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コンピュータによる数の表現
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Naoki Kato
PRO
April 26, 2023
Education
3
660
コンピュータによる数の表現
Naoki Kato
PRO
April 26, 2023
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Transcript
by Naoki Kato ©Naoki Kato ©Naoki Kato ͷදݱ Computer Science,
Engineering and Literacy
by Naoki Kato © Naoki Kato © Naoki Kato ใͱ
ҙຯ Λ࣋ͭͷΛ֓͘͢͞೦ ใ
by Naoki Kato © Naoki Kato © Naoki Kato ແܗͰ͋ΔใΛ
ه͢Δʹɼ͑Δʹɼʜ දݱ͠ͳ͚ΕͳΒͳ͍ දݱͷํ๏ʢදݱϝσΟΞʣ ମදݱɿൃɼৼΓɼݴ༿ɼʜ ه߸දݱɿจࣈɼࣈɼه߸ɼࣜɼදɼʜ ύλϯදݱɿֆɼਤɼө૾ɼԻָɼʜ ใ
by Naoki Kato © Naoki Kato © Naoki Kato ใͷهͱୡ
ମදݱ ͑Δ͜ͱՄ ه߸ɾύλϯදݱ ͨͱ͑ࢴ্ʹ ༷ʑͳୡϝσΟΞϚεϝσΟΞར༻Մೳ ใ
by Naoki Kato © Naoki Kato © Naoki Kato ίϯϐϡʔλͰѻ͑Δͷೋͭͷঢ়ଶ
ҰൠతͳίϯϐϡʔλిؾతͳεΠονͷू߹ ೖྗɼిؾ͕ྲྀΕ͍ͯΔ͔ɼྲྀΕ͍ͯͳ͍͔ ग़ྗɼిؾ͕ྲྀΕ͍ͯΔ͔ɼྲྀΕ͍ͯͳ͍͔ ిѹ͕͔͔͍ͬͯΔ͔ʢ)ʣɼ͔͔͍ͬͯͳ͍͔ʢ- ίϯϐϡʔλʹ͓͚Δใͷදݱ 電流を流す 電流を流さない
by Naoki Kato © Naoki Kato © Naoki Kato ίϯϐϡʔλͰѻ͑Δͷೋͭͷঢ়ଶ
ͲΜͳεΠονճ࿏ѻ͑Δঢ়ଶೋͭͷঢ়ଶ ίϯϐϡʔλʹ͓͚Δใͷදݱ X Y S C HかLか HかLか HかLか HかLか D LD CK D LD CK D0 D1 CK LD HかLか HかLか
by Naoki Kato © Naoki Kato © Naoki Kato ίϯϐϡʔλͰѻ͑Δͷೋͭͷঢ়ଶ
͜ͷೋͭͷঢ়ଶΛͱͰදݱ Ϗοτ CJUɿCJOBSZEJHJU ίϯϐϡʔλʹ͓͚Δใͷදݱ
by Naoki Kato © Naoki Kato © Naoki Kato ΑΓଟ࠼ͳঢ়ଶͱͷ߹ͤͰදݱ
ೋͭͷϏοτΛΈ߹ΘͤΔͱछྨͷঢ়ଶ ࡾͭͷϏοτΛΈ߹ΘͤΔͱछྨͷঢ়ଶ /ݸͷϏοτΛΈ߹ΘͤΔͱ /छྨͷঢ়ଶ͕දݱՄೳ ίϯϐϡʔλʹ͓͚Δใͷදݱ ビット列
by Naoki Kato © Naoki Kato © Naoki Kato ͓·͚
ίϯϐϡʔλʹ͓͚Δใͷදݱ ̍ ̌ ̌ ̍ ̎ ̌ ̍ ̌ ̏ ̌ ̍ ̍ ̐ ̍ ̌ ̌ ̑ ̍ ̌ ̍ ̒ ̍ ̍ ̌ ̓ ̍ ̍ ̍ ਓ͍Δͱ ʢCJU͋Δͱʣ ࠷େछྨ ʣ Λ۠ผՄೳ
by Naoki Kato © Naoki Kato © Naoki Kato ίϯϐϡʔλͷϚϧνϝσΟΞԽ
ใΛϏοτྻͰදݱ͢Δͱ ίϯϐϡʔλʹೖྗʢهԱʣ͢Δ͜ͱ͕Ͱ͖Δ ͳΜΒ͔ͷॲཧΛ͢Δ͜ͱ͕Ͱ͖Δ ίϯϐϡʔλʹ͓͚Δใͷදݱ ⽂字や絵図 映像 ⾳楽
by Naoki Kato © Naoki Kato © Naoki Kato ใͷදه
ϏοτྻͩͱͨΒ͍͠ ϏοτྻΛೋਐه๏ʹΑΔͱΈͳ͠ ेਐه๏IΛ༻͍ͯදݱ͢Δ͜ͱ͕ଟ͍ ίϯϐϡʔλʹ͓͚Δใͷදݱ
by Naoki Kato © Naoki Kato © Naoki Kato ਐه๏ͱਐه๏ͱਐه๏
ʢࢀߟʣجม 00000000 0 0h 00000001 1 1h 00000010 2 2h 00000011 3 3h : : : 00001010 10 0ah : : : 00001111 15 0fh 00010000 16 10h : : :
by Naoki Kato © Naoki Kato © Naoki Kato ίϯϐϡʔλ͔ΒใΛग़͠ೖΕ͢Δ
ίϯϐϡʔλʹใΛೖΕΔʹɼ ใΛϏοτྻʢೋਐه๏ͷʣʹม͢Δ ූ߸Խ ίϯϐϡʔλ͔ΒใΛग़͢ʹɼ Ϗοτྻʢೋਐه๏ͷʣΛใʹ͢ ෳ߹Խ ίϯϐϡʔλʹ͓͚Δใͷදݱ
by Naoki Kato © Naoki Kato © Naoki Kato ූ߸Խͱෳ߹Խ
ίϯϐϡʔλʹ͓͚Δใͷදݱ 東 西 南 北 00 01 10 11 東 西 南 北 符 号 化 複 合 化
by Naoki Kato © Naoki Kato © Naoki Kato ΛϏοτྻͰදݱ͢Δ
جຊɼ୯७ʹɼΛೋਐه๏Ͱද͢ ͷදݱ 0010101010001010(2) 2A8A(16)
by Naoki Kato © Naoki Kato © Naoki Kato ࣗવͱͷූ߸Խ
ͦͷ··ೋਐදه๏Λར༻ ̌ ̌̌̌̌̌̌̌̌ ̍̌ ̌̌̌̌̍̌̍̌ ̍ ̌̌̌̌̌̌̌̍ ̍̍ ̌̌̌̌̍̌̍̍ ̎ ̌̌̌̌̌̌̍̌ ̍̎ ̌̌̌̌̍̍̌̌ ̏ ̌̌̌̌̌̌̍̍ ̍̏ ̌̌̌̌̍̍̌̍ ̐ ̌̌̌̌̌̍̌̌ ̍̐ ̌̌̌̌̍̍̍̌ ̑ ̌̌̌̌̌̍̌̍ ̍̑ ̌̌̌̌̍̍̍̍ ̒ ̌̌̌̌̌̍̍̌ ̍̒ ̌̌̌̍̌̌̌̌ ̓ ̌̌̌̌̌̍̍̍ ̍̓ ̌̌̌̍̌̌̌̍ ̔ ̌̌̌̌̍̌̌̌ ̍̔ ̌̌̌̍̌̌̍̌ ̕ ̌̌̌̌̍̌̌̍ ɿ ʢϏοτͷ߹ʣ ͷදݱ
by Naoki Kato © Naoki Kato © Naoki Kato ेਐه๏͔Βೋਐه๏ͷม
̎ͰׂΓࢉΛ͍ͯ͘͠ ̎ʣ̍̕ ̎ʣ ̕ ̍ ̎ʣ ̐ ̍ ̎ʣ ̎ ̌ ̎ʣ ̍ ̌ ̌ ̍ ̍̕ʢ̍̌ʣ ʹ̍̌̌̍̍ʢ̎ʣ ʢࢀߟʣجม 商 余り 余りを逆順に読む
by Naoki Kato © Naoki Kato © Naoki Kato ͷූ߸Խ
ෛͷΛͲ͏͢Δ͔͕ϙΠϯτ ූ߸Ծ෦ ࠷্ҐϏοτΛූ߸ͱ͢Δ ʴ̓ ̌̍̍̍ ʵ̓ ̍̍̍̍ ʴ̒ ̌̍̍̌ ʵ̒ ̍̍̍̌ ʴ̑ ̌̍̌̍ ʵ̑ ̍̍̌̍ ʴ̐ ̌̍̌̌ ʵ̐ ̍̍̌̌ ʴ̏ ̌̌̍̍ ʵ̏ ̍̌̍̍ ʴ̎ ̌̌̍̌ ʵ̎ ̍̌̍̌ ʴ̍ ̌̌̌̍ ʵ̍ ̍̌̌̍ ʴ̌ ̌̌̌̌ ʢʵ̌ ̍̌̌̌ʣ ʢ˞̐Ϗοτͷ߹ʣ ͷදݱ
by Naoki Kato © Naoki Kato © Naoki Kato ̍ͷิ
ෛͷɼશϏοτΛసͤ͞Δ ʢɾɾ͔ΒҾ͘ʣ ʴ̓ ̌̍̍̍ ʵ̓ ̍̌̌̌ ʴ̒ ̌̍̍̌ ʵ̒ ̍̌̌̍ ʴ̑ ̌̍̌̍ ʵ̑ ̍̌̍̌ ʴ̐ ̌̍̌̌ ʵ̐ ̍̌̍̍ ʴ̏ ̌̌̍̍ ʵ̏ ̍̍̌̌ ʴ̎ ̌̌̍̌ ʵ̎ ̍̍̌̍ ʴ̍ ̌̌̌̍ ʵ̍ ̍̍̍̌ ʴ̌ ̌̌̌̌ ʢʵ̌ ̍̍̍̍ʣ ʢ̐Ϗοτͷ߹ʣ ͷදݱ
by Naoki Kato © Naoki Kato © Naoki Kato ̍ͷิͷ߹ͷՃࢉ
ೋਐه๏ͱͯ͠Ճࢉޙɼ ܻ͕͋;Εͨͱ͖ͦΕΛՃࢉ ʴ̏ʢ̌̌̍̍ʣ ʴʣʴ̍ʢ̌̌̌̍ʣ ʢ̌̍̌̌ʣʴ̐ ʴ̍ʢ̌̌̌̍ʣ ʵ̍ʢ̍̍̍̌ʣ ʴʣʵ̎ʢ̍̍̌̍ʣ ʴʣʵ̎ʢ̍̍̌̍ʣ ̍̍̍̌ ʵ̍ ̍̍̌̍̍ ̍ ̍̍̌̌ ʵ̏ ͷදݱ
by Naoki Kato © Naoki Kato © Naoki Kato ͷิ
ෛͷɼܻଟ͍ͷ͖ͷ͔ΒҾ͘ ʵ̔ ̍̌̌̌ʢ ̔ͱಉ͡ʣ ʴ̓ ̌̍̍̍ ʵ̓ ̍̌̌̍ʢ ̕ͱಉ͡ʣ ʴ̒ ̌̍̍̌ ʵ̒ ̍̌̍̌ʢ̍̌ͱಉ͡ʣ ʴ̑ ̌̍̌̍ ʵ̑ ̍̌̍̍ʢ̍̍ͱಉ͡ʣ ʴ̐ ̌̍̌̌ ʵ̐ ̍̍̌̌ʢ̍̎ͱಉ͡ʣ ʴ̏ ̌̌̍̍ ʵ̏ ̍̍̌̍ʢ̍̏ͱಉ͡ʣ ʴ̎ ̌̌̍̌ ʵ̎ ̍̍̍̌ʢ̍̐ͱಉ͡ʣ ʴ̍ ̌̌̌̍ ʵ̍ ̍̍̍̍ʢ̍̑ͱಉ͡ʣ ʴ̌ ̌̌̌̌ ʢ̐Ϗοτͷ߹ʣ ͷදݱ
by Naoki Kato © Naoki Kato © Naoki Kato ͷิͷ߹ͷՃࢉ
ೋਐه๏ͷͷՃࢉΛ͢ΕΑ͍ ʢܻ͋;Εແࢹʣ ʴ̏ʢ̌̌̍̍ʣ ʴ̍ʢ̌̌̌̍ʣ ʴʣʴ̍ʢ̌̌̌̍ʣ ʴʣʵ̍ʢ̍̍̍̍ʣ ʢ̌̍̌̌ʣʴ̐ ̍̌̌̌̌ ̌ ʴ̍ʢ̌̌̌̍ʣ ʵ̍ʢ̍̍̍̍ʣ ʴʣʵ̎ʢ̍̍̍̌ʣ ʴʣʵ̎ʢ̍̍̍̌ʣ ̍̍̍̍ ʵ̍ ̍̍̍̌̍ ʵ̏ ͷදݱ
by Naoki Kato © Naoki Kato © Naoki Kato ेਐه๏ͱೋਐه๏ͷҙຯ
ेਐه๏ ̍ ̌ ̕ ೋਐه๏ ̍ ̌ ̍ ʹ ࣮ͷදݱ 102=百が⼀個 101=⼗は無し 100=⼀が九個 22=四が⼀個 21=⼆は無し 20=⼀が⼀個
by Naoki Kato © Naoki Kato © Naoki Kato ेਐه๏ͱೋਐه๏ͷҙຯ
ेਐه๏ ̌ɽ̍ ̌ ̕ ೋਐه๏ ̌ɽ̍ ̌ ̍ ʹ ʴ ʹ ࣮ͷදݱ 10-1=⼗分の⼀が⼀個 10-2=百分の⼀は無し 10-3=千分の⼀が九個 2-1=⼆分の⼀が⼀個 2-2=四分の⼀は無し 2-3=⼋分の⼀が⼀個
by Naoki Kato © Naoki Kato © Naoki Kato ݻఆখ
C C ɽC C ʹ C º C º C º C º Ϗοτɼখ෦Ϗοτͷ߹ʣ ̌̌̌̌ ʹ ̌ ̌̌̌̍ ʹ ̌ɽ̎̑ ̍̍̍̍ ʹ ʔ̌ɽ̎̑ ̌̌̍̌ ʹ ̌ɽ̑ ̍̍̍̌ ʹ ʔ̌ɽ̑ ̌̌̍̍ ʹ ̌ɽ̓̑ ̍̍̌̍ ʹ ʔ̌ɽ̓̑ ̌̍̌̌ ʹ ̍ ̍̍̌̌ ʹ ʔ̍ ̌̍̌̍ ʹ ̍ɽ̎̑ ̍̌̍̍ ʹ ʔ̍ɽ̎̑ ̌̍̍̌ ʹ ̍ɽ̑ ̍̌̍̌ ʹ ʔ̍ɽ̑ ̌̍̍̍ ʹ ̍ɽ̓̑ ̍̌̌̍ ʹ ʔ̍ɽ̓̑ ࣮ͷදݱ
by Naoki Kato © Naoki Kato © Naoki Kato ेਐه๏ͷখΛೋਐه๏ʹม͢
Δํ๏ খ෦ʹ̎Λֻ͚͍ͯ͘ ̌ɽ̒̎̑ ̎ ̍ɽ̎̑̌ ̎ ̌ɽ̑̌ ̎ ̍ɽ̌ ̌ɽ̒̎̑ʢ̍̌ʣ ʹ̌ɽ̍̌̍ʢ̎ʣ ʢࢀߟʣجม
by Naoki Kato © Naoki Kato © Naoki Kato ݻఆখͰදݱͰ͖Δ࣮
খ෦Ϗοτͷ߹ɼ දݱͰ͖Δͷʢʣ୯Ґ খ෦̏Ϗοτͷ߹ɼʢʣ୯Ґ খ෦̐Ϗοτͷ߹ɼʢʣ ɿ OͰͷͰ͋ΒΘͤͳ͍ ΛਐͰදه͢Δͱ॥খ ̌ɽ̌̍̌̍̌̍̌̍ɾɾɾ ࣮ͷදݱ
by Naoki Kato © Naoki Kato © Naoki Kato ݻఆখͰදݱͰ͖Δ࣮
̍ʗ̏ ʹ ̌ɽ̌̍̌̍̌̍̌̍ɾɾɾ ʹ ̌ɽ̌̍̌̍ ʹʁ ̌ɽ̌̍̌̍ ̌ɽ̌̍̌̍ ʴʣ̌ɽ̌̍̌̍ ̌ɽ̍̍̍̍ʹ̌ɽ̏̓̑̕ ࣮ͷදݱ & 丸め誤差
by Naoki Kato © Naoki Kato © Naoki Kato ίϯϐϡʔλʹΑΔܭࢉ࣌ͷ
㱣 Є̎OΛܭࢉ͍ͨ͠ O ແݶճ܁Γฦ͢͜ͱͰ͖ͳ͍ͷͰ/ճͰଧͪΓ 㱣 Є̎Oͷޡ͕ࠩൃੜ O/ ʢࢀߟʣ࣮ͷදݱ 打ち切り誤差
by Naoki Kato © Naoki Kato © Naoki Kato ݻఆখͰදݱͰ͖Δ࣮
Ϗοτͷ߹ɼͯ͢Λ෦ʹͬͨͱͯ͠ ʙ ʙ Ϗοτͷ߹ɼʙ ϏοτͰɼʙ ʙͷൣғ খ෦Λ͏ͱɼ͞Βʹൣғڱ·Δ ΑΓදݱൣғΛ͍͛ͨ ුಈখ ࣮ͷදݱ
by Naoki Kato © Naoki Kato © Naoki Kato ුಈখ
ූ߸෦ɼࢦ෦ɼԾ෦Ͱදݱ ࣮ͷઈର ʹ Ծ෦ºجࢦ෦ ̌̍̍̍̍̍̌ ʹ ʴ̌ɽ̍̍̌º̎̍̍̍ ʹ ʴ̌ɽ̓̑º̎ʵ̍ ʹ ʴ̌ɽ̏̓̑ ʢූ߸෦̍Ϗοτʴࢦ෦̏ϏοτʴԾ෦̏Ϗοτʣ ࣮ͷදݱ
by Naoki Kato © Naoki Kato © Naoki Kato ුಈখ
ਐه๏Ͱߟ͑ͯΈ·͢ɽɽɽ ܻ͑Δͱ͖ ݻఆখͩͱ ʙ ුಈখʢԾ෦ܻʣͩͱ º ʙ º º ʙº ࣮ͷදݱ
by Naoki Kato © Naoki Kato © Naoki Kato ුಈখͷಛ
ʢ◯◯×◯) ࣮ͷදݱ 0.0 1.0×100 0.1×101 1.0×101 0.1×102 (10.0×100) 1.0×102 ◯.◯×102で表現できる数 ◯.◯×101で表現できる数 ◯.◯×100で表現できる数 (10.0×101) (10.0×102)
by Naoki Kato © Naoki Kato © Naoki Kato ුಈখͷಛ
ͨͱ͑ ɾɾɾɾɾɾ 9º9º ͨͱ͑ º ɼ º ɼ º ࣮ͷදݱ
by Naoki Kato © Naoki Kato © Naoki Kato ුಈখදݱʹ͓͚Δਖ਼نԽ
ʴ̍ʗ̏ ΛුಈখͰදݱ͢Δͱ ʢූ߸෦̍Ϗοτʴࢦ෦̏ϏοτʴԾ෦̏Ϗοτʣ ʴ̍ʗ̏ ʹ ʴ̌ɽ̌̍̌ ʹ ʴ̌ɽ̌̍̌º̎̌ ʹ ʴ̌ɽ̌̍̌º̎̌̌̌ ̌̌̌̌̌̍̌ ʹ ʴ̌ɽ̍̌̍º̎ʵ̍ ʹ ʴ̌ɽ̍̌̍º̎̍̍̍ ̌̍̍̍̍̌̍ ࣮ͷදݱ 正規化 有効桁数の増加
by Naoki Kato © Naoki Kato © Naoki Kato ුಈখදݱʹ͓͚Δਖ਼نԽ
ʴ̍ʗ̏ ΛුಈখͰදݱ͢Δͱ ʢූ߸෦̍Ϗοτʴࢦ෦̏ϏοτʴԾ෦̏Ϗοτʣ ʴ̍ ʹ ʴ̍̌̌º̎̌̌̌ ʹ ʴ̌̍̌º̎̌̌̍ ʹ ʴ̌̌̍º̎̌̍̌ ʹ ʴ̍̌̌º̎̌̌̌ ʹ ʴ̍̌̌º̎̌̍̍ ʹ ̌̌̍̍̍̌̌ ࣮ͷදݱ 正規化(選択) ゲタをはかせる
by Naoki Kato © Naoki Kato © Naoki Kato ුಈখʹΑΔܭࢉ࣌ͷ
͍ۙಉ࢜ͷݮࢉΛ͢Δͱɽɽɽ º ༗ޮܻܻ ʔʣº ༗ޮܻܻ º ʹº ༗ޮܻܻ ࣮ͷදݱ 桁落ち
by Naoki Kato © Naoki Kato © Naoki Kato ුಈখʹΑΔܭࢉ࣌ͷ
ೋ࣍ํఔࣜͷղͷެࣜ ͰBD͕ݶΓͳ͘ʹ͍ۙͱ খ͍͞ղΛٻΊΔͱ͖ ʢݶΓͳ͘Cʹ͍ۙrCʣͷܭࢉ͕ൃੜ ܻམ͕ͪൃੜ͠ɼղ͕ෆਖ਼֬ʹʂ ˞খ͍͞ղЌɼ େ͖͍ղЋΛٻΊ͔ͯΒ ͰٻΊΔ ࣮ͷදݱ x = −b± b2 − 4ac 2a 1 α c a
by Naoki Kato © Naoki Kato © Naoki Kato ුಈখʹΑΔܭࢉ࣌ͷ
ઈର͕େ͖͘ҟͳΔͷՃݮࢉΛߦ͏ͱ ʴ Λ༗ޮܻܻͷਐͰܭࢉ͢Δͱ º ʴʣº º ʴʣº º ࣮ͷදݱ 情報落ち
by Naoki Kato © Naoki Kato © Naoki Kato ࣮ͷූ߸Խ
ුಈখ ܻམͪɼใམͪ ؙΊޡࠩͱଧͪΓޡࠩ͋Δ ݻఆখʹൺɼ ѻ͑Δઈରͷൣғ૿͑Δ͕ɼਫ਼མͪΔ ܭࢉॲཧෳࡶʹ͍ ར༻͢Δͷൣғ͕ݶΒΕɼ ਫ਼͕ٻΊΒΕΔܭࢉʹݻఆখ͕ΘΕΔ ࣮ͷදݱ
by Naoki Kato © Naoki Kato © Naoki Kato ࣮ͷޡࠩΛମݧͯ͠ΈΑ͏ʂ
࣮ͷදݱ =IF(A1=B1,"◦","×")
by Naoki Kato © Naoki Kato © Naoki Kato ࣮ͷޡࠩΛମݧͯ͠ΈΑ͏ʂ
࣮ͷදݱ =400.2-400 =1305-1352 =130.5-135.2
by Naoki Kato © Naoki Kato © Naoki Kato ޡ͕ࠩ͋Δͱ·͍ͣ໘͕͍Ζ͍Ζ͋Δ
ۚ༥ܭࢉͳͲͰޡ͕ࠩग़ͨΒେมʂʂ ిͰͤΊͯɼ׺ʹͳͬͯ΄͍͠ ेਐͷੈքΛγϛϡϨʔτ͢Δ ೋਐͷ গɼ OͷͰදݱ ͳͲݱࣾձͰ༻͍ΒΕΔ جఈ͕ແݶখʹ༗ݶܻͰਖ਼֬ʹදݱͰ͖ͳ͍ʂ ޡࠩͷগͳ͍ͷදݱ
by Naoki Kato © Naoki Kato © Naoki Kato ೋਐԽेਐදݱʢ#$%#JOBSZDPEFE
EFDJNBMʣ ेਐه๏ͷܻΛϏοτͷೋਐه๏Ͱදݱ ̌ ̌̌̌̌ ̍ ̌̌̌̍ ̎ ̌̌̍̌ ̏ ̌̌̍̍ ̐ ̌̍̌̌ ̑ ̌̍̌̍ ̒ ̌̍̍̌ ̓ ̌̍̍̍ ̔ ̍̌̌̌ ̕ ̍̌̌̍ ޡࠩͷগͳ͍ͷදݱ
by Naoki Kato © Naoki Kato © Naoki Kato κʔϯܗࣜ
ेਐه๏ܻΛ ܻͷκʔϯϏοτͱܻͷϏοτͰදݱ ͨͩ͠ɼ࠷ޙͷܻκʔϯϏοτͰͳ͘ɼූ߸Ϗοτ κʔϯϏοτ κʔϯϏοτɼϏοτͱ͋ΘͤͯϏοτ͕ ͦͷΛද͢จࣈͷίʔυϙΠϯτʹରԠ ූ߸Ϗοτ ·ܾͬͨ͘·Γ͕ͳ͍ ̐ɽ̏ ʹ b` b` ޡࠩͷগͳ͍ͷදݱ
by Naoki Kato © Naoki Kato © Naoki Kato ύοΫܗࣜ
ϏοτͰɼेਐج๏ʹΑΔܻͷΛදݱ ࠷ޙͷϏοτූ߸Ϗοτʢਖ਼ɿɼෛɿʣ ̐ɽ̏̑ ʹ ʵ̎̍ɽ̏̏ ʹɽ ޡࠩͷগͳ͍ͷදݱ
by Naoki Kato © Naoki Kato © Naoki Kato ͓͠·͍
ͷදݱ