View source for 十二進制

'''十二進制'''者，[[基數]]之以十二也，其[[十]]記曰ᘔ，一作χ；[[十一]]記曰Ɛ，一作ε。故非[[信息技術]]之「A」「B」也，且不混淆於[[代數]]之「a」「b」。
[[檔案:Keys in dozenal clock.svg|無|縮圖|十二進制之基數]]
基數：<math>0,1,2,3,4,5,6,7,8,9,\chi,\varepsilon</math>。

== 例 ==
1ᘔƐ<sub>(12)</sub>=1×12<sup>2</sup>+10×12<sup>1</sup>+11×12<sup>0</sup>=144+120+11=275，亦可記曰1ᘔƐ°°

10<sub>(12)</sub>=12，亦可記曰10°°

11<sub>(12)</sub>=13，亦可記曰11°°

== 四則運算 ==
[[檔案:Dozenal multiplication table.png|無|縮圖|十二進制乘法表]]
其表雖繁，然其甚有律於十進制，故易學之。

=== 加法表 ===
{| class="wikitable"
|+
! colspan="11" |a+b
|-
|1+1=2
|
|
|
|
|
|
|
|
|
|
|-
|1+2=3
|2+2=4
|
|
|
|
|
|
|
|
|
|-
|1+3=4
|2+3=5
|3+3=6
|
|
|
|
|
|
|
|
|-
|1+4=5
|2+4=6
|3+4=7
|4+4=8
|
|
|
|
|
|
|
|-
|1+5=6
|2+5=7
|3+5=8
|4+5=9
|5+5=ᘔ
|
|
|
|
|
|
|-
|1+6=7
|2+6=8
|3+6=9
|4+6=ᘔ
|5+6=Ɛ
|6+6=10
|
|
|
|
|
|-
|1+7=8
|2+7=9
|3+7=ᘔ
|4+7=Ɛ
|5+7=10
|6+7=11
|7+7=12
|
|
|
|
|-
|1+8=9
|2+8=ᘔ
|3+8=Ɛ
|4+8=10
|5+8=11
|6+8=12
|7+8=13
|8+8=14
|
|
|
|-
|1+9=ᘔ
|2+9=Ɛ
|3+9=10
|4+9=11
|5+9=12
|6+9=13
|7+9=14
|8+9=15
|9+9=16
|
|
|-
|1+ᘔ=Ɛ
|2+ᘔ=10
|3+ᘔ=11
|4+ᘔ=12
|5+ᘔ=13
|6+ᘔ=14
|7+ᘔ=15
|8+ᘔ=16
|9+ᘔ=17
|ᘔ+ᘔ=18
|
|-
|1+Ɛ=10
|2+Ɛ=11
|3+Ɛ=12
|4+Ɛ=13
|5+Ɛ=14
|6+Ɛ=15
|7+Ɛ=16
|8+Ɛ=17
|9+Ɛ=18
|ᘔ+Ɛ=19
|Ɛ+Ɛ=1ᘔ
|}

=== 乘法表 ===
{| class="wikitable"
|+
! colspan="11" |a×b
|-
|1×1=1
|
|
|
|
|
|
|
|
|
|
|-
|1×2=2
|2×2=4
|
|
|
|
|
|
|
|
|
|-
|1×3=3
|2×3=6
|3×3=9
|
|
|
|
|
|
|
|
|-
|1×4=4
|2×4=8
|3×4=10
|4×4=14
|
|
|
|
|
|
|
|-
|1×5=5
|2×5=ᘔ
|3×5=13
|4×5=18
|5×5=21
|
|
|
|
|
|
|-
|1×6=6
|2×6=10
|3×6=16
|4×6=20
|5×6=26
|6×6=30
|
|
|
|
|
|-
|1×7=7
|2×7=12
|3×7=19
|4×7=24
|5×7=2Ɛ
|6×7=36
|7×7=41
|
|
|
|
|-
|1×8=8
|2×8=14
|3×8=20
|4×8=28
|5×8=34
|6×8=40
|7×8=48
|8×8=54
|
|
|
|-
|1×9=9
|2×9=16
|3×9=23
|4×9=30
|5×9=39
|6×9=46
|7×9=53
|8×9=60
|9×9=69
|
|
|-
|1×ᘔ=ᘔ
|2×ᘔ=18
|3×ᘔ=26
|4×ᘔ=34
|5×ᘔ=42
|6×ᘔ=50
|7×ᘔ=5ᘔ
|8×ᘔ=68
|9×ᘔ=76
|ᘔ×ᘔ=84
|
|-
|1×Ɛ=Ɛ
|2×Ɛ=1ᘔ
|3×Ɛ=29
|4×Ɛ=38
|5×Ɛ=47
|6×Ɛ=56
|7×Ɛ=65
|8×Ɛ=74
|9×Ɛ=83
|ᘔ×Ɛ=92
|Ɛ×Ɛ=ᘔ1
|}

== 分數 ==
{| class="wikitable"
|+
!n
!分解
!1÷n
!1÷n°°
!分解°°
!n°°
|-
|1
|1
|1抑<math>0.\dot9</math>
|1抑<math>0.\dot\varepsilon</math>
|1
|1
|-
|2
|2
|0.5
|0.6
|2
|2
|-
|3
|3
|<math>0.\dot3</math>
|0.4
|3
|3
|-
|4
|2
|0.25
|0.3
|2
|4
|-
|5
|5
|0.2
|<math>0.\dot249\dot7</math>
|5
|5
|-
|6
|2,3
|<math>0.1\dot6</math>
|0.2
|2,3
|6
|-
|7
|7
|<math>0.\dot14285\dot7</math>
|<math>0.\dot186\chi3\dot5</math>
|7
|7
|-
|8
|2
|0.125
|0.16
|2
|8
|-
|9
|3
|<math>0.\dot1</math>
|0.14
|3
|9
|-
|10
|2,5
|0.1
|<math>0.1\dot249\dot7</math>
|2,5
|ᘔ
|-
|11
|11
|<math>0.\dot0\dot9</math>
|<math>0.\dot1</math>
|Ɛ
|Ɛ
|-
|12
|2,3
|<math>0.08\dot3</math>
|0.1
|2,3
|10
|-
|13
|13
|<math>0.\dot07692\dot3</math>
|<math>0.\dot0\dot\varepsilon</math>
|11
|11
|-
|14
|2,7
|<math>0.0\dot71428\dot5</math>
|<math>0.0\dot\chi3518\dot6</math>
|2.7
|12
|}

== 英文釋名 ==

# duodecimal
# dozenal

== 協會 ==
[http://www.dozenalsociety.org.uk/ 大不列顛十二進制劦會]

[http://www.dozenal.org/ 美利堅合十二進制聯合會]

[[:en:Duodecimal#Recurring_digits|英文原表]]

# 

[[分類:進制]]