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Table Of Contents  CertiGuide to Network+
 9  Appendix B:  Decoding Math

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Base 2
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Base 10

Our everyday lives typically use some math that we call "checkbook" math. The scientific name for this is known as Base 10 math. Let's look at why it is called that.

Begin by looking at the value of zero, or nothing. It is displayed as a 0. While zero is empty of a positive value, it still is a value. It isn't positive, and it isn't negative. It is used to either indicate the value of neither positive nor negative, or can be a placeholder that contains nothing. To make the point, let's look at the following example, and use US dollars as currency. $1,000,000.00

That is a base 10 expression of one million United States dollars. Not one penny more or less. The six zeros before the decimal point indicates no amounts of hundred(s)-thousands, ten(s) thousand(s), thousand(s), hundred(s), ten(s), or single dollar(s). The zeros after the period indicate no fractions of a US dollar. Now visualize yourself having $1,000,000.00

OK, now mentally give it to your authors. Now tell us the zero has NO value. Great, will just remove the items with no value. Now you have $1.00. "Oops". No value with the two zeros after the decimal point. Now you have $.01, or a US copper penny. Still want to say zero has no value? As you can see, it is more accurate to see the zero as neither a positive or negative value. It does indeed have a value, even if it is as a place holder.

OK. Let's do some counting with checkbook math. Starting with zero.


Now count the number of digits used. See? Ten, including the zero. Viola. Base 10 math.

We're willing to bet that you don't have to be as skilled as an NSA cryptographer to guess the next highest value is 10. Let's pick this apart a bit more. The zero is a placeholder meaning no positive values are contained in the units’ column. And the value in the second column is indicated with a 1 for one unit of tens. If you continue counting you get 11. This creates one value in the unit column, and one in the tens column. This continues until you get to twenty, or 20. This is because you have exhausted all the possibilities in the units’ column using base ten, and have to notch up the ten column. Of course this continues until you exhaust both columns with ninety-nine or 99. Once again, the two columns zero out and a third column gets a one or 1, and becomes one-hundred or 100.

In math theory, this can go on forever.

Now as clever as computers seem to be, they really are only made up of a form of an earth element known as silicon. In other words, sand. Now, how smart is sand? It’s about as smart as a rock. In fact, computers are nothing more than "sand with an attitude". Let’s take a look at how dumb computers really are in the next section.

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