: Category:Book:Occupational Health

title: Category:Book:Occupational Health


text: Category:Book:Old English

title: Category:Book:Old English


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Category:Book:OpenOffice.org

fr:Catégorie:OpenOffice.org (livre) it:Categoria:OpenOffice.org ja:カテゴリ:OpenOffice.org ka:კატეგორია:OpenOffice.org pt:Categoria:Livro/OpenOffice.org

title: Category:Book:OpenOffice.org


text: Category:Book:Open Culture

title: Category:Book:Open Culture


text: Category:Book:Open Source

title: Category:Book:Open Source


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Macroeconomics/Measuring Domestic Output

GDP
GDP stands for gross domestic product. You've probably heard this term on the news or read about it in the paper when the national or global economy is being discussed. GDP is defined as the value of all the final goods and services produced in a country during a given time period. Intermediate goods aren't counted because they would in effect cause double-counting to occur. GDP also refers to the income of the country as well. GDP also only refers to goods produced within a certain country. This means that if a firm is located in one country but manufactures goods in another, those goods are counted as part of the foreign country's GDP, not the firm's home country. For example, BMW is a German company but cars manufactured in the United States are counted as part of the American GDP.

You can think of it another way, GDP is a way for us to measure how productive a country is on the whole. Let's break down the name for concrete understanding. Gross refers to the summation of all the country's resources towards producing output. Domestic just relates the output to the country from which the output was produced. Lastly, product just refers to the goods and services that make up output.

GDP can be written algebraically as:

$$ \mathrm\ GDP = C + G + I + (EX - IM) $$

Where:

C is aggregate consumption

G is government spending

I is investment

EX is exports

IM is imports

Consumption is essentially the aggregate of all the goods and services consumed in the country. Haircuts, hamburgers, gasoline etc. are all part of the GDP in the country in which they are purchased.

Government Spending is just what it sounds like, it is the sum of all the goods and services purchased by the government.

Investment is a bit trickier because most people confuse this term with financial investment. In economics, we refer to investment as the purchase of new capital by firms or individual consumers. That is, firms can buy non-residential capital (buildings, equipment etc.) and individual consumers can purchase residential capital (i.e. houses). If we ever mean the kind of investment done through the stock market or finances, we will specifically use the term financial investment. So unless otherwise noted, investment will always mean capital investment.

Exports are all the goods and services exported to foreign countries. That is, the goods and services produced by the domestic country and consumed by foreign countries.

Imports are just the opposite. These are goods and services produced by other countries but consumed by the domestic country.

Together $$ EX - IM = NX $$ or net exports. This is just a way of getting the net value of the goods traded between the domestic country and the rest of the world. Why do we add exports but subtract imports? Well, exports are added to the GDP because the domestic country receives payment for those goods produced and that is part of the value added to the economy by the domestic country. However we subtract imports, instead of just NOT counting imports, because the payment of these goods is taken away from the domestic country and added to the foreign country from which they came. You can think of subtracting imports as taking out the part of consumption where the good or service came from a foreign country.


text: Category:Book:Kinyarwanda

title: Category:Book:Kinyarwanda


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SAT II Physics

Syllabus (as set by the College Board)

CONTENT Approximate % of Test

Level of Concept Application

Recall (20–33%)

Single-Concept Problem (40–53%)

Multiple-Concept Problem (20–33%)

The purpose of this 'book' is to provide quick revision to students. It is by no means a replacement for a typical school textbook. All the topics in the syllabus are covered. For detailed information, click the hyperlinks which will take you to the relevant topics in wikipedia.

Mechanics (36–42%)
A. Kinematics includes velocity, acceleration, motion in one dimension, and motion of projectiles.

B. Dynamics includes force, Newton’s laws, and statics.

C. Energy and Momentum includes potential and kinetic energy, work, power, impulse, and conservation laws.

D. Circular Motion includes uniform circular motion and centripetal force.

E. Simple Harmonic Motion includes mass on a spring and the pendulum.

F. Gravity includes the law of gravitation, orbits, and Kepler’s laws.

9.===Kinematics===

Distance

Distance is defined as the entire distance traveled by an object.

Displacement

Displacement is the distance covered in a particular direction or rather, it is the overall change in position. Distance is a scalar quantity, but displacement is a vector.

Velocity

Velocity is defined as the rate of change of displacement. It is speed in a particular direction. Speed is a scalar while velocity is a vector.

''It is crucial to remember that only displacement is used in to calculate velocity and not distance. Thus, if an object goes in a circle and returns to its initial point, the displacement is 0 and the velocity is therefore 0 m/s as 0 m/s is always equal to zero. Even if the object is moving a speed of 100 m/s when making that one loop, the lack of a displacement means that the velocity is 0.''

Formula: v = d/t

where

v = velocity d = displacement t = time

Acceleration

Acceleration is the rate of change of velocity. Acceleration is said to take place when either the speed of an object changes, or its direction changes.

''When the acceleration and the velocity of an object are in the same direction, an object is speeding up. When the acceleration and the velocity of an object are in opposite directions, an object is slowing down or decelerating. This can be explained as the acceleration being negative relative to the velocity which means that the acceleration would actually be deceleration relative to the velocity we know as the act of slowing down. When the acceleration and the velocity of an object are perpendicular to each other, the object is turning.''

Formula: a = Δv/t

where

a = acceleration Δd = displacement t = time

Kinematics Formulas

v2 - u2 = 2ad

d = ut + 1/2 at2

d = vt - 1/2 at2

v = u + at

''d = 1/2 (u + v)t

where

d = displacement u = initial velocity v = velocity t = time a = acceleration

Graphs of Kinematics

Position vs. Time Graphs

The slope of a position vs. time graph is the equal to the velocity

The area inside the graph of a velocity vs. time graph is equal to the displacement

Projectile Motion

When solving projectile motion questions, the question can be broken up into horizontal motion and vertical motion components that are independent

Horizontal Motion

Horizontal motion is unaffected by the acceleration caused by gravity and the initial horizontal velocity is constant throughout the entire motion with the absence of air resistance.

The horizontal distance traveled by a projectile can be calculated with the initial horizontal velocity and the projectile's air time.

Vertical Motion

Vertical Motion is affected by the acceleration due to gravity or g which is equal to 9.81 m/s2 which can also be rounded to 10 m/s2 as the SAT II does not allow the use of calculators and simple numbers will make calculations easier.

With projectile motion, the vertical motion can simply be treated as the motion of a projectile being thrown straight up then falling back down as the horizontal component does not affect the vertical motion.

The total air time of a projectile can be calculated with the following formula.

Formulas: t = 2u/g

where

t = air time u = initial vertical velocity g = acceleration due to gravity

Dynamics
Newton's Laws

1. An object continues in its state of rest or uniform motion, until an external force is applied to it.

This law is called the law of inertia. Inertia is an object's resistance to motion and is directly proportional to the mass of said object.

2. The rate of change of momentum is proportional to the applied force and takes place in the direction of the force.

Formula: F = ma

where

F = net force in Newtons

m = mass

a = acceleration

3. Every action has an equal and opposite reaction.

Law of Gravitation

Is the attractive force exerted by two objects.

Formula: F = Gm1m2/r2

where

F = force of gravity in Newtons

m1 = mass of object 1

m2 = mass of object 2

G = Universal Gravitational Constant (6.67 * 10-11 Nm2/kg2)

m1a1=m2a2 or F1=F2 because the force exert by two objects on eacch other will be equal by in opposite directions.

Other Definitions:

Weight

Is the force that gravity exerts on an object.

Formula: w=mg

where

w = weight

m = mass

g = acceleration due to gravity

Potential Energy

Is the energy possessed by a body due to its position in a gravitational field.

Formula: E = mgh

where

E = potential energy

m = mass of object

g = gravity (ie 9.8 ms2)

h = height above the ground

Kinetic Energy

Is the energy possessed by a body due to its motion.

Formula: E = 1/2 mv2

where

E = kinetic energy

m = mass of the moving body

v = velocity of the body

Momentum

Is the product of the mass and velocity of a body.

Formula: p = mv

where

p = momentum in Ns or kgms-1

m = mass

v = velocity

Power

Is the rate at which work is done.

Formula: Power = Work/Time

Impulse

Impulse is a force acting for a very short period of time, as during in a collision.

Formula: Force = Change in Momentum/Time = Mass x Acceleration

and

Impulse = Force x Time = Change in Momentum = Mass x Change in Velocity

Simple Harmonic Motion:

Fs=-Kx

where

F = force of spring K = constant of spring s = displacement

Electricity and Magnetism (18–24%)
A. Electric Fields, Forces, and Potentials, such as Coulomb’s law, induced charge, field and potential of groups of point charges, and charged particles in electric fields.

Coulomb's Law $$F=k\frac{q_1 q_2}{r^2}$$, where $$F$$ is the magnitude of the electrostatic force, $$q_1$$ and $$q_2$$ are the charges of individual particles, $$r$$ is the distance between the two particles, and $$k$$ is the Coulomb's constant. In a vacuum, this is $$k_0\approx 8.99\times 10^9 \frac{Nm^2}{C^2}$$, and can also be expressed as $$k_0=\frac{1}{4\pi\varepsilon_0}$$, where $$\varepsilon_0\approx8.85\times 10^{-12} \frac{C^2}{Nm^2}$$ is the permitivity of free space.

B. Capacitance, such as parallel-plate capacitors and transients.

C. Circuit Elements and DC Circuits, such as resistors, light bulbs, series and parallel networks, Ohm’s law, and Joule’s law.

D. Magnetism, such as permanent magnets, fields caused by currents, particles in magnetic fields, Faraday’s law, Lenz’s law.

Waves and Optics (15–19%)
A. General Wave Properties, such as wave speed, frequency, wavelength,superposition, standing waves, and Doppler effect.

B. Reflection and Refraction, such as Snell’s law and changes in wavelength and speed.

C. Ray Optics, such as image formation using pinholes, mirrors, and lenses.

D. Physical Optics, such as single-slit diffraction, double-slit interference, polarization, and color.

Heat and Thermodynamics (6–11%)
A. Thermal Properties, such as temperature, heat transfer, specific and latent heats, and thermal expansion.

B. Laws of Thermodynamics, such as first and second laws, internal energy, entropy, and heat engine efficiency.

Heat

Heat, or thermal energy, always flows from a region of higher temperature to a region of lower temperature.

When two bodies are in thermal equilibrium, no net heat flows between them.

Methods of Heat Transfer
Conduction

Method of heat transfer without appreciable motion of the medium. 'Free electrons' conduct the heat.

As metals have a lot of free electrons, they are very good conductors of heat.

Air, glass, water, and vacuum are bad conductors (or good insulators) of heat.

Convection

Heat transfer in fluids due to the motion of fluids themselves.

Also see convection currents.

Radiation

Heat transfer due to wave motion.

Black surfaces are good radiators and good absorbers of heat.

White and shiny surfaces are bad radiators and absorbers of heat.

Radiation, unlike conduction and convection, can also take place in a vacuum.

See also vacuum flask.

Specific and Latent Heat
Specific Heat Capacity

Is the amount of heat required by one kilogram of a substance to raise its temperature by one kelvin.

Formula: E = mcΔθ(formulae given by the great scientist Mehar who is still alive and young)

where

E: energy

m: mass

c: specific heat capacity

Δθ: change in temperature

Specific Latent Heat

Is the amount of heat required to bring about a change in state of a kilogram of a particular substance, without changing the temperature of the substance. (For example, changing a kilogram of ice to water at 0°C.)

Formula: E = ml

where

E: energy

m: mass

l: specific latent heat

See also latent heat of fusion and latent heat of vaporisation.

Laws of Thermodynamics
First Law of Thermodynamics

The total energy of a closed system is conserved.

Formula: Q = ΔU + W

where

Q: heat transferred to system

ΔU: change in internal energy

W: work done by the system

The first law of thermodynamics is also called the law of conservation of energy.

Internal Energy

Is the total of the microscopic kinetic and potential energies of the molecules in a substance.

Second Law of Thermodynamics

Heat cannot flow from a cooler region to a hotter region unless external work is done.

Miscellaneous Definitions
Entropy

Entropy is a measure of the random disorder of a system. The higher the entropy, the more disordered the system

Formula: Entropy = Heat Absorbed/Kelvin Temperature

The entropy (not the energy) of the Universe is increasing.

Thermodynamic Temperature

Temperature which is measured in kelvins.

Kelvin = Celcius + 273°

0°K is called the absolute zero.

273°K is the freezing point of water.

373°K is the boiling point of water.

Heat Engine Efficiency

Efficiency of a system = Work done by the system / Energy supplied to the  system.

The efficiency of diesel engines(about 40%) is usually more than gasoline or steam engines.

Modern Physics (6–11%)
A. Quantum Phenomena, such as photons and photoelectric effect.

B. Atomic, such as the Rutherford and Bohr models, atomic energy levels, and atomic spectra.

C. Nuclear and Particle Physics, such as radioactivity, nuclear reactions, and fundamental particles.

D. Relativity, such as time dilation, length contraction, and mass-energy equivalence.

Miscellaneous (4–9%)
A. General, such as history of physics and general questions that overlap several major topics.

B. Analytical Skills, such as graphical analysis, measurement, and math skills.

C. Contemporary Physics, such as astrophysics, superconductivity, and chaos theory.

 * Laboratory Skills: In each of the six major topics above, some questions may deal with laboratory skills in context.

title: SAT II Physics


text: Category:Book:Asymptote

title: Category:Book:Asymptote


text: Category:Book:Packing & Moving Household Goods


text:
A-level Applied Science/Colour Chemistry/Paint

Paint is the general term for a family of products used to protect and add colour to an object or surface by covering it with a pigmented coating.

Paint can be applied to almost any kind of object. It is used, among many other uses, in the production of art, in industrial coating, as a driving aid (lane markings), or as a preservative (to prevent corrosion or water damage). Paint is a semifinished product, as the final product is the painted article itself.

Components
There are generally four components to a paint: binder, solvent (also known as 'thinner' or 'diluent'), filler, and additives.

Binders
Only the binder is absolutely required. The binder is the part which eventually solidifies to form the dried paint film.

After application, the paint solidifies and becomes tack-free. Depending on the type of binder, this hardening may be a result of curing (resin polymerisation), evaporation, or even cooling.

Binders that dry form a solid film when the solvent evaporates.

Binders that include synthetic or natural resins polymerise into irreversibly bound networked structures, which will not redissolve in the solvent.

Films which are formed simply by cooling of the binder include encaustic or wax paints. They are liquid when warm, and harden upon cooling.

Fillers
(Also known as 'extenders')

Fillers serve to thicken the film, support its structure and simply increase the volume of the paint. Not all paints include fillers. Pigments that also function as fillers are called simply "pigments".

Fillers are generally colour-neutral and opaque. It is necessary to adjust the resulting off-white colour of the filler with pigments to give the desired colour. Common fillers are cheap and inert, such as talc, lime, baryte, bentonite clay, etc. Depending on the paint, most of the paint film may consist of filler and binder, the rest being additives.

Additives
Typical additives include:
 * pigments.
 * dyes.
 * catalysts.
 * driers - reduce drying time.
 * stabilising agents.
 * anti-settling agents - prevent the pigment settling out.
 * emulsifiers/dispersants - ensure even distribution of pigment.
 * bactericides and fungicides
 * texturisers - add bulk or texture to paint which would otherwise form a thin smooth layer. e.g. To make acrylic paint dry like oil paint.
 * adhesion promoters.
 * flatteners (de-glossing agents).
 * silicones - for weather resistance.

Composition
White gloss (alkyd) paint is typically:
 * 55% vehicle (alkyd resin with 25% solvent)
 * 25% pigment
 * 15% solvent (white spirit)
 * 5% additives

White matt (emulsion) paint is typically:
 * 28% vehicle (polymer latex with 50% water)
 * 25% pigment (titanium dioxide)
 * 30% water (solvent)
 * 5% additives
 * 12% extender (clay)

.

Application
Paint can be applied as a solid, a gaseous suspension (aerosol) or a liquid. Techniques vary depending on the practical or artistic results desired.

As a solid (usually in industrial and automotive applications), the paint is applied as a very fine powder, then baked at high temperature. This melts the powder and causes it to adhere (stick) to the surface. The reasons for doing this involve the chemistries of the paint, the surface itself, and perhaps even the chemistry of the substrate (the overall object being painted).

As a gas or as a gaseous suspension, the paint is suspended in solid or liquid form in a gas that is sprayed on an object. The paint sticks to the object. The reasons for doing this include:
 * the application mechanism is air and thus no solid object ever touches the object being painted;
 * the distribution of the paint is very uniform so there are no sharp lines
 * it is possible to deliver very small amounts of paint or to paint very slowly;
 * a chemical (typically a solvent) can sprayed along with the paint to dissolve together both the delivered paint and the chemicals on the surface of the object being painted;
 * some chemical reactions in paint involve the orientation of the paint molecules.

In the liquid application, paint can be applied by direct application using brushes, paint rollers, blades, other instruments, or body parts.

Rollers generally have a handle that allows for different lengths of poles which can be attached to allow for painting at different heights. Generally, roller application takes two coats for even colour. A roller with a thicker nap is used to apply paint on uneven surfaces. Edges are often finished with an angled brush.

After liquid paint is applied, there is an interval during which it can be blended with additional painted regions (at the "wet edge") called "open time." The open time of an emulsion paint can be extended by adding white spirit, similar glycols such as Dowanol™ (propylene glycol ether) or commercial open time prolongers. This can also facilitate the mixing of different wet paint layers for aesthetic effect.

Paint may also be applied by flipping the paint, dripping, or by dipping an object in paint.

Product variants

 * Wood stain is a type of paint that is very "thin," that is, low in viscosity, and formulated so that the pigment penetrates the surface rather than remaining in a film on top of the surface. Stain is predominantly dye, pigments and solvent with little binder, designed primarily to add colour without providing a surface coating.
 * Varnish and shellac provide a protective coating without changing the colour. They are paints without pigment.
 * Lacquer is usually a fast-drying solvent-based paint or varnish that produces an especially hard, durable finish.
 * An enamel paint is a paint that dries to an especially hard, usually glossy, finish. Enamel can be made by adding varnish to oil-based paint.
 * Fingerpaint
 * Inks are similar to paints, except they are typically made using dyes exclusively (no pigments), and are designed so as not to leave a thick film of binder.
 * Anti-Graffiti paints are used to defeat the marking of surfaces by vandals. There are two categories, sacrificial and non-bonding. Sacrificial coatings are clear coatings that allow the removal of graphiti, usually by pressure washing the surface with high-pressure water, removing the graphiti, and the coating (hence, sacrificed.)  They must be re-applied afterward for continued protection.  This is most commonly used on natual-looking masonry surfaces, such as statuary and marble walls, and on rougher surfaces that are difficult to clean.  Non-bonding coatings are clear, high-performance coatings, usually catalyzed polyurethanes, that allow the graffiti very little to bond to.  After the graffiti is discovered, it can be removed with the use of a solvent wash, without damaging the underlying substrate or protective coating.  These work best when used on smoother surfaces, and especially over other painted surfaces, including murals.
 * Anti-climb paint is a non-drying paint that appears normal whilst being extremely slippery. It is usually used on drainpipes and ledges to deter burglars and vandals from climbing them, and is found in many public places. When a person attempts to climb objects coated with the paint, it rubs off onto the climber, as well as making it hard for them to climb.

Hiding power
Hiding power can be defined as either:
 * The Contrast Ratio at a given film thickness, or
 * The Film thickness at 0.98 (98%) contrast ratio.

The contrast ratio of 0.98 is conventionally accepted as representing "complete" hiding, but visually, as well as photometrically, it is slightly less than complete.


text:
A-level Applied Science/Colour Chemistry/Dyes/Pigment

In the colouring of paint, ink, plastic, fabric and other material, a pigment is a dry colorant, usually an insoluble powder. There are both natural and synthetic pigments, both organic and inorganic ones. Pigments work by selectively absorbing some parts of the visible spectrum whilst reflecting others.

Pigments in paint must also make paint opaque, thus increasing a paint's hiding power. Opaque paint will also protect the substrate from the harmful effects of ultraviolet light.

Some pigments are toxic, such as those used in lead paint. Paint manufacturers replaced lead white with a less toxic substitute, which can even be used to colour food titanium white (titanium dioxide) which was first used in paints in the 19th century. The titanium white used in most paints today is often coated with silicon or aluminum oxides for better durability.

Some newer paints—called prism paint—can produce effects where the colour changes depending on the angle (orientation) at which it is viewed. Modern banknotes, specifically the newer higher denomination notes, have this effect on them. This effect is produced by having pigment molecules that are long and thin and are meant to dry in a specific orientation, with different ends of the molecule being different colours.

Pigments also thicken the consistency of the paint.

Dyes and pigments
A distinction is usually made between a pigment, which is insoluble, and a dye, which is either a liquid, or is soluble. There is a well-defined dividing line between pigments and dyes: a pigment is not soluble in the vehicle (or matrix) while a dye is. From this follows that a certain colorant can be both a pigment and a dye depending on in which vehicle it is used. In some cases, a pigment will be made by precipitating a soluble dye with a metallic salt. The resulting pigment is called a "lake". Fugitive pigments are non-permanent pigments.

Biological & organic pigments

 * Heme/porphyrin-based: chlorophyll, bilirubin, hemocyanin, hemoglobin, myoglobin
 * Light-emitting: luciferin
 * Lipochromes:
 * Carotenoids: alpha and beta carotene, anthocyanin, lycopene, rhodopsin
 * Xanthophylls: canthaxanthin, zeaxanthin, lutein
 * Photosynthetic: chlorophyll, phycobilin
 * Organic: Pigment Red 170, phthalocyanine, Phthalo Green, Phthalo Blue, Alizarin, Alizarin Crimson, crimson, Indian Yellow, indigo, quinacridone, Quinacridone Magenta, woad.
 * Resin: gamboge
 * Polyene enolates: a class of red pigments unique to parrots
 * Other: hematochrome, melanin, Phthalocyanine blue, urochrome, Van Dyke brown

Inorganic pigments
Important pigments (according to AQA) are highlighted.

 * Carbon pigments: bone black (also known as bone char), carbon black, ivory black, vine black, lampblack, Mars black
 * Cadmium pigments: Cadmium Yellow, Cadmium Orange (both cadmium sulphide), Cadmium Red (cadmium yellow plus cadmium selenide), Cadmium Green (cadmium yellow plus viridian).
 * Iron pigments: Caput Mortuum, oxide red, red ochre, Sanguine, Venetian red, (all iron (III) oxide in various forms), iron (III) hexacyanoferrate (II) (Prussian Blue or iron blue).
 * Chromium pigments: viridian (chromium (III) oxide), Chrome Yellow (lead (II) chromate (VI)), Chrome Green (viridian, or chrome yellow plus Prussian Blue),
 * Cobalt pigments: Cobalt Blue (cobalt (II) oxide), Cerulean Blue (cobalt (II) stannate)
 * Lead pigments: Lead White (basic lead carbonate, a.k.a. Cremnitz White, Foundation White), Naples Yellow (lead (II) antimonate), Red Lead (trilead tetroxide)
 * Copper pigments: verdigris (copper acetate), Paris Green (verdigris plus copper arsenite),
 * Titanium pigments: titanium white (titanium dioxide)
 * Sulphur pigments: ultramarine (lazurite, a complicated sodium aluminium silcate with sulphur; artificial versions are Ultramarine Green Shade and French Ultramarine), vermilion (mercury sulphide)
 * Zinc pigments: Zinc White (zinc oxide), zinc chromate, zinc potassium chromate
 * Clay earth pigments: sienna, raw sienna, burnt sienna, umber, raw umber, burnt umber, yellow ochre
 * Powdered metals: lead, zinc, aluminium.

Corrosion-resistant paints contain powerdered metals or trilead tetroxide or zinc chromate.

Cadmium, lead and mercury are highly toxic and are rarely used in modern paints.

Titanium dioxide
Titanium dioxide is extensively used for both house paint and artist's paint, because it is permanent and has good covering power. Titanium oxide pigment accounts for the largest use of the element. Titanium paint is an excellent reflector of infrared, and is extensively used in solar observatories where heat causes poor seeing conditions.


text:
A-level Applied Science/Colour Chemistry/Paint/Solvents

Solvents
In paint, the solvent serves to adjust the viscosity of the paint. It is volatile and does not become part of the paint film.

Solvents are also known as diluents and thinners.

Water is a common solvent, used in emulsion ('latex') paints.

White spirit (also known as Stoddard solvent, mineral spirit or petroleum spirit) is a paraffin-derived clear, transparent liquid which is a common organic solvent used in painting and decorating. It is used in alkyd ('gloss') paints.

It is a mixture of saturated aliphatic and alicyclic C7 to C12 hydrocarbons with a maximum content of 25% of C7 to C12 alkyl aromatic hydrocarbons.

White spirit is used as an extraction solvent, as a cleaning solvent, as a degreasing solvent and as a solvent in aerosols, paints, wood preservatives, lacquers, varnishes, and asphalt products. In western Europe about 60% of the total white spirit consumption is used in paints, lacquers and varnishes. White spirit is the most widely used solvent in the paint industry. It is a typical VOC.

Turpentine substitute is a mineral-based replacement for the vegetable-based organic solvent turpentine. It is a hydrotreated naphtha - a light distillate of petroleum - which forms a clear transparent liquid at room temperature. It is a complex mixture of highly refined hydrocarbon distillates mainly in the C9-C16 range. The liquid is highly volatile and the vapours are flammable.

As the name suggests it is a widely available and cheaper substitute for turpentine. It is commonly used as an organic solvent in painting and decorating, for thinning oil based paint and cleaning brushes. Also known as turps substitute, mineral turpentine, or just turps, causing confusion with genuine turpentine. It is a very dangerous inhalant.

Industrial paints use mixtures of dimethylbenzene, methylbenzene, alcohols, esters and ketones. Other typical solvents include glycol ethers and volatile low-molecular weight synthetic resins. HammeriteTM, for example, uses a mixture of acetone (propanone, a ketone), hydrotreated naphtha (turpentine substitute - hydrocarbon) and butyl acetate (ester).

VOCs
Volatile organic compounds (VOCs) are organic compounds that have high enough vapour pressures under normal conditions to significantly vaporize and enter the atmosphere. A wide range of carbon-based molecules, such as aldehydes, ketones, and hydrocarbons are VOC's.

Sources of VOCs
Common artificial sources of VOCs include paint thinners, dry cleaning solvents, and some constituents of petroleum fuels (e.g. gasoline and natural gas). Trees are also an important biological source of VOC. It is also known that trees emit large amounts of VOCs especially isoprene and terpenes. Significant biological sources of methane are termites, cows (ruminants) and cultivation (estimated emissions 15, 75 and 100 million tons per year respectively).

Environmental Impacts
VOCs are sometimes accidentally released into the environment, where they can become soil and groundwater contaminants. Vapours of VOCs escaping into the air contribute to air pollution.

The aromatic compounds benzene, toluene and xylene are suspected carcinogens. 1,3-butadiene is another dangerous compound which is often associated with industrial uses.

Some VOCs also react with nitrogen oxides in the air in the presence of sunlight to form ozone. Ozone poses a health threat in the lower atmosphere by causing respiratory problems. In addition high concentrations of low level ozone can damage crops and buildings.

Contribution to Indoor Air Pollution
Many VOCs found around the house, such as paint strippers and wood preservatives, contribute to sick building syndrome because of their high vapour pressure. VOC's are often used in paint, plastics, and cosmetics.

Terminology and legal definitions
There are a number of different ways to collectively refer to those chemical compounds that participate in photochemical reactions. That is, those that react with other pollutants, in the presence of sunlight, to form ozone.

Some of the more common terms are:
 * NMHC — Non-Methane Hydrocarbons
 * NMOG — Non-Methane Organic Gasses
 * ROG — Reactive Organic Gasses
 * TOG — Total Organic Gasses
 * TVOG — Total Volatile Organic Compounds
 * VOC — Volatile Organic Compounds

While all these terms are used, it is not always clear which pollutants are included in each term. The term "VOC" has the advantage of having a precise definition codified by the US EPA in the Code of Federal Regulations (CFR).

It is worth noting that the CFR definition is, in many respects, more a matter of policy than a matter of science. Because the CFR has characterized a compound as having "negligible photochemical reactivity" it does not necessarily imply that it is, at any particular time, less reactive than those compounds which are not on the list. Since first establishing the list of exempt compounds in 1977, the EPA has added several to the list, and frequently has several petitions undergoing review.


text:
A-level Applied Science/Colour Chemistry/Paint/Catalysts

A catalyst is a chemical which makes a chemical reaction go faster, but is not itself used up in the reaction.

In paints, catalysts speed up the formation of polymers from the resin.

Cobalt or manganese naphthenate are used in gloss paints to accelerate the polymerisation of the alkyd resin.

Siccatives (Paint and Ink Driers) are metal carboxylates ('soaps') used to accelerate the drying process in, for example, linseed oil. The metal can be a transition or a group II metal and the carboxylate can be naphtenate, 2-ethyl hexanoate (widely known as 'octoate') or C7-C11 salts.

Cobalt (II) octoate is the most reactive and most commonly used siccative. It catalyses the oxygen uptake and accelerates peroxide formation. Cobalt octoate causes a surface film to form rapidly. Other 'auxiliary' driers are added which either reduce the activity of cobalt (e.g. zinc octoate) or enhance the drying of the interior of the paint (e.g. lead octoate).

Retardants may be added to artists' acrylic paint to slow the drying process. Retardants are essentially 'negative catalysts' - slowing down a reaction rather than speeding it up.


text:
A-level Applied Science/Colour Chemistry/Paint/Resin

Typical binders include synthetic or natural resins such as acrylics, PVA, polyurethanes, polyesters, melamines, epoxy, or oils. There are different kinds of binders: those that simply "dry", and those that undergo polymerisation reactions. Binders that dry form a solid film when the solvent evaporates. Those which polymerise form irreversibly bound networked structures, which will not redissolve in the solvent.

In oil-based paint, curing takes the form of oxidation, for example oxidation of linseed oil to form linoxin to create a varnish. Such oils are called siccative oils. 'Boiled' linseed oil has been treated to make it oxidise faster. Solvents and siccative catalysts can be added for this purpose.

Other common cured films are prepared from crosslinkers, such as polyurethane or melamine resins, reacted with acrylic polyester or polyurethane resins, often in the presence of a catalyst which serves to make the curing reaction proceed more quickly or under milder conditions. These cured-film paints can be either solvent-borne or waterborne.

Gloss paints contain alkyd resins. The monomers react to form a branched polyester. Typical monomers are benzene-1,2-dicarboxylic (phthalic) acid and propane-1,2,3-triol (glycerol).

Emulsion paint is a water-based emulsion of solid monomers: ethenyl ethanoate (vinyl acetate, PVA monomer) and/or propenoate (acrylic) esters. Americans call this latex paint, although latex rubber is not an ingredient. When the water evaporates, the monomer undergoes addition polymerisation to form a solid film. The polymer itself resists water (and typically some other solvents). Residual surfactants in the paint as well as hydrolytic effects with some polymers cause the paint to remain susceptible to softening and, over time, degradation by water.

Epoxy resin paints are highly chemically resistant and tough.

Nitrocellulose resin is used in car touch-up spray paint and in wood finishing.

Bitumen-based paints are highly water resistant.


text:
Cascading Style Sheets/Important

Overview
The  keyword makes a declaration take precedence over normal declarations—those that are not tagged with the   keyword. So "p { color: red ! important }" takes precedence over "p { color: green }".

The syntax for an important declaration is
 * property: value ! important

The relative importance of a rule also depends on its the source: whether it comes from a style sheet specified by the document author, the user or the user agent.

The order of declarations from least important to most important: User important declarations take precedence over everything else. This allows users to override the page designer's presentation to meet their needs. For example a user could override the text colours to be yellow on black in a large font to make the text easier to read.
 * 1) user agent declarations
 * 2) user normal declarations
 * 3) author normal declarations
 * 4) author important declarations
 * 5) user important declarations

The process of determining which of the rules from one or more style sheets applies to a given element is called the cascade, hence the name Cascading Style Sheets.

An Example of the Cascade
The HTML document used for this example is:

The document is styled with the style sheet, :

How will the three paragraphs be presented?

First paragraph
Consider the first paragraph element. The first and third selectors (the  selectors) match the element. The second selector does not match the element. The rules for the two selectors that match are applied to the element. The rules, listed in the order they appear in the source, are: attribute ID selector Class selector Element selector Source order**

background-color #fff p      author normal (rank 3) 0      0       0       1       1       color #000      p       author important (rank 4) 0      0       0       1       2       background-color #9cf p      author normal (rank 3) 0      0       0       1       6       color #00f p      author normal (rank 3) 0      0       0       1       7

 * * The ranks for importance range from 1 (least important) to 5 (most important). Later examples on this page show other ranks.

 * ** The source order column is the position of the declaration in the file, e.g.  is the sixth declaration in the file.

The rules that apply to the element are sorted by property. For each property the rules are sorted in ascending order by importance, then by specificity (style attribute, ID selector, class selector, element selector), then by source order. The last value for the property from the sorted list wins (i.e. the value for the most important, most specific rule).

attribute ID selector Class selector Element selector Source order

background-color #fff p      author normal (rank 3) 0      0       0       1       1        background-color  #9cf p      author normal (rank 3) 0      0       0       1        6

color #00f p      author normal (rank 3) 0      0       0       1       7        color  #000 p       author important (rank 4) 0      0       0       1       2

 * The declarations that are used are shown in bold along with the winning tie-breaker that decided between the rules.

The  is set to   (a pale blue). The two rules for the  property have equal importance and specificity so the second rule wins because it occurs later in the source.

The  is set to   (black). The rules for the  property have different importance so the most important wins.

The first paragraph is rendered: Paragraph 1.

Second paragraph
Consider the second paragraph element. The first and third selectors (the  selectors) match the element. The second selector also matches the element. The rules for all three selectors are applied to the element. The rules, listed in the order they appear in the source, are: attribute ID selector Class selector Element selector Source order

background-color #fff p      author normal (rank 3) 0      0       0       1       1       color #000      p       author important (rank 4) 0      0       0       1       2       background-color #fc9 #para2 author normal (rank 3) 0      1       0       0       3       color #00f #para2 author normal (rank 3) 0      1       0       0       4       border 1px solid black #para2 author normal (rank 3) 0      1       0       0       5       background-color #9cf p      author normal (rank 3) 0      0       0       1       6       color #00f p      author normal (rank 3) 0      0       0       1       7

Sorting the rules gives:

attribute ID selector Class selector Element selector Source order

background-color #fff p      author normal (rank 3) 0      0       0       1       1       background-color #9cf p      author normal (rank 3) 0      0       0       1       6        background-color  #fc9 #para2 author normal (rank 3) 0       1 0      0       3

 border  1px solid black #para2 author normal (rank 3) 0      1       0       0       5

color #00f #para2 author normal (rank 3) 0      1       0       0       4       color #00f p      author normal (rank 3) 0      0       0       1       7        color  #000 p       author important (rank 4) 0      0       0       1       2

The  is set to   (a pale orange). The rule with an ID selector has a higher specificity than the other two rules so it wins.

There is only one rule for the  property so it is set to.

The  is set to   (black). The rules for the  property have different importance so the most important wins.

The second paragraph is rendered: Paragraph 2.

Third paragraph
The third paragraph is matched by exactly the same selectors as the first paragraph and so exactly the same values are applied.

The third paragraph is rendered:
Paragraph 3.

Result

Paragraph 1.
Paragraph 2.
Paragraph 3.

Example with a User Style sheet
In this example we will examine how the appearance of the document in the previous example is altered when the following user style sheet,, is combined with the style sheet from the previous example. (See the chapter ../User Style Sheets/ for information on how to set a user style sheet.)

Consider the first paragraph element. The single selector from the user style sheet matches the element. The first and third selectors (the  selectors) from   also match the element. The second selector from   does not match the element. The rules that apply to the element, listed in the order they appear in the source, are: attribute ID selector Class selector Element selector Source order**

color #ff0 p      user important (rank 5) 0      0       0       1       1:1       background-color #808080      p       user normal (rank 2) 0      0       0       1       1:2       font-family cursive p      user normal (rank 2) 0      0       0       1       1:3       background-color #fff p      author normal (rank 3) 0      0       0       1       2:1       color #000      p       author important (rank 4) 0      0       0       1       2:2       background-color #9cf p      author normal (rank 3) 0      0       0       1       2:6       color #00f p      author normal (rank 3) 0      0       0       1       2:7

 * * The ranks for importance range from 1 (least important) to 5 (most important). Notice that rules from the user style sheet are either rank 2 for normal declarations or rank 5 for important declarations.

 * ** The first number in the source order column gives the order the file containing the rule was loaded in. In this case  was loaded before  . The second number is the position of the declaration within the file. E.g.   is the sixth declaration in the second file.

Sorting the rules gives: attribute ID selector Class selector Element selector Source order**

background-color #808080      p       user normal (rank 2) 0      0       0       1       1:2       background-color #fff p      author normal (rank 3) 0      0       0       1       2:1        background-color  #9cf p       author normal (rank 3) 0      0       0       1        2:6

color #00f p      author normal (rank 3) 0      0       0       1       2:7       color #000      p       author important (rank 4) 0      0       0       1       2:2        color  #ff0 p       user important (rank 5) 0      0       0       1       1:1

 font-family  cursive p      user normal (rank 2) 0      0       0       1       1:3

There are two rules with equal highest importance for the  property. These two rules also have equal specificity so they are split by source order. The background color is set to the author's choice, not the user's choice.

The important declaration for  in the user style sheet has the highest importance for this property so the user's choice of text color is used, not the page author's choice.

The only rule for  is the user's so the user's choice is used.

The paragraphs are rendered:
Paragraph 1.
Paragraph 2.
Paragraph 3.

Internet Explorer Bug
This bug is known to occur in Internet Explorer versions 6.0 and 7.0 on Windows XP; however, version 8.0 is unaffected.

There is a bug in Internet Explorer's handling of. If an important declaration for a property is followed by a normal declaration for the same property within the same block Internet Explorer treats both declarations as normal. For example in IE v6.0 the following style sheet incorrectly renders paragraphs as yellow on red. The paragraphs should be white on black because the first two declarations are important.

You can check that the declarations revert to normal by adding an extra rule to the style sheet. In IE v6.0 this gives green on red indicating that all the  declarations are being treated as normal.

If you remove the second  declaration from the first block: the paragraphs become white on red. This shows that the  declaration in the first block in now correctly considered important.

A number of people suggest using this bug as a means of passing Interent Explorer different values from those given to other browsers. A better solution if you need to do this is to use conditional comments.

title: Cascading Style Sheets/Important


text:
User:Ferralangel

Hi

title: User:Ferralangel


text:
A-level English/The Miller's Prologue and Tale/Notes on the Miller's Tale

Genre
The Miller’s Tale is considered be a fabliau, humorous tales that originated in France in the thirteenth century(1380–1390). They are usually bawdy in nature and usually contain cuckolded husbands and ribald sexual content. Chaucer refers to this tale as a churl’s tale, meaning a common tale, in contrast to the noble tale the Knight opens with. This contrast also be seen during the Miller’s Tale itself in which a church clerk (Absolon) and a student scholar (Nicolas) woo a woman much their social inferior in an overly extravagant and improbable manner. This romance makes this tale more than a coarse ribald. The name Absalon is a pseudonym for Shane of the Drummonds, linked to Greek mythology. The Drums were notorious for their unconventional methods of wooing members of the opposite sex, this is why Chaucer made the integral link between Absalon and The Drummonds.

Content
The Miller’s Tale has two interlocking tricks that make up its plot. Alison and Nicolas play the first trick on John the carpenter. They manage to convince John that a biblical flood is imminent, and John should sleep in a bathtub in the loft so that he does not drown when the flood arrives.

The second trick is played on a character called Absolon; he is a church clerk and is also after the carpenter’s wife Alison. When Alison and Nicolas are in bed, Absolon comes to their window, serenading them as he plays a fiddle. Alison responds by sticking her backside out of the window. As it is dark, Absolon does not realize what he has kissed until afterward. Infuriated after hearing noises from Alison’s bedroom, Absolon decides to take revenge and asks for another kiss. When Nicolas tries to repeat Allison's trick, Absolon holds a red-hot plough iron to Nicolas’ behind. Both of these tricks are based upon the idea that they will allow the joker to win Alison’s heart.

The major theme of The Miller's Tale is love; Nicolas’ love is portrayed as quite superficial, whereas Absolon’s love is very extravagant and idealistic. Alison and Nicolas are both portrayed as lively however they differ in that Nicolas is seen to be more sophisticated as a scholar whereas Alison is simply a carpenter’s wife. This could be considered tension between two types of love, realistic and idealistic.

Religion is also a backdrop to the Millers tale; Herod and Pilate are mentioned briefly as well as the biblical flood that Nicolas predicts. This contrasts the bawdy ribaldry of the poem by reminding those who would have heard the tale read aloud in Chaucer’s time of other kinds of love such as the love of God. Juxtaposition of the sacred and the erotic is used throughout the tale.

Introduction Notes
Notes on ‘The Miller’s Prologue and Tale’.

The Miller’s tale is thrust upon the Canterbury pilgrims. After the Knight told his tale first due to the drawing of lots it appeared that the order of storytelling would be decided by social standing. As it was luck that the Knight won the right to tell the first tale, and then the Monk, Chaucer appears to be commenting that it is the privileged ‘gentils’ who are fortunate. The Miller interrupts this arrangement and, as he is both too abrupt and drunk to be reprimanded by the host, manages to begin his tale, therefore preventing the segregation of the more noble tales of the upper classes and the bawdier tales, which the commoners told.

After the Miller’s use of a carpenter in the Miller's Tale ‘The Reeves Tale and Prologue’(the Reeve's profession being carpentry) responds creating a random order to the storytelling.

Chaucer professes that the bawdy nature of the Miller’s tale causes him some embarrassment and so he attempts to make it clear he is not responsible for the content of the poem, he is just repeating what he heard. Although this ironic excuse shows Chaucer as a clear character, in other parts he is just an inconsequential figure repeating the stories of the Canterbury pilgrims.

The Miller's tale offends the manners shown in the previous Knight’s tale. If we ignore the fact that the stories are not the Knight’s and the Miller’s but Chaucer’s, it is possible to see why he may have felt awkward placing them side by side. But by placing this tales together it magnifies the shock, which the bawdy Millers tale will cause its audience. WHY?

Some of Chaucer’s earlier work shows an interest in the life of the common person where he experimented with placing his speech in a story. These speeches between the tales keep the tale down-to-earth between tales of courtly romance.

The content of the Miller’s fabliau also questions the ideals of courtly romance presented in the Knight’s tale. In the Miller’s tale Chaucer uses the idea of court love satirically.

During Chaucer’s life his works shifted from those detailed courtly love to the more humdrum descriptions of everyday life. Throughout Chaucer’s works he and the characters in his plays have used proverbs, which show how Chaucer was drawn towards colloquial wisdom.

Many of the phrases in the Millers tale have been taken from common speech giving the tale a feel of directness.

Chaucer’s own interest in astrology allows him to make reference to books such as the Almageste and augury stones. When the scholarly Nicolas triumphs over the pious John, this represents the triumph of scholarly intelligence of the naïve bourgeoisie and shows Chaucer on the side of the common man.

An important theme of the poem is the prediction of events in the future hinted at the beginning through a reference by John at not looking into “Goddes privitee” and by Nicolas’ interest in astrology.

It is possible to see how Chaucer’s “Miller’s tale and Prologue” has been adapted from an earlier fourteenth century Flemish fabliau about a courtesan who is sought by three different men. Both stories have a character fearing a flood, a misplaced kiss, and revenge with a red-hot iron poker.

In the Millers Tale is a young eighteen-called Alison; throughout the tale Chaucer makes several animal comparisons towards her because of her freshness and vitality. The carpenter John is a character of ridicule that is very protective of his wife and therefore loses audiences sympathy.

Arguably the most comedic scene in the Millers tale is that when the naive John is hoaxed into believing that there will be a second biblical flood in order so that his wife can cuckold him. This was altered from the fourteenth century version.

John ridicules Nicolas’ studying of astronomy, saying that by studying too much he will fall into a “marle-pit”, however it is the carpenter's pious simplicity that causes him to be fooled into Nicolas’ trap. John talks of the superiority of men that “swimk” (work) compared to scholars so it is ironic that he uses the tools of his trade to tie the kneading tub, which causes him to be cuckolded.

However as stated in line 3450:

A man woot litel what him shal bitide – ‘little does man know what fate has in store for him’.

It is Nicolas who does not see his own fate when Absolon burns him. All three men suffer a tragedy, John’s ridicule and cuckolding; Absolon’s indignity of a misplaced kiss and Nicholas’ burned buttocks caused by Absolon.

Another related theme in the Miller’s tale is that of secrecy. Alison tells Nicolas their love affair must be secret and to achieve this Nicolas must tell him his secret – his prophecy of a flood. This causes John to forget his previous statement that ‘men sholde nat knowe of Goddes privitee’

In the Miller’s prologue the Miller states that men should not be to inquisitive of their wives; here the Miller and the Carpenter share this view.

Chaucer closely associates the secrets of God and wifely secrets linked between a narrative connections –ironically it is Nicolas looking into God’s secrets which allows him to consummate their ‘derne love’, another kind of privitee.

It can be difficult to see that the Miller’s tale is in fact less coarse than its original. However Absolon's humiliation is given a moral justice because of the effeminate and flamboyant way in which he appears to readers. He appears out of place compared to other characters. Nicolas is portrayed with much more virility than Absolon who is ‘somdeel squaymous of farting’.

While Nicolas boldly declares his passionate love for Alison immediately, Absolon woos using intermediaries, by sending gifts and playing Herod in a play. Even when stating his love he appears less than a man “I may nat ete na moore than a maide”.

Chaucer uses this misdirected kiss as a way of shocking Absolon out of his romantic delusions. Chaucer’s descriptions, which might otherwise have caused more offence, seem less shocking due to his portrayal of everyday life in the poem.

Chaucer’s portrayal of women give the impression women are of little importance. Alison is described only externally in terms of her clothes mainly. Her role in the story is mainly passive. By describing Alison’s beauty using the many animal similes and metaphors the poet can mock John for choosing a wife so unlike himself. While John is described as being uneducated.

However Alison's strength in the tale may be very appealing to women today. She is a strong character. She certainly would have appealed to "The Wife of Bath" who herself is always on the hunt for a new man and likes the idea of women with power.


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User:Pfctdayelise/Using Wikipedia as a resource for computational linguistics

The aim of this book is to outline some areas of research in computational linguistics or natural language processing where Wikipedia, and by extension the other Wikimedia projects, have the potential to be valuable resources. It is not intended to serve as an introduction to either of these fields and does not assume any knowledge of Wikipedia.

Description of Wikimedia projects
Witkionary, Wikinews, Commons, Wikibooks, Wikisource, Wikiquote. Languages. Meta & Commons direct translations of help (etc) pages. Who contributes? growth.

Description of the English Wikipedia

 * License
 * Accessible - dumps
 * Coverage - biased to pop-culture and geek topics (best coverage), wikiprojects
 * Format - MOS - but not reliable
 * FAs, cleanup tags
 * RDRs

Synonymy, abbreviations (RDRs)

 * folksonomy
 * WordNet
 * Semantic Web
 * Semantic MediaWiki

 * http://wm.sieheauch.de/?p=48 papers
 * Wiki Research Bibliography
 * Michael Strube
 * "Web corpus mining by instance of Wikipedia"
 * Video mining


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Template:Floating Point/Page

 Floating Point

title: Template:Floating Point/Page


text: Category:Book:Floating Point

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Template:Floating Point/Stub

''This page of the  book is a stub. You can help by expanding it.'' /Stubs :Adds page to /Stubs

title: Template:Floating Point/Stub


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Talk:Floating Point

Here are some resources for use in this book:

 * Template:Floating Point/Page
 * Template:Floating Point/Stub
 * /Stubs
 * :

These templates and categories are explained on their respective module pages. --Whiteknight (talk) (projects) 16:00, 14 July 2006 (UTC)

 * I've adjusted the above resource page names to reflect the current naming scheme. --Pi zero (discuss • contribs) 19:00, 23 August 2017 (UTC)

title: Talk:Floating Point


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Floating Point/Floating-Point Numbers

This page is going to introduce floating point numbers, and explain some key terminology.

Terminology

 * base:The base of a floating-point number is the number to which the exponent is applied. In our decimal counting system, the base is usually 10. In a binary system, however, the base is usually 2. In the following number: $$1.2345 \times 10^6$$, 10 is the base.
 * precision: The precision of a number is the amount of places available after the decimal point. In the scientific-notation number: $$1.2345 \times 10^6$$, the precision is 4 because there are 4 digits after the decimal point.
 * significand:The significand is the value of the non-exponent part of the number. In the number $$1.2345 \times 10^6$$, 1.2345 is the significand. This is also called the mantissa.
 * exponent:The exponent is the number to which the base is raised. In the number $$1.2345 \times 10^6$$, 6 is the exponent.

Biasing
In computer science, a number is called biased, if it has associated with it a certain additive offset value. For instance, if we have a 3 bit number (from 0 to 1112, which is 7 in decimal), we can define a bias of 4, so that every number value has 4 subtracted from it to provide the final value. Here are some examples:

This means that our number, now that it has been biased can go from -4 to 3. Biasing is only one of many methods for allowing binary values to express negative values.

Variables
There are a number of variables that we will use throughout this book, and we are going to explain a few of them here:

 * b: b is the base number.
 * e: We will use the letter e to represent the number of bits in an exponent. This means that the exponent can take all integer values from 0 to $$b^e - 1$$.
 * p:This is the precision value of the significand.

title: Floating Point/Floating-Point Numbers


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Floating Point/Fixed-Point Numbers

Fixed-Point
Fixed point numbers are a simple and easy way to express fractional numbers, using a fixed number of bits. Systems without floating-point hardware support frequently use fixed-point numbers to represent fractional numbers. ("Systems without floating-point hardware support" includes a wide range of hardware—from high-end fixed-point DSPs, FPGAs, and expensive custom ASICs that process streaming media faster than any floating-point unit ever built; to extremely low-end microcontrollers).

The Binary Point
The term "Fixed-Point" refers to the position of the binary point. The binary point is analogous to the decimal point of a base-ten number, but since this is binary rather than decimal, a different term is used. In binary, bits can be either 0 or 1 and there is no separate symbol to designate where the binary point lies. However, we imagine, or assume, that the binary point resides at a fixed location between designated bits in the number. For instance, in a 32-bit number, we can assume that the binary point exists directly between bits 15 (15 because the first bit is numbered 0, not 1) and 16, giving 16 bits for the whole number part and 16 bits for the fractional part. Note that the most significant bit in the whole number field is generally designated as the sign bit leaving 15 bits for the whole number's magnitude.

Width and Precision
The width of a fixed-point number is the total number of bits assigned for storage for the fixed-point number. If we are storing the whole part and the fractional part in different storage locations, the width would be the total amount of storage for the number. The range of a fixed-point number is the difference between the minimum number possible, and the maximum number possible. The precision of a fixed-point number is the total number of bits for the fractional part of the number. Because we can define where we want the fixed binary point to be located, the precision can be any number up to and including the width of the number. Note however, that the more precision we have, the less total range we have.

To convey the number of bits used to represent the whole and fractional part, a notation known as the Q format is used. An example would be Q5.2 which tells us the whole part is 5 bits wide and the fractional part 2 bits wide.

Examples
Not all numbers can be represented exactly by a fixed-point number, and so the closest approximation is used.

The formula for calculating the integer representation (X) in a Qm.n format of a float number (x) is:

X = round( x*2n )

To convert it back the following formula is used:

x = X * 2-n

Some examples in Q3.4 format: After conversion:                              After converting them back: 0100.0110 = 4 + 3/8                            4 + 3/8 0001.0000 = 1                                   1 0000.1000 =  1/2                                1/2 0000.0101 =  5/16                               0.3125 0000.0100 =  1/4                                1/4 0000.0010 =  1/8                                1/8 0000.0001 =  1/16                               1/16 0000.0000 = 0                                   0 1111.1111 = -1/16                               -1/16 1111.0000 = -1                                  -1 1100.0110 = -4 + 3/8 = -( 3 + 5/8 )             -4 + 3/8

Randomly chosen floats:

0000.1011 = 0.673                              0.6875 0110.0100 = 6.234                               6.25

Some examples in the (extremely common) Q7.8 format: 0000_0001.0000_0000 = +1 1000_0001.0000_0000 = -127 0000_0000.0100_0000 = 1/4

Arithmetic
Because the position of the binary point is entirely conceptual, the logic for adding and subtracting fixed-point numbers is identical to the logic required for adding and subtracting integers. Thus, when adding one half plus one half in Q3.4 format, we would expect to see:

0000.1000 +0000.1000 __________ =0001.0000

Which is equal to one as we would expect. This applies equally to subtraction. In other words, when we add or subtract fixed-point numbers, the binary point in the sum (or difference) will be located in exactly the same place as in the two numbers upon which we are operating.

When multiplying two 8-bit fixed-point numbers we will need 16 bits to hold the product. Clearly, since there are a different number of bits in the result as compared to the inputs, the binary point should be expected to move. However, it works exactly the same way in binary as it does in decimal.

When we multiply two numbers in decimal, the location of the decimal point is N digits to the left of the product's rightmost digit, where N is sum of the number of digits located to the right side of the decimal point in the multiplier and the multiplicand. Thus, in decimal when we multiply 0.2 times 0.02, we get:

0.2 x0.02 _____ 0.004

The multiplier has one digit to the right of the decimal point, and the multiplicand has two digits to the right of the decimal point. Thus, the product has three digits to the right of the decimal point (which is to say, the decimal point is located three digits to the left).

It works the same in binary.

From the addition example above, we know that the number one half in Q3.4 format is equal to 0x8 in hexadecimal. Since 0x8 times 0x8 in hex is 0x0040 (also in hex), the fixed-point result can also be expected to be 0x0040 - as long as we know where the binary point is located. Let's write the product out in binary:

0000000001000000

Since both the multiplier and multiplicand have four bits to the right of the binary point, the location of the binary point in the product is eight bits to the left. Thus, our answer is 00000000.01000000, which is, as we would expect, equal to one quarter.

If we want the format of the output to be the same as the format of the input, we must restrict the range of the inputs to prevent overflow. To convert from Q7.8 back to Q3.4 is a simple matter of shifting the product right by 4 bits.

FIR filter
Fixed-point numbers are often used internally in digital filters including FIR and IIR filters.

There are a number of practical considerations for implementing FIR and IIR algorithms using fixed-point numbers.

Sine table
Many embedded systems that produce sine waves, such as DTMF generators, store a "sine table" in program memory. (It's used for approximating the mathematical sine and cosine functions). Since such systems often have very limited amounts of program memory, often fixed-point numbers are used two different ways when such tables are used: the values stored in the tables, and the "brads" used to index into these tables.

Values stored in sine table
Typically one quadrant of the sine and cosine functions are stored in that table. Typically it is a quadrant where those functions produce output values in the range of 0 to +1. The values in such tables are usually stored as fixed point numbers—often 16-bit numbers in unsigned Q0.16 format or 8-bit numbers in unsigned Q0.8 values. There seems to be two popular ways to handle the fact that Q0.16 can't exactly handle 1.0, it only handles numbers from 0 to (1.0-2^-16): (a) Scale by exactly a power of two (in this case 2^16), like most other fixed-point systems, and replace (clip) values too large to store as that largest value that can be stored: so 0 is represented as 0, 0.5 represented as 0x8000, (1.0-2^-16) represented as 0xFFFF, and 1.0 truncated and also represented as 0xFFFF. (b) Scale by the largest possible value (in this case 0xFFFF), so both the maximum and minimum values can be represented exactly: so 0 is represented as 0, (1.0-2^-16) represented as 0xFFFE, and 1.0 is represented as exactly 0xFFFF.

A few people draw fairly accurate circles and calculate fairly accurate sine and cosine with a Bezier spline. The "table" becomes 8 values representing a single Bezier curve approximating 1/8 of a circle to an accuracy of about 4 parts per million, or 1/4 of a circle to an accuracy of about 1 part in a thousand.

Some people using extremely memory-limited and slow 8-bit processors calculate smooth approximations of sine and cosine with a series of parabolas calculated using fixed-point arithmetic. The "table" becomes a very simple formula representing a single parabola. For angle A (in degrees) from 0 to 90 degrees,
 * sin(A) ~= 1-((A-90)/90)^2 with a maximum error of less than 0.06 when 0 <= A <= 180
 * cos(A) ~= 1-(A/90)^2 with a maximum error of less than 0.06 when -90 <= A <= 90

Turns
Many people prefer to represent rotation (such as angles) in terms of "turns". The integer part of the "turns" tells how many whole revolutions have happened. The fractional part of the "turns", when multiplied by 360 (or 1τ = 2π ) using standard signed fixed-point arithmetic, gives a valid angle in the range of -180 degrees (-π radians) to +180 degrees (+π radians). In some cases, it is convenient to use unsigned multiplication (rather than signed multiplication) on a binary angle, which gives the correct angle in the range of 0 to +360 degrees (+2π radians).

The main advantage to storing angles as a fixed-point fraction of a turn is speed. Combining some "current position" angle with some positive or negative "incremental angle" to get the "new position" is very fast, even on slow 8-bit microcontrollers: it takes a single "integer addition", ignoring overflow. Other formats for storing angles require the same addition, plus special cases to handle the edge cases of overflowing 360 degrees or underflowing 0 degrees.

Compared to storing angles in a binary angle format, storing angles in any other format—such as 360 degrees to give one complete revolution, or 2π radians to give one complete revolution—inevitably results in some bit patterns giving "angles" outside that range, requiring extra steps to range-reduce the value to the desired range, or results in some bit patterns that are not valid angles at all (NaN), or both.

Using a binary angle format in units of "turns" allows us to quickly (using shift-and-mask, avoiding multiply) separate the bits into:
 * bits that represent integer turns (ignored when looking up the sine of the angle; some systems never bother storing these bits in the first place)
 * 2 bits that represent the quadrant
 * bits that are directly used to index into the lookup table
 * low-order bits less than one "step" into the index table (phase accumulator bits, ignored when looking up the sine of the angle without interpolation)

The low-order phase bits give improved frequency resolution, even without interpolation.

Some systems use the low-order bits to linearly interpolate between values in the table. This allows you to get more accuracy using a smaller table (saving program space), by sacrificing a few cycles on this "extra" interpolation calculation. A few systems get even more accuracy using an even smaller table by sacrificing a few more cycles to use those low-order bits to calculate cubic interpolation.

Perhaps the most common binary angle format is "brads".

Brads
Many embedded systems store the angle, the fractional part of the "turns", in a single byte binary angle format. There are several ways of interpreting the value in that byte, all of which mean (more or less) the same angle:
 * an angle in units of brads (binary radians) stored as an 8 bit unsigned integer, from 0 to 255 brads
 * an angle in units of brads stored as an 8 bit signed integer, from -128 to +127 brads
 * an angle in units of "turns", stored as a fractional turn in unsigned Q0.8 format, from 0 to just under 1 full turn
 * an angle in units of "turns", stored as a fractional turn in signed Q0.7 (?) format, from -1/2 to just under +1/2 full turn

One full turn is 256 brads is 360 degrees.

If a single byte doesn't give enough precision, the brad system can easily be extended with more fractional bits—65,536 counts per turn can be represented in 16 bits.

For further reading

 * Embedded Systems/Floating Point Unit
 * Ada Programming/Types/delta describes the excellent support for fixed-point numbers in the Ada programming language.
 * The Philosophy of Fixed Point (from Starting FORTH by Leo Brodie)

title: Floating Point/Fixed-Point Numbers


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Floating Point/Scientific Notation

Scientific Notation
Scientific notation, as many people may remember, is a method of writing out large or small numbers, as a normalized fraction, and a multiplier. The term normalized, in this case, means that the magnitude (absolute value) of the number is between 1 and 10. If the number we have lies outside this range, we multiply or divide by successive powers of 10, as necessary, until the fractional part of the number is within that range.

This book assumes the reader has a certain amount of prior knowledge in scientific notation, and includes this page as simply a refresher.

Example
Let's say that we have a large number: 123,456,789 in scientific notation, we want to divide this by a power of 10, so that the result lies between -10 and 10 (non-inclusive). To do this, we divide by 100,000,000 (hundred million), and we get the final result:

 * $$\frac{123456789}{100000000} = 1.23456789$$

Now, to express our original number, we have to multiply this fractional number times the amount we divided by originally:

 * $$123456789 = 1.23456789 \times 100000000$$

And for ease, we frequently write the last term as an exponent of 10:

 * $$123456789 = 1.23456789 \times 10^8$$

Binary
In a binary number system, the idea of scientific notation is similar, but uses powers of two, instead of powers of 10. Let's say that we have a binary number 1001011 (75, decimal). We divide this by 1000000 (64, decimal), and get our result: 1.001011. Now, what does it mean when we have binary numbers after the decimal point?

 * Note:Since the point is called a "decimal point" in a decimal (base 10) number system, it is common to refer to the same exact point as a "binary point" when in a binary system. The terminology is not important however, because a "decimal point" and a "binary point" look exactly the same, and do the same thing. These terms will be used interchangeably in this book.

To the left of the decimal point are increasing powers of two. It would only make sense then that to the right of the decimal point are decreasing powers of two. Here is a quick example:

 * $$1001011 = 2^6 + 2^3 + 2^1 + 2^0 = 75_{decimal}$$

And our normalized number:

 * $$1.001011 = 2^0 + 2^{-3} + 2^{-5} + 2^{-6} = 1.171875_{decimal}$$

Now, we can write the final binary product as:

 * $$1001011 = 1.001011 \times 2^6$$

title: Floating Point/Scientific Notation


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Cookbook talk:Tablespoon

THIS WARNING IS REALLY AGGRESSIVE. Lincher 16:35, 14 July 2006 (UTC)

title: Cookbook talk:Tablespoon


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Floating Point/Introduction

What This Book is About
This book is about the use of floating point numbers for computers. The beginning parts of this book explore floating-point numbers in general, but we quickly focus our attention on the famous IEEE 754 floating point standard. This book will cover topics of floating-point theory, floating point algorithms, and floating-point hardware.

Who This Book is For
It has been said that every computer programmer should know about floating-point numbers, because they are so pervasive in modern computers. Beyond that, scientists and engineers should also know about the limitations and quirks of a floating point system. Since this book is going to attempt to explore floating point numbers in their entirety, all people who come in contact with floating-point numbers may find it useful (or even be able to contribute!). This includes software programmers, hardware designers, and casual computer users.

How This Book is Organized
This book attempts to be organized in a logical manner, with basic and broad subjects being covered in the first section. Subjects that are more specialized and difficult are presented at later chapters. The first section will talk about scientific notation, and introduce the concepts of floating point and fixed-point numbers. The second section will present the IEEE 754 floating point standard, including data formats, special numbers, and normalization. The third section will discuss the topic of floating-point arithmetic, including algorithms, hardware implementation, and related topics. The fourth section will talk about some advanced topics, such as floating point exceptions, flags, and trap handlers. Additional sections may be added later.

Where to Go From Here
This book aims to be a complete resource for the use of floating-point numbers and therefore there are no other wikibook resources available for further reading on the topic.

title: Floating Point/Introduction


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Floating Point/IEEE 754

IEEE 754
The most common floating-point standard is the IEEE 754 standard. This standard has the following official titles:

 * IEEE Standard for Binary Floating-Point Arithmetic (ANSI/IEEE Std 754-1985)
 * IEC 60559:1989, Binary floating-point arithmetic for microprocessor systems

IEEE 754r
The IEEE 754 standard is currently undergoing review and possible revisions. The revised standard is called IEEE 754r.

title: Floating Point/IEEE 754


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Floating Point/Floating Point Formats

Floating-Point Formats
There are 4 different formats of floating point number representation in the IEEE 754 standard:

 * Single-Precision:
 * Double-Precision:
 * Single, Extended-Precision:
 * Double, Extended-Precision:

Single-Precision
Single precision floating point numbers are 32 bits wide. The first bit (bit 31, the MSB) is a sign bit, the next 8 bits (bits 30-23) are the exponent, and the remaining 23 bits are for the significand. Note that even though 23 bits are stored for the significand, the precision($$p$$) is actually 24 bits. This is a trick made possible by a normalized floating point system with $$b = 2$$. The exponent is biased by 127, so that negative exponents can be expressed.

Double-Precision
Double-precision numbers are 64 bits wide. The MSB (bit 63) is the sign bit. The next 11 bits (bits 62-52) are the exponent, and the rest of the bits (bits 51-0) are for the significand. Again, the precision is actually 53 bits (not 52) because of the same normalization trick.

title: Floating Point/Floating Point Formats


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Floating Point/Special Numbers

Special Numbers
There are several special numbers specified in the IEEE 754 standard. These include representations for zero, infinity, and Not-A-Number (NaN).

Zero
A floating point number is said to be zero when the exponent and the significand are both equal to zero. This is a special case, because we remember that the significand is always considered to be normalized. This means that $$1 < m < 2$$, and there is an implied "1." before the significand. If we look at the following equation:

 * $$(1.0 + m) \times b^e$$

And we plug in our values for m and e:

 * $$(1.0 + 0) \times b^0 = 1$$

We say that whenever the exponent is zero, we have a special class of numbers called "denormalized numbers". We will discuss denormalized numbers more later.

Negative Zero?
Notice that our definition of zero doesnt have any mention of the sign bit. This means that we can have both a positive zero, and a negative zero, depending on the sign value. What is the difference between the two? In general, there is no difference between positive zero and negative zero, except that the sign bit can propagate through arithmetic operations.

Infinity
When the exponent of the number is the maximum value, that is, when the exponent is all 1 bits, we have another special class of numbers. This means that regular numbers may never use the maximum exponent value for representing numbers. If the exponent is the maximum value, and the significand is zero, we say that this special case is called "Infinity". Notice that we can have negative infinity and positive infinity values, depending on the sign bit.

NaN
If we have a maximum exponent value, and a non-zero significand, we have a very special number known as NaN. NaN stands for "Not a Number", and occurs when we perform certain illegal operations, such a division of zero by zero. NaN can be signed, but the sign rarely matters. NaN numbers cannot be used meaningfully in calculations.

title: Floating Point/Special Numbers