Difference between revisions of "Programming Club - Tutorials - MATH - Basics"

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==Arithmetic==
 
==Arithmetic==
 
===Counting===
 
===Counting===
 +
In mathematical problems, there is a difference between the way you count ''numbers'' and ''values''.  In simple base 10 math, the methods appear to be the same; However, if you intend to use an alternative base for your mathematical problems, you can immediately see the difference.
 +
 +
A numerical representation for a value, is divided into exponents according to it's base.  For example, in base 10 math, the digits representing values are read from right to left as ''ones'', ''tens'', ''hundreds'', ''thousands'', etc. - which are all multiples of 10.
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 +
In base ''two'' math, they read from right to left as ''ones'', ''twos'', ''fours'', ''eights''.  Similarly, base ''three'' math reads ''ones'', ''threes'', ''nines'', ''twenty-sevens'', etc.
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 +
<table>
 +
<tr>
 +
 +
 +
<td>Base One</td>
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<td>
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<tr>1 = 1</tr>
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<tr>10 = 2</tr>
 +
<tr>100 = 3</tr>
 +
<tr>1000 = 4</tr>
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</td>
 +
 +
<td>Base Two</td>
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<td>
 +
<tr>1 = 1</tr>
 +
<tr>10 = 2</tr>
 +
<tr>100 = 4</tr>
 +
<tr>1000 = 8</tr>
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</td>
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 +
<td>Base Three</td>
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<td>
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<tr>1 = 1</tr>
 +
<tr>10 = 3</tr>
 +
<tr>100 = 9</tr>
 +
<tr>1000 = 27</tr>
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</td>
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 +
<td>Base Four</td>
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<td>
 +
<tr>1 = 1</tr>
 +
<tr>10 = 4</tr>
 +
<tr>100 = 16</tr>
 +
<tr>1000 = 64</tr>
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</td>
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 +
<td>Base Five</td>
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<td>
 +
<tr>1 = 1</tr>
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<tr>10 = 5</tr>
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<tr>100 = 25</tr>
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<tr>1000 = 125</tr>
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</td>
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<td>Base Six</td>
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<td>
 +
<tr>1 = 1</tr>
 +
<tr>10 = 6</tr>
 +
<tr>100 = 36</tr>
 +
<tr>1000 = 216</tr>
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<td>
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 +
<td>Base Seven</td>
 +
<td>
 +
<tr>1 = 1</tr>
 +
<tr>10 = 7</tr>
 +
<tr>100 = 49</tr>
 +
<tr>1000 = 343</tr>
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<td>
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 +
<td>Base Eight</td>
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<td>
 +
<tr>1 = 1</tr>
 +
<tr>10 = 8</tr>
 +
<tr>100 = 64</tr>
 +
<tr>1000 = 512</tr>
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<td>
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 +
<td>Base Nine</td>
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<td>
 +
<tr>1 = 1</tr>
 +
<tr>10 = 9</tr>
 +
<tr>100 = 81</tr>
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<tr>1000 = 729</tr>
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</td>
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 +
<td>Base Ten</td>
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<td>
 +
<tr>1 = 1</tr>
 +
<tr>10 = 10</tr>
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<tr>100 = 100</tr>
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<tr>1000 = 1000</tr>
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</td>
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 +
 +
</tr>
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</table>
 +
 
===Addition===
 
===Addition===
 
===Subtraction===
 
===Subtraction===

Revision as of 06:24, 24 August 2009

Arithmetic

Counting

In mathematical problems, there is a difference between the way you count numbers and values. In simple base 10 math, the methods appear to be the same; However, if you intend to use an alternative base for your mathematical problems, you can immediately see the difference.

A numerical representation for a value, is divided into exponents according to it's base. For example, in base 10 math, the digits representing values are read from right to left as ones, tens, hundreds, thousands, etc. - which are all multiples of 10.

In base two math, they read from right to left as ones, twos, fours, eights. Similarly, base three math reads ones, threes, nines, twenty-sevens, etc.

1 = 110 = 2100 = 31000 = 4 </td> 1 = 110 = 2100 = 41000 = 81 = 110 = 3100 = 91000 = 271 = 110 = 4100 = 161000 = 641 = 110 = 5100 = 251000 = 1251 = 110 = 6100 = 361000 = 2161 = 110 = 7100 = 491000 = 3431 = 110 = 8100 = 641000 = 5121 = 110 = 9100 = 811000 = 7291 = 110 = 10100 = 1001000 = 1000 </tr>
Base One
Base Two
Base Three
Base Four
Base Five
Base Six
Base Seven
Base Eight
Base Nine
Base Ten

Addition

Subtraction

Multiplication

Division

Exponents

Roots

Irrational/Fractional Numbers

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