Difference between revisions of "Octal math"

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{{Note|This article is about octal, which is a real thing. For more information, consult [https://en.wikipedia.org/wiki/Octal the other wiki].}}
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The people of Delgar use '''octal math'''. This is because of the way they count on their fingers, counting 1-4 on the fingers then raising thumb and counting again for 5-8, then using the other hand to count to a total of 16 on both hands (or 64 in the positional style, where the left hand is counted as 8x the shown value).
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{| class="wikitable"
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|+
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!Number
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!Thumb
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!Index
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!Middle
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!Ring
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!Pinky
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|-
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|1
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|down
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|'''up'''
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|down
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|down
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|down
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|-
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|2
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|down
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|'''up'''
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|'''up'''
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|down
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|down
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|-
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|3
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|down
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|'''up'''
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|'''up'''
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|'''up'''
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|down
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|-
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|4
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|down
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|'''up'''
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|'''up'''
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|'''up'''
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|'''up'''
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|-
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|5
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|'''up'''
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|'''up'''
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|down
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|down
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|down
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|-
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|6
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|'''up'''
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|'''up'''
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|'''up'''
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|down
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|down
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|-
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|7
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|'''up'''
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|'''up'''
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|'''up'''
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|'''up'''
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|down
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|-
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|8 (10<sub>8</sub>)
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|'''up'''
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|'''up'''
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|'''up'''
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|'''up'''
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|'''up'''
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|}
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This is why Delgar's [[currencies]] are divided into multiples of 8 instead of multiples of 10.
  
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The people of Delgar use '''octal math'''. What this means is that they write the number 7 with one symbol ("7") but they write the number 8 with two symbols ('10"). If you've ever studied numeric bases for some reason (probably computer science) you probably already understand this, but in case it's confusing, here's the basic idea:
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What's with that "10<sub>8</sub>" you ask? Well, in writing, they write the number 7 with one symbol ("7") but they write the number 8 with two symbols ('10"). If you've ever studied numeric bases for some reason (probably computer science) you probably already understand this, but in case it's confusing, here's the basic idea:{{Note|The remainder of this article is primarily about octal itself, which is a real thing. For more information, consult [https://en.wikipedia.org/wiki/Octal the other wiki].}}
  
 
In decimal (the numbers you know and love) we have 10 different symbols for numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. When counting, after passing 9, we have no individual symbol to write the number 10, so we write it with two symbols: one in the "ten's place" and one in the "one's place", like so:
 
In decimal (the numbers you know and love) we have 10 different symbols for numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. When counting, after passing 9, we have no individual symbol to write the number 10, so we write it with two symbols: one in the "ten's place" and one in the "one's place", like so:
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|1
 
|1
 
|0
 
|0
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|1×10<sup>1</sup> + 1×10<sup>0</sup>
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|1×10<sup>1</sup> + 0×10<sup>0</sup>
 
|10
 
|10
 
|}
 
|}
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|1
 
|1
 
|0
 
|0
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|1×8<sup>1</sup> + 1×8<sup>0</sup>
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|1×8<sup>1</sup> + 0×8<sup>0</sup>
 
|8
 
|8
 
|}
 
|}
 
Okay, but now when I see the number "10" how do I know if it's a ten or an eight? Easy: Unless specified otherwise, it's ten. To do anything else would be very confusing. When a number is octal, it will be indicated with a subscript 8, like so: 10<sub>8</sub> = 8.
 
Okay, but now when I see the number "10" how do I know if it's a ten or an eight? Easy: Unless specified otherwise, it's ten. To do anything else would be very confusing. When a number is octal, it will be indicated with a subscript 8, like so: 10<sub>8</sub> = 8.
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{{Note|1=For single digit numbers, this distinction is irrelevant. 5<sub>8</sub> = 5<sub>10</sub>}}
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{{Note|1=For single digit numbers, this distinction is irrelevant. 5<sub>8</sub> = 5<sub>10</sub>, and an 8 or a 9 has to be base 10 because octal doesn't use those symbols.}}Here are some common values in octal and decimal for comparison:
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{| class="wikitable"
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|+
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!Octal
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!Decimal
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|-
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|1<sub>8</sub>
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|1
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|-
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|10<sub>8</sub>
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|8
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|-
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|11<sub>8</sub>
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|9
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|-
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|12<sub>8</sub>
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|10
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|-
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|100<sub>8</sub>
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|64
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|-
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|1,000<sub>8</sub>
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|512
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|-
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|10,000<sub>8</sub>
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|4,096
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|-
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|100,000<sub>8</sub>
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|32,768
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|}

Latest revision as of 02:36, 3 April 2021

The people of Delgar use octal math. This is because of the way they count on their fingers, counting 1-4 on the fingers then raising thumb and counting again for 5-8, then using the other hand to count to a total of 16 on both hands (or 64 in the positional style, where the left hand is counted as 8x the shown value).

Number Thumb Index Middle Ring Pinky
1 down up down down down
2 down up up down down
3 down up up up down
4 down up up up up
5 up up down down down
6 up up up down down
7 up up up up down
8 (108) up up up up up

This is why Delgar's currencies are divided into multiples of 8 instead of multiples of 10.

What's with that "108" you ask? Well, in writing, they write the number 7 with one symbol ("7") but they write the number 8 with two symbols ('10"). If you've ever studied numeric bases for some reason (probably computer science) you probably already understand this, but in case it's confusing, here's the basic idea:

Note: The remainder of this article is primarily about octal itself, which is a real thing. For more information, consult the other wiki.

In decimal (the numbers you know and love) we have 10 different symbols for numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. When counting, after passing 9, we have no individual symbol to write the number 10, so we write it with two symbols: one in the "ten's place" and one in the "one's place", like so:

Tens (101) Ones (100) Calculation Value (Decimal)
1 0 1×101 + 0×100 10

Octal works the same way, but it only has 8 symbols (like an octagon has 8 sides): 0, 1, 2, 3, 4, 5, 6, and 7. After 7, they use two symbols to write the number 8, like so: "10"

Eights (81) Ones (80) Calculation Value (Decimal)
1 0 1×81 + 0×80 8

Okay, but now when I see the number "10" how do I know if it's a ten or an eight? Easy: Unless specified otherwise, it's ten. To do anything else would be very confusing. When a number is octal, it will be indicated with a subscript 8, like so: 108 = 8.

Note: For single digit numbers, this distinction is irrelevant. 58 = 510, and an 8 or a 9 has to be base 10 because octal doesn't use those symbols.

Here are some common values in octal and decimal for comparison:

Octal Decimal
18 1
108 8
118 9
128 10
1008 64
1,0008 512
10,0008 4,096
100,0008 32,768
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