All Your Base
Counting in Other Bases
Ben Ramsey
Nashville PHP
11 February 2020
Are belong to us
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Base !!
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Base-10
■ Otherwise known as “the decimal system”
■ Greek déka; Latin decem
■ decade, decagon, decameter, December
■ A numeral system having 10 symbols to
represent numbers
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No content
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1
24
432
1 489
12 794 676
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5 6 7 8 9
0 1 2 3 4
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12 794 676
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12 794 676
ones
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12 794 676
tens
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12 794 676
hundreds
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12 794 676
thousands
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12 794 676
ten thousands
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12 794 676
hundred thousands
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12 794 676
millions
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12 794 676
ten millions
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Each place (or position) in the
number represents a value.
Base-16
■ Hexadecimal
■ A numeral system having 16 symbols to
represent numbers
■ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and commonly
A, B, C, D, E, and F for numbers 10-15
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fab1
16
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fab1
16
0
1
2
3
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F A B 1
⨉ 163 ⨉ 162 ⨉ 161 ⨉ 160
( ) ( ) ( ) ( )
+ + +
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F A B 1
⨉ 163 ⨉ 162 ⨉ 161 ⨉ 160
( ) ( ) ( ) ( )
+ + +
61440 2560 176 1
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F A B 1
⨉ 163 ⨉ 162 ⨉ 161 ⨉ 160
( ) ( ) ( ) ( )
+ + +
61440 2560 176 1
= 64177