powers for Rong 1

First, numbers are represented in different ways depending on the number base you are using.

 

We are used to number base 10.

 

The number base shows how many symbols you use.

 

For example, number base 10 has 10 symbols ( 1,2,3,4,5,6,7,8,9,0)

and number base 2 has 2 symbols (0,1)

 

Number bases all have a 0 which indicates the absence on any quantity.

 

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Second, when I refer to columns I go from right to left:

 

column number: 10 9 8 7 6 5 4 3 2 1

 

and each column has a value:

 

for number base 10:

column value: 1000 100 10 1

column number: 4 3 2 1

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NUMBER 2 4 3 6

Compute 2 (1000) + 4 (100) + 3 (10) + 1 (10)

Equals 2000 + 400 + 30 +1 = 2431

 

for number base 2:

column value: 8 4 2 1

column number: 4 3 2 1

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NUMBER 1 1 0 1

Compute 1(8) + 1 (4 ) + 0 (2) + 1 (1 )

Equals 8 + 4 +0 +1 = 13

 

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Third

The second column always has the value of the number base you are dealing with.

for number base 10:

column value: 1000 100 10 1

 

for number base 2:

column value: 8 4 2 1

 

for number base 8:

column value: 512 64 8 1

 

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Fourth

The column values are computed in this fashion:

Column 1 = Number Base ^0 (this means it is always 1)

Column 2 = Number Base

Column 3 = Previous column times number base

and all other column follow the rule of column 3.

For number base 2 the column values are:

Column 1 = 1

Column 2 = 2

Column 3 = 2 * 2 = 4

Column 4 = 4 * 2 = 8

For number base 3 the column values are:

Column 1 = 1

Column 2 = 3

Column 3 = 3 * 3 = 9

Column 4 = 9 * 3 = 27

 

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Fifth

Another way of phrasing the column values is:

Column 1 = Number base ^0 (or ^column number -1)

Column 2 = Number base ^1 (or ^column number -1)

Column 3 = Number base ^2 (or ^column number -1)

Column 4 = Number base ^3 (or ^column number -1)

Column 5 = Number base ^4 (or ^column number -1)

 

 

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