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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Henry Ford, Bill Hewlett & Dave Packard, Steve Jobs & Steve Wozniak, Howard Schultz, Ray Kroc and Richard Branson

Posted by PITHOCRATES - February 25th, 2014

 History 101

(Originally published May 8th, 2012)

Capitalism allows Entrepreneurs to bring their Great Ideas to Life

Entrepreneurs start with an idea.  Of how to do something better.  Or to create something we must have that we don’t yet know about.  They think.  They create.  They have boundless creative energies.  And the economic system that best taps that energy is capitalism.  The efficient use of capital.  Using capital to make profits.  And then using those profits to make capital.  So these ideas of genius that flicker in someone’s head can take root.  And grow.  Creating jobs.  And taxable economic activity.  Creating wealth for investors and workers.  Improving the general economy.  Pulling us out of recessions.  Improving our standard of living.  And making the world a better place.  Because of an idea.  That capitalism brought to life.

Entrepreneurs Risked Capital to bring Great Things to Market and to Create Jobs

Henry Ford established the Detroit Automobile Company in 1899.  Which failed.  He reorganized it into the Henry Ford Company in 1901.  Ford had a fight with his financial backers.  And quit.  Taking the Ford name with him.  And $900.  The Henry Ford Company was renamed Cadillac and went on to great success.  Ford tried again and partnered with Alexander Malcomson.  After running short of funds they reorganized and incorporated Ford Motor Company in 1903 with 12 investors.  The company was successful.  Some internal friction and an unexpected death of the president put Ford in charge.  Ford Motor built the Model A, the Model K and the Model S.  Then came the Model T.  And the moving assembly line.  Mass production greatly increased the number of cars he could build.  But it was monotonous work for the assembly line worker.  Turnover was high.  So to keep good workers he doubled pay in 1914 and reduced the 9-hour shift to 8 hours.  This increased productivity and lowered the cost per Model T.  Allowing those who built the cars to buy what they built.  In 2011 the Ford Motor Company employed approximately 164,000 people worldwide.

Bill Hewlett and Dave Packard established Hewlett-Packard (HP) in 1939.  In a garage.  They raised $538 in start-up capital.  In that garage they created their first successful commercial product.  A precision audio oscillator.  Used in electronic testing.  It was better and cheaper than the competition.  Walt Disney Productions bought this oscillator to certify Fantasound surround sound systems in theaters playing the Disney movie Fantasia.  From this garage HP grew and gave us calculators, desktop and laptop computers, inkjet and laser printers, all-in-one multifunction printer/scanner/faxes, digital cameras, etc.  In 2010 HP employed approximately 324,600 employees worldwide.  (Steve Wozniak was working for HP when he designed the Apple I.  Which he helped fund by selling his HP calculator.  Wozniak offered his design to HP.  They passed.)

Steve Jobs had an idea to sell a computer.  He convinced his friend since high school, Steve Wozniak, to join him.  They sold some of their things to raise some capital.  Jobs sold his Volkswagen van.  Wozniak sold his HP scientific calculator.  They raised about $1,300.  And formed Apple.  They created the Apple I home computer in 1976 in Steve Jobs’ garage.  From these humble beginnings Apple gave us the iPad, iPhone, iPod, iMac, MacBook, Mac Pro and iTunes.  In 2011 Apple had approximately 60,400 full time employees.

Jerry Baldwin, Zev Siegl, and Gordon Bowker opened the first Starbucks in 1971 in Seattle, Washington.  About 10 years later Howard Schultz drank his first cup of Starbucks coffee.  And he liked it.  Within a year he joined Starbucks.  Within another year while traveling in Italy he experienced the Italian coffeehouse.  He loved it.  And had an idea.  Bring the Italian coffeehouse to America.  A place to meet people in the community and converse.  Sort of like a bar.  Only where the people stayed sober.  Soon millions of people were enjoying these tasty and expensive coffee beverages at Starbucks throughout the world.  In 2011 Starbucks employed approximately 149,000 people.

Ray Kroc sold Prince Castle Multi-Mixer milk shakes mixers to a couple of brothers who owned a restaurant.  Who made hamburgers fast.  Richard and Maurice McDonald had implemented the Speedee Service System.  It was the dawn of fast food.  Kroc was impressed.  Facing tough competition in the mixer business he opened a McDonald’s franchise in 1955.  Bringing the grand total of McDonald’s restaurants to 9.  He would go on to buy out the McDonald brothers (some would say unscrupulously).  Today there are over 30,000 stores worldwide.  In 2010 McDonald’s employed approximately 400,000 people.

Richard Branson started a magazine at 16.  He then sold records out of a church crypt at discount prices.  The beginning of Virgin Records.  In 1971 he opened a record store.  He launched a record label in 1972.  And a recording studio.  Signing the Sex Pistols.  And Culture Club.  In 1984 he formed an airline.  Virgin Atlantic Airways.  In 1999 he went into the cellular phone business.  Virgin Mobile.  In 2004 he founded Virgin Galactic.  To enter the space tourism business.  His Virgin Group now totals some 400 companies.  And employs about 50,000 people.

The Decline of Capitalism and the Rise of the Welfare State caused the European Sovereign Debt Crisis

And we could go on.  For every big corporation out there will have a similar beginning.  Corporations that use capital efficiently.  Bringing great things to market.  Introducing us to new things.  Always making our lives better.  And more comfortable.  One thing you will not find is a great success story like this starting in the Soviet Union.  The People’s Republic of China (back in the days of Mao Zedong).  East Germany (before the Berlin Wall fell).  North Korea.  Or Cuba.  No.  The command economies of communist countries basically froze in time.  Where there was no innovation.  No ideas brought to life.  Because the government kind of frowned on that sort of thing.

There is a reason why the West won the Cold War.  And why we won that war without the Warsaw Pack and NATO forces fighting World War III.  And why was this?  Because we didn’t need to.  For the communist world simply could not withstand the forces of living well in the West.  Whenever they could their people escaped to the West.  To escape their nasty, short and brutish lives.  In the command economies of their communist states.  Where the state planners failed to provide for their people.  Even failing to feed their people.  The Soviet Union, the People’s Republic of China and North Korea all suffered population reducing famines.  But not in the West.  Where we are not only well fed.  But our poor suffer from obesity.  Which is not a good thing.  But it sure beats dying in a famine.

Sadly, though, the West is moving towards the state planning of their one time communist foes.  Social democracies are pushing nations in the European Union to bankruptcy.  Japan’s generous welfare state is about to implode as an aging population begins to retire.  Even in the United States there has been a growth of government into the private sector economy like never before.  Which is causing the Great Recession to linger on.  As it caused Japan’s lost decade to become two decades.  And counting.  As it is prolonging the European sovereign debt crisis.  With no end in sight.  The cause of all their problems?  The decline of capitalism.  And the rise of the welfare state.  Which just kills the entrepreneurial spirit.  And the creation of jobs.  Which is one cure for all that ails these countries.  And the only one.  For only robust economic activity can pull a country out of recession.  And for that you need new jobs.  And the entrepreneurial spirit.  In short, you need capitalism.

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Henry Ford, Bill Hewlett & Dave Packard, Steve Jobs & Steve Wozniak, Howard Schultz, Ray Kroc and Richard Branson

Posted by PITHOCRATES - May 8th, 2012

History 101

Capitalism allows Entrepreneurs to bring their Great Ideas to Life

Entrepreneurs start with an idea.  Of how to do something better.  Or to create something we must have that we don’t yet know about.  They think.  They create.  They have boundless creative energies.  And the economic system that best taps that energy is capitalism.  The efficient use of capital.  Using capital to make profits.  And then using those profits to make capital.  So these ideas of genius that flicker in someone’s head can take root.  And grow.  Creating jobs.  And taxable economic activity.  Creating wealth for investors and workers.  Improving the general economy.  Pulling us out of recessions.  Improving our standard of living.  And making the world a better place.  Because of an idea.  That capitalism brought to life.

Entrepreneurs Risked Capital to bring Great Things to Market and to Create Jobs

Henry Ford established the Detroit Automobile Company in 1899.  Which failed.  He reorganized it into the Henry Ford Company in 1901.  Ford had a fight with his financial backers.  And quit.  Taking the Ford name with him.  And $900.  The Henry Ford Company was renamed Cadillac and went on to great success.  Ford tried again and partnered with Alexander Malcomson.  After running short of funds they reorganized and incorporated Ford Motor Company in 1903 with 12 investors.  The company was successful.  Some internal friction and an unexpected death of the president put Ford in charge.  Ford Motor built the Model A, the Model K and the Model S.  Then came the Model T.  And the moving assembly line.  Mass production greatly increased the number of cars he could build.  But it was monotonous work for the assembly line worker.  Turnover was high.  So to keep good workers he doubled pay in 1914 and reduced the 9-hour shift to 8 hours.  This increased productivity and lowered the cost per Model T.  Allowing those who built the cars to buy what they built.  In 2011 the Ford Motor Company employed approximately 164,000 people worldwide.

Bill Hewlett and Dave Packard established Hewlett-Packard (HP) in 1939.  In a garage.  They raised $538 in start-up capital.  In that garage they created their first successful commercial product.  A precision audio oscillator.  Used in electronic testing.  It was better and cheaper than the competition.  Walt Disney Productions bought this oscillator to certify Fantasound surround sound systems in theaters playing the Disney movie Fantasia.  From this garage HP grew and gave us calculators, desktop and laptop computers, inkjet and laser printers, all-in-one multifunction printer/scanner/faxes, digital cameras, etc.  In 2010 HP employed approximately 324,600 employees worldwide.  (Steve Wozniak was working for HP when he designed the Apple I.  Which he helped fund by selling his HP calculator.  Wozniak offered his design to HP.  They passed.)

Steve Jobs had an idea to sell a computer.  He convinced his friend since high school, Steve Wozniak, to join him.  They sold some of their things to raise some capital.  Jobs sold his Volkswagen van.  Wozniak sold his HP scientific calculator.  They raised about $1,300.  And formed Apple.  They created the Apple I home computer in 1976 in Steve Jobs’ garage.  From these humble beginnings Apple gave us the iPad, iPhone, iPod, iMac, MacBook, Mac Pro and iTunes.  In 2011 Apple had approximately 60,400 full time employees.

Jerry Baldwin, Zev Siegl, and Gordon Bowker opened the first Starbucks in 1971 in Seattle, Washington.  About 10 years later Howard Schultz drank his first cup of Starbucks coffee.  And he liked it.  Within a year he joined Starbucks.  Within another year while traveling in Italy he experienced the Italian coffeehouse.  He loved it.  And had an idea.  Bring the Italian coffeehouse to America.  A place to meet people in the community and converse.  Sort of like a bar.  Only where the people stayed sober.  Soon millions of people were enjoying these tasty and expensive coffee beverages at Starbucks throughout the world.  In 2011 Starbucks employed approximately 149,000 people.

Ray Kroc sold Prince Castle Multi-Mixer milk shakes mixers to a couple of brothers who owned a restaurant.  Who made hamburgers fast.  Richard and Maurice McDonald had implemented the Speedee Service System.  It was the dawn of fast food.  Kroc was impressed.  Facing tough competition in the mixer business he opened a McDonald’s franchise in 1955.  Bringing the grand total of McDonald’s restaurants to 9.  He would go on to buy out the McDonald brothers (some would say unscrupulously).  Today there are over 30,000 stores worldwide.  In 2010 McDonald’s employed approximately 400,000 people.

Richard Branson started a magazine at 16.  He then sold records out of a church crypt at discount prices.  The beginning of Virgin Records.  In 1971 he opened a record store.  He launched a record label in 1972.  And a recording studio.  Signing the Sex Pistols.  And Culture Club.  In 1984 he formed an airline.  Virgin Atlantic Airways.  In 1999 he went into the cellular phone business.  Virgin Mobile.  In 2004 he founded Virgin Galactic.  To enter the space tourism business.  His Virgin Group now totals some 400 companies.  And employs about 50,000 people.

The Decline of Capitalism and the Rise of the Welfare State caused the European Sovereign Debt Crisis

And we could go on.  For every big corporation out there will have a similar beginning.  Corporations that use capital efficiently.  Bringing great things to market.  Introducing us to new things.  Always making our lives better.  And more comfortable.  One thing you will not find is a great success story like this starting in the Soviet Union.  The People’s Republic of China (back in the days of Mao Zedong).  East Germany (before the Berlin Wall fell).  North Korea.  Or Cuba.  No.  The command economies of communist countries basically froze in time.  Where there was no innovation.  No ideas brought to life.  Because the government kind of frowned on that sort of thing.

There is a reason why the West won the Cold War.  And why we won that war without the Warsaw Pack and NATO forces fighting World War III.  And why was this?  Because we didn’t need to.  For the communist world simply could not withstand the forces of living well in the West.  Whenever they could their people escaped to the West.  To escape their nasty, short and brutish lives.  In the command economies of their communist states.  Where the state planners failed to provide for their people.  Even failing to feed their people.  The Soviet Union, the People’s Republic of China and North Korea all suffered population reducing famines.  But not in the West.  Where we are not only well fed.  But our poor suffer from obesity.  Which is not a good thing.  But it sure beats dying in a famine.

Sadly, though, the West is moving towards the state planning of their one time communist foes.  Social democracies are pushing nations in the European Union to bankruptcy.  Japan’s generous welfare state is about to implode as an aging population begins to retire.  Even in the United States there has been a growth of government into the private sector economy like never before.  Which is causing the Great Recession to linger on.  As it caused Japan’s lost decade to become two decades.  And counting.  As it is prolonging the European sovereign debt crisis.  With no end in sight.  The cause of all their problems?  The decline of capitalism.  And the rise of the welfare state.  Which just kills the entrepreneurial spirit.  And the creation of jobs.  Which is one cure for all that ails these countries.  And the only one.  For only robust economic activity can pull a country out of recession.  And for that you need new jobs.  And the entrepreneurial spirit.  In short, you need capitalism.

www.PITHOCRATES.com

Share

Tags: , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,