Binary Numbers and Computer Speed

Posted by PITHOCRATES - April 2nd, 2014

Technology 101

Computers are Good at Arithmetic thanks to Binary Numbers

Let’s do a fun little experiment.  Get a piece of paper and a pen or a pencil.  And then using long division divide 4,851 by 34.  Time yourself.  See how long it takes to complete this.  If the result is not a whole number take it to at least three places past the decimal point.  Okay?  Ready……..start.

Chances are the older you are the faster you did this.  Because once upon a time you had to do long division in school.  In that ancient era before calculators.  Younger people may have struggled with this.  Because the result is not a whole number.  Few probably could do this in their head.  Most probably had a lot of scribbling on that piece of paper before they could get 3 places past the decimal point.  The answer to three places past the decimal point, by the way, is 142.676.  Did you get it right?  And, if so, how long did it take?

Probably tens of seconds.  Or minutes.  A computer, on the other hand, could crunch that out faster than you could punch the buttons on a calculator.  Because one thing computers are good at is arithmetic.  Thanks to binary numbers.  The language of all computers.  1s and 0s to most of us.  But two different states to a computer.  That make information the computer can understand and process.  Fast.

A Computer can look at Long Streams of 1s and 0s and make Perfect Sense out of Them

The numbers we use in everyday life are from the decimal numeral system.  Or base ten.  For example, the number ‘4851’ contains four digits.  Where each digit can be one of 10 values (0, 1, 2, 3…9).   And then the ‘base’ part comes in.  We say base ten because each digit is a multiple of 10 to the power of n.  Where n=0, 1, 2, 3….  So 4851 is the sum of (4 X 103) + (8 X 102) + (5 X 101) + (1 X 100).  Or (4 X 1000) + (8 X 100) + (5 X 10) + (1 X 1).  Or 4000 + 800 + 50 + 1.  Which adds up to 4851.

But the decimal numeral system isn’t the only numeral system.  You can do this with any base number.  Such as 16.  What we call hexadecimal.  Which uses 16 distinct values (0, 1, 2, 3…9, A, B, C, D, E, and F).  So 4851 is the sum of (1 X 163) + (2 X 162) + (15 X 161) + (3 X 160).  Or (1 X 4096) + (2 X 256) + (15 X 16) + (3 X 1).  Or 4096 + 512 + 240 + 3.  Which adds up to 4851.  Or 12F3 in hexadecimal.  Where F=15.  So ‘4851’ requires four positions in decimal.  And four positions in hexadecimal.  Interesting.  But not very useful.  As 12F3 isn’t a number we can do much with in long division.  Or even on a calculator.

Let’s do this one more time.  And use 2 for the base.  What we call binary.  Which uses 2 distinct values (0 and 1).  So 4851 is the sum of (1 X 212) + (0 X 211) + (0 X 210) + (1 X 29) + (0 X 28) + (1 X 27) + (1 X 26) + (1 X 25) + (1 X 24) + (0 X 23) + (0 X 22) + (1 X 21) + (1 X 20).  Or (1 X 4096) + (0 X 2048) + (0 X 1024) + (1 X 512) + (0 X 256) + (1 X 128) + (1 X 64) + (1 X 32) + (1 X 16) + (0 X 8) + (0 X 4) + (1 X 2) + (1 X 1).  Or 4096 + 0 + 0 + 512 + 0 + 128 + 64 + 32 + 16 + 0 + 0 + 2 + 1.  Which adds up to 4851.  Or 1001011110011 in binary.  Which is gibberish to most humans.  And a little too cumbersome for long division.  Unless you’re a computer.  They love binary numbers.  And can look at long streams of these 1s and 0s and make perfect sense out of them.

A Computer can divide two Numbers in a few One-Billionths of a Second

A computer doesn’t see 1s and 0s.  They see two different states.  A high voltage and a low voltage.  An open switch and a closed switch.  An on and off.  Because of this machines that use binary numbers can be extremely simple.  Computers process bits of information.  Where each bit can be only one of two things (1 or 0, high or low, open or closed, on or off, etc.).  Greatly simplifying the electronic hardware that holds these bits.  If computers processed decimal numbers, however, just imagine the complexity that would require.

If working with decimal numbers a computer would need to work with, say, 10 different voltage levels.  Requiring the ability to produce 10 discrete voltage levels.  And the ability to detect 10 different voltage levels.  Greatly increasing the circuitry for each digit.  Requiring far more power consumption.  And producing far more damaging heat that requires more cooling capacity.  As well as adding more circuitry that can break down.  So keeping computers simple makes them cost less and more reliable.  And if each bit requires less circuitry you can add a lot more bits when using binary numbers than you can when using decimal numbers.  Allowing bigger and more powerful number crunching ability.

Computers load and process data in bytes.  Where a byte has 8 bits.  Which makes hexadecimal so useful.  If you have 2 bytes of data you can break it down into 4 groups of 4 bits.  Or nibbles.  Each nibble is a 4-bit binary number that can be easily converted into a single hexadecimal number.  In our example the binary number 0001 0010 1111 0011 easily converts to 12F3 where the first nibble (0001) converts to hexadecimal 1.  The second nibble (0010) converts to hexadecimal 2.  The third nibble (1111) converts to hexadecimal F.  And the fourth nibble (0011) converts to hexadecimal 3.  Making the man-machine interface a lot simpler.  And making our number crunching easier.

The simplest binary arithmetic operation is addition.  And it happens virtually instantaneously at the bit level.  We call the electronics that make this happen logical gates.  A typical logical gate has two inputs.  Each input can be one of two states (high voltage or low voltage, etc.).  Each possible combination of inputs produces a unique output (high voltage or low voltage, etc.).  If you change one of the inputs the output changes.  Computers have vast arrays of these logical gates that can process many bytes of data at a time.  All you need is a ‘pulsing’ clock to sequentially apply these inputs.  With the outputs providing an input for the next logical operation on the next pulse of the clock.

The faster the clock speed the faster the computer can crunch numbers.  We once measured clock speeds in megahertz (1 megahertz is one million pulses per second).  Now the faster CPUs are in gigahertz (1 gigahertz is 1 billion pulses per second).  Because of this incredible speed a computer can divide two numbers to many places past the decimal point in a few one-billionths of a second.  And be correct.  While it takes us tens of seconds.  Or even minutes.  And our answer could very well be wrong.

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Silicon, Semiconductor, LED, Photon, Photovoltaic Effect, Photocell, Solar Panel, Converter, Battery and Solar Power Plant

Posted by PITHOCRATES - July 4th, 2012

Technology 101

A Photocell basically works like a Light Emitting Diode (LED) in Reverse

Solar power is based on the same technology that that gave us the electronic world.  Silicon.  That special material in the periodic table that has four electrons in its valence (i.e., outer most) shell.  And four holes that can accept an electron.  Allowing it to form a perfect silicon crystal.  When these silicon atoms come together their four valence electrons form covalent bonds with the holes in neighboring silicon atoms.  These silicon atoms share their valence electrons so that each silicon atom now has a full valence shell of eight electrons (with four of their own electrons and four shared electrons).  Making that perfect crystal structure.  Which is pretty much useless in the world of semiconductors.  Because you need free electrons to conduct electricity.

When we add impurities (called ‘doping’) to silicon is where the magic starts.  If we add a little bit of an element with five electrons in its valence shell we introduce free electrons into the silicon crystal.  Giving it a negative charge.  If we instead add a little bit of an element with 3 electrons in its valence shell we introduce extra holes looking for an electron to fill it.  Giving it a positive charge.  When we bring the positive (P) and the negative (N) materials together they from a P-N junction.  The free electrons cross the junction to fill the nearby holes.  Creating a neutrally charged depletion zone between the P and the N material.  This is a diode.  If we apply a forward biased voltage (positive battery terminal to the P side and the negative battery terminal to the N side) across this junction current will flow.  Like charges repel each other.  The negative charge pushes the free electrons on the N side of the junction towards the junction.  And the positive charge pushes the holes on the P side of the junction towards the junction.  Where they meet.  With free electrons filling available holes causing current to flow.  A reverse bias does the reverse.  Pulls the holes and electrons away from the junction so they can’t combine and cause current to flow.

It takes energy to move an electron out of its ‘hole’.  And when an electron combines with a hole it emits energy.  Typically this energy is not in a visible wavelength so we see nothing.  However, with the proper use of materials we can shift this wave length into the visible spectrum.  So we can see light.  Or photons.  This is the principle behind the light emitting diode.  Or LED.  An electric current through a P-N junction causes electrons to leave their holes and then recombine with holes.  And when they recombine they give off a photon in the visible spectrum of light.  Which is what we see.  A photocell basically works the other way.  Instead of using voltage and current to create photons we use photons from the sun to create voltage and current.

A Solar Array that could Produce 12,000 Watts under Ideal Conditions may only Produce 2,400 Watts in Reality

When we use the sun to bump electrons free from their shells we call this the photovoltaic (PV) effect.  This produces a small direct current (DC) at a low voltage.  A PV cell (or solar cell) then is basically a battery when hit with sunlight.  Electric power is the product of voltage and current.  So a small DC current and a low voltage won’t power much.  So like batteries in a flashlight we have to connect solar cells together to increase the available power.  So we connect solar cells into modules and modules into arrays.  Or what we commonly call solar panels.  Small panels can power small loads.  Like emergency telephones along the highway that are rarely used.  To channel buoys that can charge a battery during the day to power a light at night.  And, of course, the electronics on our spacecraft.  Where PV cells are very useful as there are no utility lines that run into space.

These work well for small loads.  Especially DC loads.  But it gets a little complicated for AC loads.  The kind we have in our homes.  A typical 1,000 square foot home may have a 100 amp electric service at 240 volts.  Let’s assume that at any given time there could be as much as half of that service (50 amps) in use at any one time.  That’s 12,000 watts.  Assuming a solar panel array generates about 10 watts per square foot that means this house would need approximately 1,200 square feet of solar panels (such as a 60 foot by 20 foot array or a 40 foot by 30 foot array).  But it’s not quite that simple.

The sun doesn’t shine all of the time.  The capacity factor (the percentage of actual power produced divided by the total possible it could produce under the ideal conditions) is only about 15-20%.  Meaning that a 1,200 square foot solar array that could produce 12,000 watts under ideal conditions may only produce 2,400 watts (at a 20% capacity factor).  Dividing this by 120 volts gives you 20 amps.  Or approximately the size of a single circuit in your electrical panel.  Which won’t power a lot.  And it sure won’t turn on your air conditioner.  Which means you’re probably not going to be able to disconnect from the electric grid by adding solar panels to your house.  You may reduce the amount of electric power you buy from your utility but it will come at a pretty steep cost.

Solar Power Plants can be Costly to Build and Maintain even if the Fuel is Free 

Everything in your house that uses electricity either plugs into a standard 120V electrical outlet, a special purpose 240V outlet (such as an electric stove) or is hard-wired to a 240V circuit (such as your central air conditioner).  All of these circuits go back to your electrical panel.  Which is wired to a 240V AC electrical service.  A lot of electronic devices actually operate on DC power but even these still plug into an AC outlet.  Inside these devices there is a power supply that converts the AC power into DC power.  So you’ll need to convert all that DC power generated by solar panels into useable AC power with a converter.  Which is costly.  And reduces the efficiency of the solar panels.  Because when you convert energy you always end up with less than you started with.  The electronics in the converters will heat up and dissipate some of that generated electric power as heat.  If you want to use any of this power when the sun isn’t shining you’ll need a battery to store that energy.  Another costly device.  Another place to lose some of that generated electric power.  And something else to fail.

We typically build large scale solar power plants in the middle of nowhere so there is nothing to shade these solar panel arrays.  From sun up to sun down they are in the sunlight.  They even turn and track the sun as it rises overhead, travels across the sky and sets.  To maximize the amount of sunlight hitting these panels.  Of course the larger the installation the larger the maintenance.  And the panels have to be clean.  That means washing these arrays to keep them dirt and bird poop free.  Some of the biggest plants in service today have about 200 MW of installed solar arrays.  One of the largest is in India.  Charanka Solar Park.  When completed it will have 500 MW of PV arrays on approximately 7.7 square miles of land.  With a generous capacity factor of 30% that comes to 150 MW.  Or about 19 MW/square mile.  The coal-fired Robert W. Scherer Electric Generating Plant in Georgia, on the other hand, generates 3,520 MW on approximately 18.75 square miles.  At a capacity factor of about 90% for coal that comes to about 3,168 MW.  Or about 169 MW/square mile.  About 9 times more power generated per square mile of land used.

 So you can see the reason why we use so much coal to generate our electric power.  Because coal is a highly concentrated source of fuel.  The energy it releases creates a lot of reliable electricity.  Day or night.  Summer or winter.  A large coal-fired electric generating facility needs a lot of real estate but the plants themselves don’t.  Unlike a solar plant.  Where the only way to generate more power is to cover more land with PV solar panels.  To generate, convert and store as much electric power as possible.  All with electronic equipment full of semiconductors that don’t operate well in extreme temperatures (which is why our electronics have vents, heat sinks and cooling fans).  So the ideal conditions to produce electricity are not the ideal conditions for the semiconductors making it all work.  Causing performance and maintenance issues.  Which makes these plants very costly.  Even if the fuel is free. 

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Carnegie, Rockefeller, Morgan, Interstate Commerce Act, Sherman Antitrust Act, Sherman Silver Purchase Act, Federal Reserve, Nixon and Reagan

Posted by PITHOCRATES - January 31st, 2012

History 101

Government Induced Inflation caused the Panic of 1893 and caused the Worst Depression until the Great Depression

Britain kicked off the Industrial Revolution.  Then handed off the baton to the United States in the latter half of the 19th century.  As American industry roared.  Great industrialists modernize America.  And the world.  Andrew Carnegie made steel inexpensive and plentiful.  He built railroad track and bridges.  And the steel-skeleton buildings of U.S. cities.  Including the skyscrapers.  John D. Rockefeller saved the whales.  By producing less expensive kerosene to burn in lamps instead of the more expensive whale oil.  He refined oil and brought it to market cheaper and more efficiently than anyone else.  Fueling industrial activity and expansion.  J.P. Morgan developed and financed railroads.  Made them more efficient.  Profitable.  And moved goods and people more efficiently than ever before.  Raising the standard of living to heights never seen before. 

The industrial economy was surging along.  And all of this without a central bank.  Credit was available.  So much so that it unleashed unprecedented economic growth.  That would have kept on going had government not stopped it.  With the Interstate Commerce Act in 1887 and the Sherman Antitrust Act of 1890.  Used by competitors who could not compete against the economy of scales of Carnegie, Rockefeller and Morgan and sell at their low prices.  So they used their friends in government to raise prices so they didn’t have to be as competitive and efficient as Carnegie, Rockefeller and Morgan.  This legislation restrained the great industrialists.  Which began the era of complying with great regulatory compliance costs.  And expending great effort to get around those great regulatory compliance costs.

Also during the late 19th century there was a silver boom.  This dumped so much silver on the market that miners soon were spending more in mining it than they were selling it for.  Also, farmers were using the latest in technology to mechanize their farms.  They put more land under cultivation and increased farm yields.  So much so that prices fell.  They fell so far that farmers were struggling to pay their debts.  So the silver miners used their friends in government to solve the problems of both miners and farmers.  The government passed the Sherman Silver Purchase Act which increased the amount of silver the government purchased.  Issuing new treasury notes.  Redeemable in both gold and silver.  The idea was to create inflation to raise prices and help those farmers.  By allowing them to repay old debt easier with a depreciated currency.  And how did that work?  Investors took those new bank notes and exchanged them for gold.  And caused a run on U.S. gold reserves that nearly destroyed the banking system.  Plunging the nation in crisis.  The Panic of 1893.  The worst depression until the Great Depression.

Richard Nixon Decoupled the Dollar from Gold and the Keynesians Cheered 

J.P. Morgan stepped in and loaned the government gold to stabilize the banking system.  He would do it again in the Panic of 1907.  The great industrialists created unprecedented economic activity during the latter half of the 19th century.  Only to see poor government policies bring on the worst depression until the Great Depression.  A crisis one of the great industrialists, J.P. Morgan, rescued the country from.  But great capitalists like Morgan wouldn’t always be there to save the country.  Especially the way new legislation was attacking them.  So the U.S. created a central bank.  The Federal Reserve System.  Which was in place and ready to respond to the banking crisis following the stock market crash of 1929.  And did such a horrible job that they gave us the worst depression since the Panic of 1893.  The Great Depression.  Where we saw the greatest bank failures in U.S. history.  Failures the Federal Reserve was specifically set up to prevent.

The 1930s was a lost decade thanks to even more bad government policy.  FDR’s New Deal programs did nothing to end the Great Depression.  Only capitalism did.  And a new bunch of great industrialists.  Who were allowed to tool up and make their factories hum again.  Without having to deal with costly regulatory compliance.  Thanks to Adolf Hitler.  And the war he started.  World War II.  The urgency of the times repealed governmental nonsense.  And the industrialists responded.  Building the planes, tanks and trucks that defeated Hitler.  The Arsenal of Democracy.  And following the war with the world’s industrial centers devastated by war, these industrialists rebuilt the devastated countries.  The fifties boomed thanks to a booming export economy.  But it wouldn’t last.  Eventually those war-torn countries rebuilt themselves.  And LBJ would become president.

The Sixties saw a surge in government spending.  The U.S. space program was trying to put a man on the moon.  The Vietnam War escalated.  And LBJ introduced us to massive new government spending.  The Great Society.  The war to end poverty.  And racial injustice.  It failed.  At least, based on ever more federal spending and legislation to end poverty and racial injustice.  But that government spending was good.  At least the Keynesians thought so.  Richard Nixon, too.  Because he was inflating the currency to keep that spending going.  But the U.S. dollar was pegged to gold.  And this devaluation of the dollar was causing another run on U.S. gold reserves.  But Nixon responded like a true Keynesian.  And broke free from the shackles of gold.  By decoupling the dollar from gold.  And the Keynesians cheered.  Because the government could now use the full power of monetary policy to make recessions and unemployment a thing of the past.

Activist, Interventionist Government have brought Great Economic Booms to Collapse 

The Seventies was a decade of pure Keynesian economics.  It was also the decade that gave us double digit interest rates.  And double digit inflation rates.  It was the decade that gave us the misery index (the inflation rate plus the unemployment rate).  And stagflation.  The combination of a high inflation rate you normally only saw in boom times coupled with a high unemployment rate you only saw during recessionary times.  Something that just doesn’t happen.  But it did.  Thanks to Keynesian economics.  And bad monetary policy.

Ronald Reagan was no Keynesian.  He was an Austrian school supply-sider.  He and his treasury secretary, Paul Volcker, attacked inflation.  The hard way.  The only way.  Through a painful recession.  They stopped depreciating the dollar.  And after killing the inflation monster they lowered interest rates.  Cut tax rates.  And made the business climate business-friendly.  Capitalists took notice.  New entrepreneurs rose.  Innovated.  Created new technologies.  The Eighties was the decade of Silicon Valley.  And the electronics boom.  Powering new computers.  Electronic devices.  And software.  Businesses computerized and became more efficient.  Machine tools became computer-controlled.  The economy went high-tech.  Efficient.  And cool.  Music videos, CD players, VCRs, cable TV, satellite TV, cell phones, etc.  It was a brave new world.  Driven by technology.  And a business-friendly environment.  Where risk takers took risks.  And created great things.

History has shown that capitalists bring great things to market when government doesn’t get in the way.  With their punishing fiscal policies.  And inept monetary policies.  Activist, interventionist government have brought great economic booms to collapse.  Who meddle and turn robust economic activity into recessions.  And recessions into depressions.  The central bank being one of their greatest tools of destruction.  Because policy is too often driven by Big Government idealism.  And not the proven track record of capitalism.  As proven by the great industrialists.  And high-tech entrepreneurs.  Time and time again.

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