Binary Numbers and How they Relate to Decimal Numbers

Forget all this introductory text and just click on Vi Hart's Binary Finger Dancing Video at youtube :-)


Humans started counting with our 10 fingers, (2 hands with 5 fingers each) as an animal species with a developing brain, long ago...

and came up with the numbers: 1,2,3,4,5,6,7,8,9,10....

(Though NOT written as these symbols, which are the modern conventional symbols we use today...)

Which is why we call our number system a "decimal" (= 10 or "base 10") system

which actually consists of the 10 digits: 0,1,2,3,4,5,6,7,8,9

The number "Ten" in the Ancient Roman Number System was represented by the capital letter "X"

The Roman Numerals that you sometimes see on old buildings, or in old books are as follows:

I, II, III, IV, V, VI,VII,VIII, IX, X... representing: 1,2,3,4,5,6,7,8,9,10...

Sometimes dates/years in history are still written with the old Roman Numerals:

such as: 1968 = MCMLXVIII MCM = 1900 + LXVIII = 68

M = 1,000

CM = 900


L = 50

C = 100

and This year: 2011 = MMXI ....

But getting back to our contemporary number symbols: 1,2,3,4,5,6,7,8,9.10.....

Something Really Big Happened during the 1900's in the United States of America:

Preface starting back in England in 1854: (from Wikipedia)

In 1854, British mathematician George Boole published a landmark paper detailing an algebraic system of logic that would become known as Boolean algebra. His logical calculus was to become instrumental in the design of digital electronic circuitry.[9]


In the United States: (from Wikipedia)

In 1937, Claude Shannon produced his master's thesis at MIT

that implemented Boolean algebra and binary arithmetic using electronic relays and switches for the first time in history.

Entitled A Symbolic Analysis of Relay and Switching Circuits,

Shannon's thesis essentially founded practical digital circuit design.[10]

In November 1937, George Stibitz, then working at Bell Labs, completed a relay-based computer

he dubbed the "Model K" (for "K**itchen", where he had assembled it), which calculated using binary addition.[11]

Bell Labs thus authorized a full research programme in late 1938 with Stibitz at the helm.


Recent photograph of Bell Labs HQ: The reason the building looks like a Fortress is because it is...

They do National Security Technology Research there; they don't want any tourists coming by... :-)

Their Complex Number Computer, completed January 8, 1940, was able to calculate complex numbers.

In a demonstration to the American Mathematical Society conference at Dartmouth College on September 11, 1940, Stibitz was able to send the Complex Number Calculator remote commands over telephone lines by a teletype.

It was the first computing machine ever used remotely over a phone line.

Some participants of the conference who witnessed the demonstration were John von Neumann, John Mauchly and Norbert Wiener, who wrote about it in his memoirs.[12][13][14]

The Computer was invented!

And it functions with "digital circuit boards", which use binary electrical (on-off) switches, which means that everything about computers and other "digital devices" use the Binary Number System!

That is why learning about binary numbers is important and it is the first lesson in Computer Science.

So here is an introductory youtube video from the Khan Academy (online learning) about

How Binary Numbers are Related to Decimal Numbers and how you can convert one type of number into the other...

and here is a "cheat sheet chart" to help you through the "blah, blah, blah..." video :-)


Have Fun...