View source for 六進制

'''六進制'''者，[[計數法]]也。[[基數]]有[[六]]，滿六進一，记曰<math>1,2,3,4,5,0</math>。以其二三得六，故其除三而得有窮小數，如下所述：

<math>\frac{1}{3}=0.3333\cdots\cdots=0.\dot3</math>

<math>\frac{1}{3}=0.2_{(6)}</math>

== 四則運算 ==

=== 加法表 ===
{| class="wikitable"
|+
! colspan="5" |
|-
|1+1=2
|
|
|
|
|-
|1+2=3
|2+2=4
|
|
|
|-
|1+3=4
|2+3=5
|3+3=10
|
|
|-
|1+4=5
|2+4=10
|3+4=11
|4+4=12
|
|-
|1+5=10
|2+5=11
|3+5=12
|4+5=13
|5+5=14
|}

=== 乘法表 ===
{| class="wikitable"
|+
! colspan="5" |
|-
|1×1=1
|
|
|
|
|-
|1×2=2
|2×2=4
|
|
|
|-
|1×3=3
|2×3=10
|3×3=13
|
|
|-
|1×4=4
|2×4=12
|3×4=20
|4×4=24
|
|-
|1×5=5
|2×5=14
|3×5=23
|4×5=32
|5×5=41
|}

== 分數除法 ==
{| class="wikitable"
|+
!n
!分解
!<math>\frac{1}{n}</math>
!<math>\frac{1}{n_{(6)}}</math>
!分解<sub>(6)</sub>
!<math>n_{(6)}</math>
|-
|1
|1
|1，亦可作<math>0.\dot9</math>
|1<sub>（6）</sub>，亦可作<math>0.\dot5_{(6)}</math>
|1
|1
|-
|2
|2
|0.5
|0.3<sub>(6)</sub>
|2
|2
|-
|3
|3
|<math>0.\dot3</math>
|0.2<sub>(6)</sub>
|3
|3
|-
|4
|2
|0.25
|0.13<sub>(6)</sub>
|2
|4
|-
|5
|5
|0.2
|<math>0.\dot1_{(6)}</math>
|5
|5
|-
|6
|2,3
|<math>0.1\dot6</math>
|0.1<sub>(6)</sub>
|2,3
|10
|-
|7
|7
|<math>0.\dot1 4285 \dot7</math>
|<math>0.\dot0\dot5_{(6)}</math>
|11
|11
|-
|8
|2
|0.125
|0.043<sub>(6)</sub>
|2
|12
|-
|9
|3
|<math>0.\dot1</math>
|0.04<sub>(6)</sub>
|3
|13
|-
|10
|2,5
|0.1
|<math>0.0\dot{3}_{(6)}</math>
|2,5
|14
|-
|11
|11
|<math>0.\dot{0}\dot{9}</math>
|<math>0.\dot{0}31345242\dot{1}_{(6)}</math>
|15
|15
|-
|12
|2,3
|<math>0.8\dot{3}</math>
|0.03<sub>(6)</sub>
|2,3
|20
|}

== 數學常數 ==
{| class="wikitable"
|+
!常數
!六進制展開
!十進制展開
|-
|π
|[[oeis:A004605|3.050330 051415etc]]
|[[oeis:A000796|3.1415926535etc]]
|-
|e
|[[oeis:A004597|2.415052 053524etc]]
|[[oeis:A001113|2.7182818284etc]]
|-
|<math>\frac{{\pi}^{2}}{6}</math>
|1.351150 013244etc
|[[oeis:A013661|1.6449340668etc]]
|-
|√2
|1.225245 314205etc
|[[oeis:A002193|1.4142135623etc]]
|-
|√3
|1.422042 321254etc
|[[oeis:A002194|1.7320508075etc]]
|-
|φ
|1.341254 554353etc
|[[oeis:A001622|1.6180339887etc]]
|-
|γ
|0.324402 323555etc
|[[oeis:A001620|0.5772156649etc]]
|}

== 兼查 ==

* [[:en:Senary|《英文維基》六進制一文簡介段]]
* [http://tool.oschina.net/hexconvert 在線進制轉化網]

[[分類:進制]]