The introduction of Hindu-Arabic numerals, the concept of zero, and the notion of "place value" led to our present notation system, the most common example of which is our monetary system. The idea that any value, no matter how large, could be represented with a limited number of symbols, was a monumental scientific breakthrough. We happen to count by tens, with only ten symbols, in all likelihood, as a result of having ten fingers!. One of the great insights, the realization that it is also possible to count by twos, with only two symbols, opened the way for the development of the electronic digital computer.

When I was teaching 7th grade mathematics, I managed to irritate my charges by suggesting that they didn't know how to add (or, for that matter, subtract, multiply, or divide). You can imagine what that did to 12 year-olds. To prove my point, I suggested that, since counting probably arose from tallying with the ten fingers, they might try those same "simple" arithmetic tasks using the idea that we had been created with only thumbs. The following morning I was met by a room full of tired eyes and satisfied grins.

Of course, what they discovered was that there is nothing magic about ten, and that our arithmetic works perfectly well whether we use a number system based on ten fingers or two. An automobile odometer will illustrate.

Imagine the odometer in your car with only one wheel. since each wheel has ten positions (including zero), after nine miles, the wheel would return to zero and our recent "Y2K" problem comes into focus.	nine
By adding another wheel and advancing it every time the one to its right returns to zero, counting can continue - in this case to 99. The notion probably derives from the inability to count past ten with the fingers, and the need to put a rock in the pocket when all of the fingers have been used. Of course it was then evident that when counting the rocks, (with the fingers) that a "stick" needed to replace each ten rocks, and so forth).	ten
Adding wheels to the odometer increases the maximum value that can be recorded. A six-wheel DECIMAL odometer can only record one less than a million. Adding another wheel allows us to continue. Thus it takes a "Seven-Figure" number to record a million - and even more	one million

When using a system based on two, we have only two fingers, and two symbols 0 and 1, the odometer in your car with only one wheel, can only represent zero and one and cannot even count to two.	one
Adding a second wheel means we can now increase our count to two and three.	two
Adding more wheels to our "Binary" odometer increases the maximum value that can be recorded, but at a MUCH slower rate since each new wheel has a value only DOUBLE that of its neighbor to the right - NOT ten times as above with a decimal system. Thus it takes a "Seven-Figure" number to record a value of sixty-four, NOT a million, as above	sixty-three sixty-four

One must have lived through the era of the Monroe mechanical calculator, with whirring (ten toothed) wheels, to appreciate the fundamental breakthrough provided by the "discovery" that that electricity can count with only two symbols "1" and "0", or "on" and "off". Suddenly mechanical machines could be replaced by electric "machines". But humans had to learn to count by twos as well as tens. The table at the right illustrates the relationship between some common values and their binary representations. Notice that seven can be represented with three bits, fifteen with four bits, and 255 with 8 bits. So the values from 1 through 255 AND zero, representing 256 different values, can be recorded with an 8 bit binary number. If you use Photoshop, you will recognize that black is represented with a value of zero and white with 255. These are the 256 shades of gray (or red, green, or blue) that the normal "8-bit" processing mode uses. Some limited functions can be performed in "10-bit" mode, and you can see that this will allow 1024 shades rather than 256. The term "Bit Depth" is sometimes used to describe the number of bits used to define these tonal values. If there are 256 shades possible with an 8 bit number for each of Red, Green, and Blue, the total is 24 - hence 24 bit color and a possible 256 x 256 x 256 (16,777,216) colors. If 10 bit numbers are used, the term 30 bit color is used, with 1024 shades each of red, green, and blue, providing over a billion colors. Early on it was observed that the alphabet and punctuation could be represented with a character set of less than 256 symbols, so 8 bits became a sort of a standard "data bunch", with the creation of the ASCII (character set), and IBM's EBCDIC (character set). IBM, when introducing their System 370, decided "the 8-bit bunch" needed a name and introduced the term "byte". So much for history.

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