計算気といえば、そろばん。
そろばんの状態遷移を考えたっていいじゃないか。
一桁そろばん
+1 -1
plantuml
@startuml
skinparam shadowing false
state0: 00000
state1: 01000
state2: 01100
state3: 01110
state4: 01111
state5: 10000
state6: 11000
state7: 11100
state8: 11110
state9: 11111
state0 --> underflow : -1
state0 --> state1 : +1
state1 --> state0 : -1
state1 --> state2 : +1
state2 --> state1 : -1
state2 --> state3 : +1
state3 --> state2 : -1
state3 --> state4 : +1
state4 --> state3 : -1
state4 --> state5 : +1
state5 --> state4 : -1
state5 --> state6 : +1
state6 --> state5 : -1
state6 --> state7 : +1
state7 --> state6 : -1
state7 --> state8 : +1
state8 --> state7 : -1
state8 --> state9 : +1
state9 --> state8 : -1
state9 --> overflow : +1
@enduml
状態遷移表
| state | 00000 | 01000 | 01100 | 01110 | 01111 | 10000 | 11000 | 11100 | 11110 | 11111 |
|---|---|---|---|---|---|---|---|---|---|---|
| 00000 | - | +1 | +2 | +3 | +4 | +5 | +6 | +7 | +8 | +9 |
| 01000 | -1 | - | +1 | +2 | +3 | +4 | +5 | +6 | +7 | +8 |
| 01100 | -2 | -1 | - | +1 | +2 | +3 | +4 | +5 | +6 | +7 |
| 01110 | -3 | ^2 | -1 | - | +1 | +2 | +3 | +4 | +5 | +6 |
| 01111 | -4 | -3 | -2 | -1 | - | +1 | +2 | +3 | +4 | +5 |
| 10000 | -5 | -4 | -3 | -2 | -1 | - | +1 | +2 | +3 | +4 |
| 11000 | -6 | -5 | -4 | -3 | -2 | -1 | - | +1 | +2 | +3 |
| 11100 | -7 | -6 | -5 | -4 | -3 | -2 | -1 | - | +1 | +2 |
| 11110 | -8 | -7 | -6 | -5 | -4 | -3 | -2 | -1 | - | +1 |
| 11111 | -9 | -8 | -7 | -6 | -5 | -4 | -3 | -2 | -1 | - |
|state|00000|01000|01100|01110|01111|10000|11000|11100|11110|11111|
|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|
|00000|-|+1|+2|+3|+4|<font color="OrangeRed">+5</font>|<font color="OrangeRed">+6</font>|<font color="OrangeRed">+7</font>|<font color="OrangeRed">+8</font>|<font color="OrangeRed">+9</font>|
|01000|-1|-|+1|+2|+3|+4|<font color="OrangeRed">+5</font>|<font color="OrangeRed">+6</font>|<font color="OrangeRed">+7</font>|<font color="OrangeRed">+8</font>|
|01100|-2|-1|-|+1|+2|+3|+4|<font color="OrangeRed">+5</font>|<font color="OrangeRed">+6</font>|<font color="OrangeRed">+7</font>|
|01110|-3|^2|-1|-|+1|+2|+3|+4|<font color="OrangeRed">+5</font>|<font color="OrangeRed">+6</font>|
|01111|-4|-3|-2|-1|-|+1|+2|+3|+4|<font color="OrangeRed">+5</font>|
|10000|<font color="OrangeRed">-5</font>|-4|-3|-2|-1|-|+1|+2|+3|+4|
|11000|<font color="OrangeRed">-6</font>|<font color="OrangeRed">-5</font>|-4|-3|-2|-1|-|+1|+2|+3|
|11100|<font color="OrangeRed">-7</font>|<font color="OrangeRed">-6</font>|<font color="OrangeRed">-5</font>|-4|-3|-2|-1|-|+1|+2|
|11110|<font color="OrangeRed">-8</font>|<font color="OrangeRed">-7</font>|<font color="OrangeRed">-6</font>|<font color="OrangeRed">-5</font>|-4|-3|-2|-1|-|+1|
|11111|<font color="OrangeRed">-9</font>|<font color="OrangeRed">-8</font>|<font color="OrangeRed">-7</font>|<font color="OrangeRed">-6</font>|<font color="OrangeRed">-5</font>|-4|-3|-2|-1|-|
| state | underflow | 00000 | 01000 | 01100 | 01110 | 01111 | 10000 | 11000 | 11100 | 11110 | 11111 | overflow |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 00000 | -1,-2,-3,-4 | - | +1 | +2 | +3 | +4 | +5 | +6 | +7 | +8 | +9 | +9 |
| 01000 | -2,-3, -4 | -1 | +1 | +2 | +3 | +4 | +5 | +6 | +7 | +8 | +9 | |
| 01100 | -3 | -2 | -1 | - | +1 | +2 | +3 | +4 | +5 | +6 | +7 | |
| 01110 | -3 | ^2 | -1 | - | +1 | +2 | +3 | +4 | +5 | +6 | ||
| 01111 | -4 | -3 | -2 | -1 | - | +1 | +2 | +3 | +4 | +5 | ||
| 10000 | -5 | -4 | -3 | -2 | -1 | - | +1 | +2 | +3 | +4 | ||
| 11000 | -6 | -5 | -4 | -3 | -2 | -1 | - | +1 | +2 | +3 | ||
| 11100 | -7 | -6 | -5 | -4 | -3 | -2 | -1 | - | +1 | +2 | ||
| 11110 | -8 | -7 | -6 | -5 | -4 | -3 | -2 | -1 | - | +1 | ||
| 11111 | -9 | -8 | -7 | -6 | -5 | -4 | -3 | -2 | -1 | - |
+1 +2 -1 -2
plantuml
@startuml
skinparam shadowing false
state0: 00000
state1: 01000
state2: 01100
state3: 01110
state4: 01111
state5: 10000
state6: 11000
state7: 11100
state8: 11110
state9: 11111
state0 --> underflow : -1
state0 --> state1 : +1
state1 --> state0 : -1
state1 --> state2 : +1
state2 --> state1 : -1
state2 --> state3 : +1
state3 --> state2 : -1
state3 --> state4 : +1
state4 --> state3 : -1
state4 --> state5 : +1
state5 --> state4 : -1
state5 --> state6 : +1
state6 --> state5 : -1
state6 --> state7 : +1
state7 --> state6 : -1
state7 --> state8 : +1
state8 --> state7 : -1
state8 --> state9 : +1
state9 --> state8 : -1
state9 --> overflow : +1
state0 --> underflow : -2
state1 --> underflow : -2
state0 --> state2 : +2
state1 --> state3 : +2
state2 --> state0 : -2
state2 --> state4 : +2
state3 --> state1 : -2
state3 --> state5 : +2
state4 --> state2 : -2
state4 --> state6 : +2
state5 --> state3 : -2
state5 --> state7 : +2
state6 --> state4 : -2
state6 --> state8 : +2
state7 --> state5 : -2
state7 --> state9 : +2
state8 --> state6 : -2
state9 --> state7 : -2
state9 --> overflow : +2
state8 --> overflow : +2
@enduml
+1 +2 +3 -1 -2 -3
plantuml
@startuml
skinparam shadowing false
state0: 00000
state1: 01000
state2: 01100
state3: 01110
state4: 01111
state5: 10000
state6: 11000
state7: 11100
state8: 11110
state9: 11111
state0 --> underflow : -1
state0 --> state1 : +1
state1 --> state0 : -1
state1 --> state2 : +1
state2 --> state1 : -1
state2 --> state3 : +1
state3 --> state2 : -1
state3 --> state4 : +1
state4 --> state3 : -1
state4 --> state5 : +1
state5 --> state4 : -1
state5 --> state6 : +1
state6 --> state5 : -1
state6 --> state7 : +1
state7 --> state6 : -1
state7 --> state8 : +1
state8 --> state7 : -1
state8 --> state9 : +1
state9 --> state8 : -1
state9 --> overflow : +1
state0 --> underflow : -2
state1 --> underflow : -2
state0 --> state2 : +2
state1 --> state3 : +2
state2 --> state0 : -2
state2 --> state4 : +2
state3 --> state1 : -2
state3 --> state5 : +2
state4 --> state2 : -2
state4 --> state6 : +2
state5 --> state3 : -2
state5 --> state7 : +2
state6 --> state4 : -2
state6 --> state8 : +2
state7 --> state5 : -2
state7 --> state9 : +2
state8 --> state6 : -2
state9 --> state7 : -2
state9 --> overflow : +2
state8 --> overflow : +2
state0 --> underflow : -3
state1 --> underflow : -3
state0 --> state3 : +3
state1 --> state4 : +3
state2 --> underflow : -3
state2 --> state5 : +3
state3 --> state0 : -3
state3 --> state6 : +3
state4 --> state1 : -3
state4 --> state7 : +3
state5 --> state2 : -3
state5 --> state8 : +3
state6 --> state3 : -3
state6 --> state9 : +3
state7 --> state4 : -3
state7 --> overflow : +3
state8 --> state5 : -3
state9 --> state6 : -3
state9 --> overflow : +3
state8 --> overflow : +3
@enduml
+1 +2 +3 +4 -1 -2 -3 -4
plantuml
@startuml
skinparam shadowing false
state0: 00000
state1: 01000
state2: 01100
state3: 01110
state4: 01111
state5: 10000
state6: 11000
state7: 11100
state8: 11110
state9: 11111
state0 --> underflow : -1
state0 --> state1 : +1
state1 --> state0 : -1
state1 --> state2 : +1
state2 --> state1 : -1
state2 --> state3 : +1
state3 --> state2 : -1
state3 --> state4 : +1
state4 --> state3 : -1
state4 --> state5 : +1
state5 --> state4 : -1
state5 --> state6 : +1
state6 --> state5 : -1
state6 --> state7 : +1
state7 --> state6 : -1
state7 --> state8 : +1
state8 --> state7 : -1
state8 --> state9 : +1
state9 --> state8 : -1
state9 --> overflow : +1
state0 --> underflow : -2
state1 --> underflow : -2
state0 --> state2 : +2
state1 --> state3 : +2
state2 --> state0 : -2
state2 --> state4 : +2
state3 --> state1 : -2
state3 --> state5 : +2
state4 --> state2 : -2
state4 --> state6 : +2
state5 --> state3 : -2
state5 --> state7 : +2
state6 --> state4 : -2
state6 --> state8 : +2
state7 --> state5 : -2
state7 --> state9 : +2
state8 --> state6 : -2
state9 --> state7 : -2
state9 --> overflow : +2
state8 --> overflow : +2
state0 --> underflow : -3
state1 --> underflow : -3
state0 --> state3 : +3
state1 --> state4 : +3
state2 --> underflow : -3
state2 --> state5 : +3
state3 --> state0 : -3
state3 --> state6 : +3
state4 --> state1 : -3
state4 --> state7 : +3
state5 --> state2 : -3
state5 --> state8 : +3
state6 --> state3 : -3
state6 --> state9 : +3
state7 --> state4 : -3
state7 --> overflow : +3
state8 --> state5 : -3
state9 --> state6 : -3
state9 --> overflow : +3
state8 --> overflow : +3
state0 --> underflow : -4
state1 --> underflow : -4
state0 --> state4 : +4
state1 --> state5 : +4
state2 --> underflow : -4
state2 --> state6 : +4
state3 --> underflow : -4
state3 --> state7 : +4
state4 --> state0 : -4
state4 --> state8 : +4
state5 --> state1 : -4
state5 --> state9 : +4
state6 --> state2 : -4
state6 --> overflow : +4
state7 --> state3 : -4
state7 --> overflow : +4
state8 --> state4 : -4
state9 --> state5 : -4
state9 --> overflow : +4
state8 --> overflow : +4
@enduml
今後の課題
状態遷移表の自動生成
Cソースコードの自動生成
桁あがり、桁下がり
５の玉を別の状態管理にするか。
色の付け方
'@twipg Qiitaのマークダウンで色をつける方法[140色]
https://qiita.com/twipg/items/d8043cd4681a2780c160
Qiitaのマークダウンで色をつける方法[140色]
https://pa-tu.work/blog/qiita-cheatsheets-collection/25842
1月６日は色(19)いろの日(1)参考資料
https://qiita.com/kaizen_nagoya/items/fcfe3901a0d7468d1528
Markdownの表でセルのバックグラウンドにカラーを
https://qiita.com/pooshikin/items/8850fd0ca53805449ffb
Markdown記法 チートシート
https://qiita.com/Qiita/items/c686397e4a0f4f11683d
Markdown記法/書き方（見出し・表・リンク・画像・文字色など）
https://notepm.jp/help/how-to-markdown