A Bit About Binary (and other number systems)...

Number Systems from Base Two through Base Sixteen, including Binary, Decimal and Hexadecimal.

Binary is a number system. We don’t tend to think of binary much outside of the computer realm, but rest assured, we use it hundreds of times a day. "Did you take out the trash?" we may be asked. "Yes" or "No", we answer.

    A number system is one which has digits representing values. Our “decimal” system is based on the number ten. We count out from zero to nine, but add another column at ten, like this…

                1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11…

     This system has been attributed to our lack of an eleventh or twelfth finger to count on. When asked to count on ones fingers a number like 37, we often resort to a representative item, such as a big toe, equal to ten fingers. In the above example, your big toe would represent the “tens” column. When we’re asked to count to a large number by hand, it usually ends up more like a mutant, solo game of “Twister” rather than higher math.

     Some cultures had managed other number systems through time, and some are a fusion of several. First we’d better look at a few to see how they work. I’ll assume we’re all familiar with decimal, so we’ll use it as a point of reference. The others below it will turn to two or three digit numbers at a different point, that being when the highest digit in their system has been surpassed in the leftmost column. Those above Base Ten replace the numbers in the teens with single-digit characters A, B, C, D, E and F, with decimal values 11, 12, 13, 14, 15 and 16 respectively. Base Sixteen, commonly known as hexadecimal (often misspelled as hexidecimal), or hex, is used to abbreviate binary, since conversion from binary into hexadecimal reduces a clumsy four digit number into a handy single digit. The colours on this web page are represented in hex, for example.

Click the diagram for a closer view.

     You’ll probably notice that as the number systems get lower, the numbers themselves get longer. The binary value (base 2) for the number 9 is 1001  !! If I gave you a system with an infinite base, where every number is a single digit, you’d need a lot of fingers, and you'd never use your toes !!

     Any “On / Off”  switch in your home is a binary switch. Any two-sided decision, including a coin toss, is in binary. Binary is the only "all or nothing" number system, making it useful in its perfect and decisive simplicity. So why don’t we examine this whole binary thing a little closer…

        Binary: Up Close and Personal

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