* Kurose and Ross, Computer Networking - - PDF document

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Feb 23, 2023 181 likes •300 views

SLIDE 1 ✂✁☎✄✝✆✞✂✟✡✠☞☛✍✌✏✎✑✌✓✒✑✔✓✒✝✕✝✒✝✖ ✗✙✘

* Kurose and Ross, “Computer Networking”

✚✂✛☎✜✝✢✣✚✂✤✦✥★✧✂✩✫✪✬✧✂✩✮✭✮✛ ✯✝✧✂✰ ✱✳✲✵✴✷✶✹✸✻✺ ✼ ✽✾✶✿✼❁❀❃❂ ✺ ✼✿❄❅✶✹❆✿❆✷❇✿❈❉❈✙❊ ❋❍●✵■✷❏❉❑❁▲✷▼✷◆P❖ ❑✿◗

✍❘❁❑❁◗

❑✿❙✹❚ ❑❁❯✬❱ ■❉◗ ❲❨❳✹❚ ❑✹❯✡●✝❑✹❘P❘✙❱ ■❉❙✑❩✿●✹❑❁❘❁●✵❚✡❑✹■✷❘ ◗❉❚ ❑P❱ ❖

P❚✿❬

❭❫❪ ❴✮❵P❛ ❜✵❴✡❜✵❝❉❞✮❡✿❢✿❣P❝✿❝☎❜✙❛✷❣❁❡✿❡☎❜❁❤✷❤✑❪ ✐✻❤✿❢❁❣❁❥ ❜P❦✍❴✡❜P❦❧❪ ♠❁❴❨♥ ♦✾♣ q❁r❁s✷t✹✉ ✈☎✇✵①❉✇✹②P②P③ ④❁t✷t❉④❁t✷⑤☎✇❁③ ④✂⑥✷t❉④P②⑦✉ ⑧✮⑨❁③ ✇❁⑩✡④✍r✿④✹✇❁②❁④✵③ t❨❶ ❷ ✉ ②✹④✵⑧❉❶✿✉ ⑨✷s❨t❉❷❁⑥❁③❉✈☎④✑✇✹⑧✷②✍②❁④✹t✷❶✿✉ ⑧☎✇❁❶✿✉ ❷P⑧✮❷✿⑨❨⑨❁③ ✇✹⑩✡④❁t✻❷P⑧❨❸P③ ❷✿✇❁②P✈❉✇✷t✷❶ ① ✉ ⑧✿❹☎t ❺✳❻✦❼❁❽ ❾ ❿❁➀✵❽ ❼★➁➂❼✹❽ ❾ ➃ ❼❁➄☎➅➇➆ ➈❍➉❉➊✙➋ ➌❁➍✹➎☞➏✷➉❉➊P➌✑➍P➐✮➑P➒ ➓❁➊P➔✡➍✹→✿➣✿➒ ↔❁↕❁↔☎➍✹➙ ➛✿➜❧➒ ➛P➋❁↔☎➛P➓✵➋ ➊✝➛P➐✷➌✝➉✷➍✹➎✡➊ ➣☎➝✡➒ ➉✷➣ ➊P➌✍→✷➛P➒ ➔ ➉❨➣ ➍✿➍✂➌✹➏✷➊✑➣☎➍✍➋ ➍❁➝❃➓✵➒ ➣✡➊✵➔❉➔ ➍✹➔✻➔ ➛❁➣ ➊✵➞ ➟➡➠➇➢❉➤P➥✑➦P➧✻➨✡➩ ➫ ➤✙➭ ➤❁➢❉➢✂➭ ➩ ➧✿➯❉➢✹➲✿➨➂➳✿➤✵➫ ➤✂➵❉➳❁➤✂➸✷➦✿➺✵➭✹➩ ➢✻➵ ➦✂➫ ➤P➥✹➻❁➼☎➤✑➤✵➫☎➫ ➦✹➫ ➢ ➵❉➳✹➻❉➢✻➺✿➽❉➦✵➩ ➥✙➩ ➧❉➸❨➤✵➧✷➥P➾ ➵ ➦✹➾ ➤✵➧✷➥✍➫ ➤✹➵❉➫ ➺✹➧☎➢✿➚❨➩ ➢❉➢✹➩ ➦✵➧☎➢ ➪✂➶☎➹✝➘✣➪✂➴✦➷★➬✂➮✫➱✬➬✂➮✮✃✮➶ ❐✝➬✂❒✫❮P❰ÐÏ✑➮✓➬✂Ñ Ò✳Ó✙Ô Õ✹Ö✬×✵Õ✷Ø❧Ù Ú✷Õ✿Ô Û Ü✬Ý✷Þ❁ß❁à á❉â✂ã✿äPå☎æ✦ä❁ä✙á✓ç❉ä✙á✷è❁äPé ç✻Þ✹á✷è✍é äPß☎ä❧à ê☎ä✵é ç ëíìPî❉î✷ï✷îñð➂ò❧ó ò❁ô✙ó õ ï✷ö❧÷ ø❍ùPú❉ú û✹ú ü✮ý✹ú ù✍þ❉ý✿ÿ✷ü❉ù✁✄✂✆☎❨ü✞✝ ✟✁✠☎ý✁✡✷ý☞☛✌☛ ù✍✠❉ÿ✷ý☞☛☞✝ û✁✠✓ý✞✠☞✎✠☎û✏✝ ü❉ù✏✑ ✒✔✓✏✕✁✖✌✕✘✗ ✙✌✕✏✚✜✛✆✕✞✢ ✕✏✖✣✢ ✤✦✥✆✚ ✕✞✤✣✕✏✧★✖✣✕✦✩☞✪✫✕✁✚✣✚ ✩✞✚ ✤✞✬ ✭✯✮ ✰✲✱✞✮ ✳✞✴✌✵✁✶ ✱✷✰✣✸✆✹✺✱✣✹✏✴★✻✞✹✁✼✾✽★✿✞✼✜✼ ✹✁✰✣✼ ✵✞✴✌✱☞❀✫✮ ✱★✱✞✮ ✿✁✴✜✿✞✼✾❁ ❂★✱★✰✜✻✏✼ ✿✞❃★✱✫✰✣✸☞✹ ❄ ✿✞✼✣✼✌❂✆❃★✰✌✹✁✻✺✽✆✼ ✵✞❀✾✹ ❅❇❆✁❈✣❈★❉★❈❋❊✏❉★❈✣❈✣●✞❍✏■ ❏ ❉★❑✘▲ ▼✔◆✾❖✁P☞◗☞❘✁❙✆❚ ❯☞◆❲❱★❳✞❨✲❩✣◗✆❖✎❨ ❖✏P✌❖✍❚ ❬✌❖✁❨✜❩ ❳✎❭ ❳✞P✣❘☞❩ ❖✺❘✁❙★❪❫P✣❳✞❨✣❨ ❖✏P✣❩✜❩✣◗☞❖ ❖✁❨✣❨ ❳✞❨✲❴✾❚ ❩✣◗✆❳✆❵★❩✷❨ ❖✆❯✣❳✞❨✌❩☞❚ ❙✣❛✫❩✌❳✺❨ ❖✞❩✣❨ ❘✁❙✌❯☞◆✫❚ ❯✣❯✞❚ ❳✁❙ ❜❫❝✌❞✦❡❢❜❫❣✐❤❦❥❫❧♥♠✦❧✲♦✺♣✲♦✦q✦♦✦r✄s❫t✈✉❫r ❥❫t✈❥❫❞✦♣✲❣✦♣✲❝ ♦✦❞ ✇❢①✁② ③☞④✺⑤ ⑥☞⑦★⑧✏⑨✜⑩✆⑨ ❶✆❷✌❶✞❸✌❶✏⑤★⑧✏③✣❷☞② ⑨ ⑧✘⑤ ⑦✎② ❹✲⑩✁⑤ ⑧✏❹✾⑧✏③✣❷ ⑧✁❺❻② ③✜❷✣❼✆⑧✺⑥✆❺✆⑥✞⑩★❷✌⑧✁⑨ ❽ ⑧✞❾✏❿ ➀★➁✏➂❫➁✁➃✁➄➅❸✌⑥✞⑨✌❺✏➆ ➇☞➄✾❺✆⑥✆⑩☞❷ ⑧✏⑨✲❷ ⑦✞⑩✞② ❸✌⑥✏⑤ ⑤ ⑦✎② ③★❸✆⑤ ➈✆❺✆⑧✞➉✞➊✞➋✍➄✾➂✄❿✁➌➎➍➏➀ ❸★❼✍② ⑩✣➉✞❿✆❼✆❶☞➉★❷✷➐✞➈★➉✺② ③✣❷ ⑧✁⑨ ➑★⑥✆❸✣⑧✍❿★⑥✞③★❺❻⑤ ② ③☞④✺② ③✣❷ ⑧✏⑨ ➑★⑥✆❸✌⑧ ➒❢➓✾➔✆→✆➣☞↔ ↕✁➙✲➛✣➜✞➝☞➞➠➟✞➡★➢✁➤ ➥☞➦☞➧ ➟✁➨✌➩✞➫☞➢✏➨★➭✣➥✆➡★➩★➯✁➲ ➥☞➦ ➢✞➩✫➳ ➩✣➢✁➦✾➩✣➢✁➵★➯★➢✍➨★➭✌➢ ➨✣➯✆➸✷➺☞➢✏➤ ➩✞➻★➼★➢✞➢✁➽✏➺✆➥✆➭☞➾❫➧ ➨✌➼★➟✏➻★➢✞➦✣➭✆➚ ➪ ➻✣➥✞➽✁➽✆➩✷➢✁➤✣➤ ➟✞➤✜➽✆➢✁➦ ➢✁➭✣➦✆➧ ➟✁➨✦➺✏➧ ➦ ➩✞➻ ➧ ➸✜➡✁➲ ➢✏➸✾➢✏➨✣➦ ➩✦➭★➶✆➥✞➨☞➨✌➢✍➲★➥✆➭☞➭✌➢✞➩✣➩✜➼★➟✞➤✲➩☞➶☞➥✞➤ ➢✁➽✎➸➹➢✏➽✍➧ ➯☞➸✫➻☞➦✣➤ ➥✞➨✌➩☞➸✫➧ ➦ ➩✜➟✁➨ ➲ ➧ ➨☞➾ ➘❢➴✾➷✆➬✆➮☞➱ ✃✁❐✜❒✌❮✆❰☞❮✏Ï Ð✣❮✺Ñ✞Ò★Ó✁Ô Õ☞Ö☞× Ñ✁Ø✌Ù✞Ú☞Ó✁Ô✣Ô Ñ✞Ô✜Û☞Ü☞Ó✁Û✆Ý✞× Ø✣Þ✫Õ✞Ø★ß✎Û✌Ñ✞Ô✣Ô Ó✁Û★Ö☞× Ñ✁Ø✞à × Ø★Ö Ó✁Ô✣Ô✌á☞Ò☞Ö Ù✦Ü☞Ñ☞Ù★Ö✜Ö Ñ✦Ù✣Ó✏Ø★ß✺â✆Ô Õ✆ã✾Ó❫á✆Ò✫Ö✣Ü✆Ó❫Ò✆Ô Ñ✆Ö Ñ✞Û✌Ñ✏ä★Ù★Ö Õ✞Û☞Ý✞à★á✆Ò✆ß✆Õ☞Ö✌Ó✆Ù Ù★Ö Õ✆Ö Ó❻× Ø✌â★Ñ❫Ô Ó✁Þ★Õ✞Ô✌ß✘× Ø✣Þ✫â★Ó✆Ó✏ß✏å✆Õ✆Û☞Ý✷Ö✌Ñ✫Ù✣Ó✍Ø★ß✆Ó✁Ô☞à★Ù✣Ó✞æ☞á✣Ó✍Ø★Û✌Ó✄Ø✣á✆ã✷å☞Ó✏Ô Ù✁à Ó✞Ö✣Û✆ç è➠é✲é✜ê✦é♥ë✯ì❫í✲ì❫î✦í✲ï ê✦ð ñ✘ò✐ó✍ô✦ñ✏õ✣õ ö✞õ✫ò✘÷✞ø✌÷✁ù✣ø☞ú ö✁û✲ü✁û★ý❫ó✞ö✁õ✌õ ÷✁ù★ø☞ú ö✏û✫þ✍ú ø ÿ✁ õ ÷✁ý✄✂✞û★ý✆ü✁û★ù✆☎✄✝ ò ô✺ò✘ü☞ø ü✟✞✆õ ö✆ø ÷✁ù✣ø✌÷✁ý✄þ✠☎✫÷✏õ✣õ ö✞õ✷ù☛✡✆÷✁ù✠☞✞ú û✍✌✏✎ ✑ ü☛☎✄ú û★ù✓✒ ✂☞ý✞÷✦ÿ★ö ✑ ÷✔✡✆÷✆ü✞ý✆÷✁õ✖✕✏ú ÷✗✒ ý✆ÿ ✘ ñ✍õ✌õ ö✞õ✷ý✆÷✞ø ÷✏ù✣ø☞ú ö✁û✦ú ÿ✦û✌ö✆ø✁✙ ✚✗✚✜✛✣✢ ✘ ✞✆õ ö✆ø ö✞ù✣ö✤✒ ✑ ü✠☎ ✑ ú ÿ✣ÿ✷ÿ✣ö ✑ ÷✺÷✁õ✣õ ö✞õ ÿ✏✎✆þ✄✂★ø✷õ ü✆õ ÷✗✒ ☎ ✘✜✥ ü✆õ✆✌★÷✏õ✷ñ✘ò✐ó✔✕✏ú ÷✗✒ ý✁☎✏ú ÷✜✒ ý✆ÿ✺þ☞÷✁ø✌ø ÷✁õ✷ý✆÷✞ø ÷✏ù✣ø☞ú ö✁û✲ü✁û★ý❫ù✣ö✞õ✣õ ÷✏ù✣ø☞ú ö✁û ✦★✧ ✩✟✪✁✫ ✬✮✭✁✯✱✰✲✧✆✳✤✴✶✵✸✷✹✬✔✺✁✻ ✼✾✽❀✿✓❁✔❂✍❃✄❄✓❁✤❅ ❆❇❃✄❈✍❄❊❉ ❋✁❂✆❃✏●✆❋☛❍☛❈ ■✓❂✍❍✆❁✏❄✹❏✠❑✱▲✄❄✏❄✗❉

✍▼✱▲❖◆✍P✄◗✏◆✍❘✤❙

❚✤❯ ❱✤❲ ❳✟❲✍❨✓❩ ❬ ❩✓❭✍❭✍❪✓❫☛❩✗❴✱❵❀❨✓❩✔❛✆❪✏❜ ❝✍❩✟❳✠❞✁❲✍❨✠❩❖❡✠❨✠❩✏❡✓❢✠❣ ❤✗✐ ❲✁✐ ❭✄❥ ❦♠❧ ♥ ♦✱♣✍q✓r✹s✍t✓✉✣✈✓r✏✇✲①✠♦✔❧✍② ③✔♥ s④♣✍q✓r✔✉✖r✄③✍③✍⑤✠⑥✠r✹♥ ③✣①✏⑦✏⑦ ⑧⑩⑨ ❶✓❷✍❸✓❹✏❺✆❻✖❼ ❽✍❹ ❾✾❿☛➀✏➁☛➂✏➃✓➄✆➅✄➆✄➀✏➇ ➈❇➅✄➉✍➆✓➊✣➂✄➉ ➀✟➋☛➌✠➅✠➊✍➀✔➈✖➍ ➋✍➌✁➂✄➎✣➀✄➏✆➀✗➎✱➎✍➐✓➑④➒✠➀✤➉✖➅✠➓✔➔☛→ ➊✓➣ ↔➙↕✜➛✄➜ ➛✤➝✍➜ ➞④➟✏➠ ➠✍➞✄➡ ➢✍➤✏➠ ➛✹➥✗➡ ➜✲➛✏➦✍➦ ➧✄➦ ➞ ➨✮➩✓➫✤➭ ➯ ➲✱➳ ➵✟➸✄➺✄➳ ➺✤➻✍➳✲➫✏➯ ➯✠➳✆➼❇➵✔➽✗➭ ➳ ➲✣➺✤➾✆➾ ➵✄➾ ➲ ➚✾➪✠➶ ➹✏➘✠➴✏➘✤➷ ➬ ➷ ➮ ➱✁➹✠✃④➴✄❐☛❐✆❒✤❮☛➮✓➷ ❰✍Ï✱➴✄❰✣❒✏➶✍➶ ➹✏❰✆❒✓➹✓Ð☛Ñ✣✃✓➶ ➴✄Ò✖❒✹➷ Ñ✁Ó✏Ô❇Õ

SLIDE 2 ÖØ×✔Ù✟×✔Ú✲Û Ú✲Û Ü✟ÝßÞàÜ✟á❊×✔â ã✾ä❀å✓æ✔ç✍è✄é✓æ✤ê ë❇è✄ì✍é✹í✄î✄ï✱ðòñ✆ó✏ô✆õ✄ö õ☛÷ õ✣ó✠ø✔ù✁ú û✓ü✗ý✍þ✠ú ÿ✁✄✂✆☎ ü✞✝✍ü✏þ✠ú þ✓ú ✟✏ý✡✠☛✟✌☞ þ✁✍✓ü✏✎✑✟✒☎✆û✔✓✖✕ ✗✙✘✆✚✒✛✢✜✒✣✒✤✒✥✢✦✄✧ ✜✩★✁✪✫✚✒✛✢✬✒✭ ✮✁✯✞✧ ✜✱✰✞✭ ✲✢✳✑✚✒✛✁✴✆✬✄★✁✤✄✮✫✴✖✵✆✶✫✷✹✸✌✺✁✻✆✼✱✽ ✼✒✾✫✿✞✽✌❀✁❁✒❂✆✼ ❃ ❁✒❄✁❂✆❅☛✿✆❄ ✼✏❆✞❆✹❆✑✸✫✿✒❇✫❂❉❈ ❈✡❈ ❊ ❋❍●❏■✆❑✏▲✁▼✒◆✆❑✖▲✡❖✄P☛◆✒❑✒◗ ❑✄▲✫◗❘❖✞❙ ❙✒❚✱❯✞❱ ◗ ❲❳❑✞❨✡❨ ▼✒❨ ❲ ❩❭❬✒❪❴❫✁❵✄❛ ❜✁❝❴❞✁❡✆❢✏❣❘❤✌✐ ❥✒❦✫❛ ❞ ❪❧❦✡❫✄♠ ❢✹♥✌❞✁❡✆❢✏♦✁❥✒♣✆❢✖♦✡❤✄❜rq✆❢✏❫✁❵✁❢✞♣❧❞✡❥❧♦✁❥✒❦✡❦ ❢✄♦✫❞❘❤ ❵✒❛ ❜✁❝✄♠ ❢✱q✹❛ ❞✢❢✄❦✁❦ ❥✒❦✁s t✈✉❴✇①✇①② ③❴④❍⑤⑦⑥❧⑧❉⑨ ⑩❍❶❸❷✹❹ ❺✫❻ ❼✄❽✫❾✡❿✱➀✔➁✁➂✒➃✆➄✖➁✡➅✄➆r➇✆➄✏➈✁➉✁➄✞➃❧➊✡➂❧➁✡➂✄➋✡➋ ➄✄➁✫➊❘➄✞➋✁➋ ➂✒➋ ➉☛➂✌➌✏➍ ➄✒➉✁➉☛➊✫➎✌➅✄➆ ➏✢➐✄➑✖➒✞➓ ➔ → ➣✙↔➙↕✆➛❳➛r➜ ➝✁➞❧➟✁➠✒➡✆➢❉➜ ➤☛↕❧➡✹➜ ➤✫➥✡↕✒➝✫➟✡➢✱➦✖➟✁➠✒➡✆➢ ➧➩➨✄➫✒➭❴➯✌➲✏➳✫➵✁➲✄➸✏➺ ➻✏➼✡➻✒➽✁➽ ➲✄➼✁➺✢➫r➻✄➭✡➲✱➯✞➾ ➺❘➲✞➽✁➽ ➻✒➽ ➚❍➪❸➶✫➹✆➘✌➴ ➷✡➬❧➮✫➱✆✃✄➮✆❐r➮✡❒✒❮✆✃ ❰➩Ï✹Ð✆Ñ✄Ò✌Ó❴Ô✹Õ Ö✡×❳Ø✒Ù Ñ✏Ö✁Ð✆Ú✌×✁Ñ❉Õ ÛrÜ✫Ú✌×✒Õ Ö✌Õ Ú✄Û✡×☛Ö✫Ð✌Ø✆Ö❘Ø✒Ù Ñ❧Ø❧Ü✫Ú✆Ý✑Ñ✄Ù❘Ú✌Þ❴Ö✡Ý✑Ú ß à á✒â✹á✌ã❏á✆ä✩á å å å æ çéè❴ê✒ë✁ë✁ì✌í✌ê✖î✹ï ð ë❳ì✒ñ ê❉ï ò❳ð✁ó✆ê❧ô✆ð✁ó✆ê✄ñ❳õ✫ô✌ë✒ï ð✆ï ô✄ò✡ë öé÷❏ø✆ù✖ú✫û ü✁ý✏þ✫ý✆ÿ✄þ✁✄✂✆☎ ü☛þ✫ý✆ÿ✄þ✝✟✞rü✁ý✌ÿ✠✞☛✡☞✂✁✞✁ÿ✒ü✍✌✝✎✠✂✆☎ ü ✞✏☎ ✑✓✒☛✌✝✞☞☎ ü✝☎ ✌✔✑✕✞ ü✁ý✁✖✌ü☛ý✝✖✝✞☛ü✁ý✆ÿ✘✗✟✙ ✚✟✛✢✜✆✣ ✚✥✤✟✦✔✚✓✣ ✧★✚✟✛✁✦✆✣ ✩✪✜✆✣ ✧✕✫☞✩ ✬✠✩ ✦✮✭✝✩ ✦✁✤☛✦✮✧✟✚ ✫✝✚✁✣ ✯✔✧✝✰ ✱✳✲✔✴☞✵✄✶✝✷✠✸✝✹✁✺✁✻✼✵✪✽ ✺✏✶✁✷✠✺☞✾☛✽✝✿ ❀✥✴✔❁ ❂❄❃✄❅❆❅❆❇ ❈✄❉❋❊❍●✠■❑❏▼▲✔❏✏◆❍❃✓❅❆❖✠P ❏✏◗ ❘❋❙❯❚✝❱ ❲ ❳✏❲✟❨✝❳✢❩✥❳✁❬☛❬✟❭✝❪☛❳✘❫✆❱ ❲ ❬✏❱ ❴✪❲✟❨✁❳✆❱ ❚★❵☞❛ ❭✁❜✕❳ ❝ ❞❡❝ ❞

places 1 2 3 4 5 6 7 _ _ 1 _ 1

❢❄❣✄❤❆❤❆✐ ❥✄❦❋❧❍♠✠♥❑♦▼♣✔♦✏q❍❣✓❤❆r✠s ♦❋t✄♠✄❥✠✉✍✈ ✇ ①③②☞④✆⑤ ⑥✁⑦⑧④✁⑨✁⑩✝❶✘❷✼❸✆❹ ❺✍⑦❼❻✝❹ ❺✕④✠❺☛❶✝④✘❸✆❹ ❽✕⑨✁❻ ❾✓④✔❿✮➀☛⑨☞❽✕➁☞❹ ⑥✔❽✍⑥✝➂✄❺✟❶✁④✢❸✆❹ ❺✔➃ ➁ ➀☛⑥✝➁☞❹ ❺✝❹ ⑥✔❽ ➄③➅☞➆✆➇ ➈✁➉⑧➆✁➊✁➋✝➌✠➍❍➎✮➏ ➐✍➉✼➑☛➏ ➐ ➆✏➍✔➒

places 1 2 3 4 5 6 7 _ _ 1 _ 1

2nd

_ 1

1st

_ 1 1

0th

_ 1

➓❄➔✄→❆→❆➣ ↔✄↕❋➙❍➛✠➜❑➝▼➞✔➝✏➟❍➔✓→❆➠✠➡ ➝❋➢✄➛✄↔✠➤✍➥ ➦ ➧▼➨✆➩ ➫ ➫☛➭☛➯✝➲✢➳☛➯✁➲✔➳✁➵✄➸✆➩ ➭ ➺✪➺✟➻✄➭✟➯✁➼✝➭✍➼☛➽✁➭ ➲✔➾✥➽☛➻✮➫ ➫ ➻✁➚✥➩ ➪✟➶✄➭✟➯✁➲✠➼☞➸✁➻✁➹✕➲✢➾ ➘✔➫ ➲ ➲✁➼☞➳☛➯✏➾ ➻✁➚➴➯✝➼✝➺★➼✔➪✍➲☞➹✕➲✆➪✓➪✟➘✁➷✪➸✁➲✔➾✥➻✝➽✓➻✔➪✕➲✁➺

places 1 2 3 4 5 6 7 1 1 1 1

2nd

1 1

1st

1 1

0th

1 1

➬➱➮❑✃▼❐❮❒✓❰✠Ï Ð✳Ñ✄ÒÔÓ❄❒✓Õ❆ÕÖÏ ×✄❰✳Ø⑧Ñ✄Ù❍✃✏Ú Û❋Ü✍Ý✕Þ✏ß✮à á★á✟â✝ã✁á✓à ä✓å✝â✝ã✔Ý✟æ☛ç✮è✄ã✁á✍á✟â✁ç✏á✟é ã☞Ý✕ä✝ê✓à á✕á ç✔è✢ê✥ç✁ä✟ä✟ã✁æ☛ç✢é ç☞ë✕ç☞ã✔ì ä à á✕ä✟ç✆ì í✔î☛ä☞à Ý☛å✕ç❑à á✍ã☛í☛í☛ç✮å✟á ä✪ç☞ï☞ã☞å✟á✝ì Þ✄á✟â✝ç✢å✝â✝ç✮å✝ð✄ß✆à á ä✓á✟â✁ã✝á å✕ñ☞é✟é ç✁ä✝ò☛ñ✔Ý☛è✏á ñ✘à á ä✏ì ñ☞å✕ã✁á✝à ñ✔Ý✁ó ô▼õ✔ö☞÷☞ø★ù☞ú û✄÷✝ü✟ü☛ý✁ø✥û✠þ☛ÿ✝÷✁þ✁✄✂ þ✁☎✝✆☛ÿ✁÷✟✞✡✠✝û✁ü✁☛✌☞ ✍✔ø✏✎❼þ ✍✒✑✔✓ ✕✏✖✘✗✄✙ ✚✒✛✢✜✌✣✡✚✡✤✟✚✥✛✦✗✦✤✧✛✦★✒✩✄✙ ✪ ✚✥✫✬✜✟✭✯✮✝✰✝✭✢✱✌✪✲✪ ✱✴✳✵✜✌✪✡✛✯✗✴✪✯✗✦✤✄✙ ✶✲✷✯✜✌✶✦✙ ✪ ✸ ✹✏✺✘✻✄✼ ✽✾✼ ✽✥✿✡✻✌❀✒❀✄❁✯❂✢❃✟❄✄✼ ❁✡❅✥❃✦❆✒❇❉❈

places 1 2 3 4 5 6 7 1 1 1 1

2nd

1 1

1st

1 1

0th

1 1 places 1 2 3 4 5 6 7 1 1 1

2nd

1s t

0th

1 1 Faulty code received Transmitted code

SLIDE 3 ❊●❋■❍✥❏▲❑✴▼ ◆P❖✒◗❘❍❘❙✾❖✴❚✒❯✴◆✾❱▲❲❳❖✒❨■◆

places 1 2 3 4 5 6 7 8 9 1 1 1 1 2 _ _ _ _

3rd

2nd

1s t

0th

❩●❬✁❬✥❭✾❪✒❫❵❴ ❛✲❭✾❜✒❭✾❝✁❝❡❞✒❬❘❩❣❢✲❢✲❞✒❢▲❤✐❭✾❫❵❭✾❪✒❫✵❴✢❞✒❜ ❥ ❞✒❦■❭✾❝ ❧♥♠✝♦✯♣✢q❵r stq ♦✡✉✁✈✯✇ ①✯②✯♣✡②✟r ③ r q ④❵q ♦✯♣ qtq ♦✯✉✁⑤ ①✡⑥✦✉✲⑦✔r ③ ③✡⑧ ①✢q⑨⑥✯✉✯q ✉✦⑤ qt♣✢⑧⑨✉✌✇ ✇ ①✦✇ ⑩ ❶❸❷❺❹✦❻✢❹✯❼✢❽✌❾✘❿✡❼⑨➀ ➁✯❹❵❹✌➂ ➂ ❿✦➂✘❽✟➃ ❾ ➀ ➂✢➃ ➄✯➅ ➀✡➃ ❿✡❼⑨❿✯➆t➀ ➁✯❹✲❼ ❹✯➀ ➇✧❿✦➂ ➈✵➉✘➃ ➊✘❻✢❿✡❾ ❾✢➃ ➄✟➋ ❹ ➀ ❿✲➊✔❿✯❽✯❹✟➋ ➌♥➍✝➎✯➏✢➐❵➑ ➒t➐ ➎✡➓✥➔⑨➑ →✯➑ ➔✘➣✡➔↔→✢➣✡➔t↕✡➓✌➙✔➛✡➜❵↕✌➑ ➐ ➒✘➐ ➎✯➏✢➐t➎✯➏✡➝ ➓❵➐ ➛✲↕✡➓✥➞ ➎✯➏✡→ ➟✯➓✯➠✁➜ ➛✯➙ ➐ ➎✯➓✁➞ ➛✡➠✦➓❵➐ ➛❵➜ ➏✯➑ ➡✡➠✯➓✡➐ ➓✌➞ ➐✢➑ → ➟✲➏✡→⑨➓✦➙ ➙ ➛✦➙ ➢ ➤➦➥✄➧✡➨✥➩⑨➫ ➭✦➫ ➩✘➯✡➩■➲✡➳t➵ ➧✯➨✲➸t➺ ➻t➻✵➼ ➽ ➾✾➚✌➼ ➪✦➶ ➺ ➽✯➹ ➘✯➴t➷✡➬t➮✡➱ ✃✲❐✢➮✦❒ ❮✔➷✡➬✲❰ Ï✡Ð✡➮✦❰ Ñ ➷✡Ò✦Ï✯Ó Ô✧➷✦❮ Ò✦➴ Õ➦Ö✄×✡Ø✥Ù✦Ú Û✦Ü Ý Þ✯ß à❵á✯âtã ä✯å✁æ á✡ç✦å è♥é✝ê✯ë✢ì✵í✘î✢ï ì✵ð✡ñ✲ì ê✡ñ✥í⑨ò ó✯ò í✘î✡í↔ô✟ò ï ì ë✡ó✡õ ñ✁ð✯ñ✡ì ö✧ñ✡ñ✦ó⑨ì ê✡ñ✁÷✡ò ø ï ìtë✢ó✡ô✒ù ë✡ï ì ñ✦ø ø ú✡ó ñ✯ú✡î✡ï⑨ð✌ò ì ït÷ ú✯ø✔ì ê✯ñ✁õ ú✯ô✯ñ❵ì ú❵÷ ë✦ò ù û➦ü✄ý✡þ✁ÿ✁ ✂ ✄ ☎✝✆✝✞ þ✠✟✯þ✝✄ ✡✧þ✡þ☛✆☞✄ ý✡þ✠✌✝ ✍ ✂ ✄✎☎✝✆✢ÿ✑✏ ☎✝✂ ✄✘þ✒✍ ✍ ✓✔✆ þ✝✓✔✕✖✂☞✟✁ ✄ ✂✗ ✂✎✄ ý✯þ ✘☛✙✝✚ ✛☛✜✣✢ ✤✝✥ ✦✎✜ ✧ ★✪✩✑✫✗✬✖✭✑✩✑✮✰✯✗✱✳✲✴✱✳✮✰✵✷✶✹✸✺✫✻✯✗✬ ✼✳✱✳✲✾✽✰✱✳✫✗✬✖✯❀✿❂❁❄❃✴✸✺✼✰❅❇❆❀❈☞❉ ❊❇❋❍●✖● ■❀❏✝❑✔▲✺▼✝◆✒▲✺❖❍▲✁P✝P✝■☛❑☛▲✴◗ ❏✗■✑❖❍■✒▼✝●✔◗ ❘

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

❙✪❚✑❯✗❱✖❲✑❚✑❳✰❨✗❩✳❬✴❩✳❳✰❭✷❪✹❫✺❯✻❨✗❱ ❴✳❩✳❬✾❵✰❩✳❯✗❱✖❨❀❛❂❜❄❝✴❫✺❴✰❞❇❡❀❢❤❣ ✐❦❥❀❧✁♠✻♥☛♦✔♣ q✑r✳s✁t ✉✝✈❀✇ q①♥✔r✒②☛t ♣✖③✑④✔⑤✒q❀④☛⑥✠❧❀✉✗q✒r✁④✔⑤✺② ❧✒⑦

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

⑧✪⑨✑⑩✗❶ ❷✺⑨✰❸✰❹✗❺✰❻✴❺✳❸✰❼❾❽➀❿✺⑩✗❹✗❶✖➁✳❺✳❻✾➂✳❺✰⑩✗❶ ❹➄➃❂➅➇➆✾❿✺➁✰➈ ➉❀➊❄➋ ➌❦➍❀➎✁➏✻➐☛➑✔➒ ➓✑➔✳→✁➣ ↔✝↕❀➙ ➓①➐✔➔✒➛☛➣ ➒✖➜✑➝✔➞✒➓❀➝☛➟✠➎❀↔✗➓✒➔✁➝✔➞✺➝✝➎➄➙ ➑✒➏✠↔ ➠✰➡✗➢✑➤✑➥✺➡✻➦✗➧ ➥✺➨➩➢✰➫➯➭✪➢✑➡✗➧✖➲✑➢✑➳✰➦✗➵✳➸✴➵✳➳✰➺✷➻✹➥✺➡✻➦✗➧ ➼✳➵✳➸ ➠✰➵✳➡✻➧ ➦➄➽➚➾❄➪✾➥✺➼✳➶ ➹❦➘❀➴✁➷✒➬✎➮ ➱✳➷❐✃ ➱✔❒ ❮✁❰☛Ï✖➬✾✃ ➱✳Ð ÑÓÒ✣Ô✁Õ Ô➄Ö✝Õ ×✠Ø❀Ù Ù✒Ú✁Û☛Ü ×✔Õ ×✠Ý☛Þ✑Ü Ý✒ß➀Ù Ô➄à✔á☛Õ✝â✑ã✰ä❍Ú❐å Õ ×

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

SLIDE 4

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

æ✺çéè ê➩ë✰ì✑ç✪ç✗í✾îðï❐ñ✑ò✻ì✑óéè ê✻î✺ô❾õ ö✳ë✰ô✾÷ùø❀ú✳ì✑ô✾î ô✾è ê✠ç✗ö✳ë✰ú✳îðû➯ü❤ý

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

þ ÿ ✁✄✂✆☎✞✝✠✟ ÿ✆✡☞☛ ✁✍✌✆✎✑✏ ✒✓☎✆✔✕✁✗✖✘☎✆✙✗✚✛✌ ✡ ✏ ✒ ☛☞☛✢✜ ☛ ✣ ✒✓✁✗✒✓✤✆✁✗✒ ✣ ✥ ✂ ✡☞✜ ✁✦✝✠✧★✖✩✒✓✤✫✪✬✧★✌ ✣ ✒ ☛ ✭✯✮✱✰✦✲✳✰✦✴ ✵✷✶ ✸ ✹✺✵✼✻✽✸ ✾✷✲☞✾✽✿✆❀✼✾❁✴✽✸ ✹❂✾✷✲✺✻ ✵✦✶✺✵✷✲❂❃✕❄✺✰✷✴✳✻✽✸ ❅✺✵✷✶✼❆✺✵❁✴✽✸ ✻ ❇✕❅✽❀✽✰✦❅✽❈ ❉✬❊✞❋✼●✓❍✺■❁❏✼●✕❑✼❏✦❏✼▲☞❑✫▲✺●✷▼◆■✽❖✕❍❂❋✼●✷❍✼P❂◗ ❘❚❙ ▼ ▲❁❯❂●✼❑❁❍❂❋✆■✽❖✆❱❲❋✦❙ ❍❂❋❳❙ ▲☞❑✕❨❂❑✼❩✽❙ ▼ ❬ ❍❂❋✼●✷❍✼P☞■✽❖❭❑✫▲❂❪❁❘✼▲✺●❁▼✗■✽❖✫▼✺❋✼●❳❘✦❙ ▼ ▲✓❙ ❫❭▼✺❋✽●❵❴◆●✼▲❂▲✺❑✽❛❂● ❜✬❝✺❞✼❡✽❢ ❣✳❤✕✐❂❥✼❦✷✐✽❧✆✐✳♠❁♥✼❦❁♦☞❞❁❡ ❦✩♣ q r❂s✼t✽✉✺✈✆✇✞①✼②✽③✆④ ⑤❁⑥ ⑦✬⑧✗⑨✗⑩✷❶✺❶ ❷✷⑨✳⑩✼❷❁❸✺❹✆❺◆❻✼❼✺❼✺❽✼❾❂❻ ❿ ❼☞❽❁➀❂➀✳❻✦➁❂➂ ❻✦➃✩❿ ➄❂➄➅❿ ❼ ❽❵➆ ❻❁❾✽❽✷➆✼➀✳❷❁➃✼❻✦➇ ➈✱❷❁➉✺➃

C M M C M C M ( ) ( ) ( )

1 2 1 2

⊕ = ⊕

( )

E C M ⊕ E

➊★➋❳➌✓➍✆➎✬➏➑➐ ➒✕➐ ➓✄➔✘➌✓➓✗➋✩→✆➣ ↔

Make each number of digits {0..8} divisible by 9

↕

Example: 823 is to be sent

➙

1. Left-shift: 8230

➛

2. Divide by 9, find remainder: 4

➜

3. Subtract remainder from 9: 9-4=5

➝

4. Add the result of step 5 to step 1: 8235

➞

5. Check that the result is divisible by 9.

➟

Detects all single-digit errors: 7235, 8335, 8255, 8237

➠

Detects several multiple-digit errors: 8765, 7346

➡

Does not detect some errors: 7335, 8775, …

➢

Detection is efficient

➤✫➥★➦✆➧ ➨✳➦✑➩➭➫✓➯✩➲✆➳✆➯✩➵✆➳✆➦✱➥➸➤➻➺✩➫✓➦✆➼ ➽➚➾➶➪✦➹✳➘✼➴✳➪✕➴❂➷✽➪❵➬◆➪✼➮✺➮✺➱✼✃❂➪❳❐❚❒ ➴ ➮❭➱❂➮ ❮✬❰✦Ï✷Ð✼Ñ Ï❁Ò✺Ï✦Ó✺Ô☞Ô✺Õ✽Ï❵Ö◆Ï❁Ò✺Ò✺×✽Ø✽Ï✆×✽Ò☞×✕Ð❂Ù✦Ú Û✷Ó✳Ù❁Ö✫Ü ×✦Ú❂Ý◆Ü Ô✺Õ✆Þ ß✞à á â❲ã✺Ù✽Ï✼ä❂ä✷Ü ã✼Ü Ï✦Ó✺Ô Ò å✬æ✞ç✼è✓é❁ê ë❚ì í✳î❭ï❚ð❚ï➻ì î✆ñ✳ò❁ó☞ô✽õ✽í è✷ö✕÷❂î øúù❲û✼ü✷ý ü✫þ✷ÿ ✂✁☎✄ ✆✞✝✠✟☛✡✌☞✂✍✎☞✑✏✠✡✂✒✓✡✕✔ ✖☛✝ ✗✘✔✞✙✚✗✎✛ ✜✕✒✓✗✘✢✣✄ ✖✕✛✠✗☛✤✦✥✧✡✕✏✧✔ ✡✧✡✩★✘✪ ✫✭✬✯✮✧✰✲✱✠✳ ✴✕✵✓✶☛✷✣✸ ✱✚✱ ✰✕✹✲✺✧✳ ✴✧✷☎✰✻✸ ✶ ✸ ✵✽✼✧✱✠✮☛✰✎✳✽✾✿✼✘✳✚✹✂❀☛✱✚✮☛✰✩✷☎✰✧✶✠✶✚✴☛❁✠✰✲✺✠✼✎❂ ❂ ✼✧✾✿✰✕✹✑❃☛❄✲✱✚✮☛✰✩❅✚✼☛✰✧✺✠✺✕✸ ❅✧✸ ✰✂✵✚✱ ✶✞✼☛✺✌❆ ❇ ❈✂❉

s D s D s D s

K K K K

( ) = + + +

− − − − 1 1 2 2

❊

c D s D D g D

( ) ( ) ( ) =       R em ainder s D D c D

( ) ( ) +

1 2 1

,s ,s , ,s s

k k

❋

− −

■❍✦❏▲❑✣▼

❍❖◆◗P❙❘❯❚ ❱✽❲✻❳❩❨✌❱✽❚ ❬

1 1 1 1 1 1 0 0 1 1 1 0 + 1 0 1 0 X 1 1 1 1 1 0 1 0 0 1 0 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 1 1 1 0 0 0 0

SLIDE 5 ❭❫❪✻❴✣❵❩❛✲❜ ❝❡❞✦❢❤❣❥✐❦❣◗❣▲❞✲❵❩❛✲❧✦♠✽❴✣♠✽♥ ❞✦♦

0101110 : ) ( 1 ) ( 1 ) ( 1 ) ( 0101

2 2 3 4 2 3 4 2 4 5 2 3 5 2 3 3 5 3 2 3 2 ♣✠q r s✽t

D D D c D D D D D D D D D D D D D D D D D D D D D s D D D g D D s M + = + + + + + + + + + + + + = + + = + = =

<− remainder

✉✭✈✕✇ ①✓②✧③✘④❯⑤✓⑥✘⑦✘② ⑧⑩⑨✽❶✓❷✕❸ ❹✘❺✠❻✦❼✎❶✧❸ ❹✣❻✕❽✚❽ ❼✘❽❯❾✠❼✎❸ ❹✕❶✓❼✘❿✣➀ ❷✎❸ ➁✭➂❯➃ ➃✚➄✕➅ ➆✚➇✕➃ ➈✩➉✂➅ ➊✽➈✕➋✚➋ ➌✘➋ ➄❯➍✘➋ ➈✌➎✘➈✘➊ ➈✕➏✠➊ ➈✕➎ ➐❤➑✧➒❯➓✕➔ →✂➣☎↔ ↕✣➙➛↔ ➜✧↔ ↕✘↔ ➝✂➞ ➟✑➝☛➠✻➡☎➢ ➤✯➥✕➦ ➦✚➧✎➨✓➨ ➩✘➨ ➫✣➭☎➯ ➲✚➳✦➩✘➵✎➵✩➸✚➺✧➻✞➼✧➧✕➨☎➩☛➽✣➩✕➸✓➧✧➫ ➥✧➨ ➧✩➵✧➧✕➲ ➧✕➾✚➲✓➧✕➵ ➚➶➪ ➹❯➘✕➴ ➷✂➬✽➮ ➱✦✃✂➮ ❐✧➮ ➱✘➮ ❒✎❮ ❰✩❒✧Ï✣Ð✲Ñ✧Ò✠➮ Ó✣➮ Ô✧➮ ❐✓❰✩Ñ✠Õ✎❮ Ï✘Ö✚Õ✘Ó✣➮ Ð✕❮✠Õ☛×✲✃✧❰✘Ø✘Ò ❰✘❰✑Ù✲Ú✠Û☛Ü Ý✓Þ✘ß Ü ß Ü✘Ú Ü Ý Ú à✞á✕â â☛Ú✓ã Þ✩ä✎å Ú à❯Ü✎æ✓æ Þ æ à å ç✣è Ü✧à✚à✚á✧é✠Ü✧à Þ☛ê â Ü✧à✚à✣Ú✚Û☛á ç✦ë✕ì í✂î ï ð ñ➶ò➛ó✘ô ó✎õ✚ô ö✞÷✕ø ø✧ù✘ú☛û ö✠ô ö✞ü☛ý✩ø ó✧ö✚ö✣ô✚þ✧÷✘ÿ✁✄✂ ☎✝✆✟✞✝✠ ✆✝✆✄✡☞☛✍✌✟✎ ✏✒✑ ✓✕✔✒✖ ✗ ✘ ✙✛✚✢✜✄✣✄✤✥✚✍✦✢✧ ✤✥★✩✜✛✪✬✫✮✭✯✫

D D D CRC D D D CRC CCITT

16 15 2 16 12 5

1 32 1 + + + − + + + − D D D CRC Ethernet, FDDI,...

22 16 12

1 + + + D D D

4 2

+ + + D D D

32 26 23

+ + + D D D

7 5 8

+ + + D D

11 10

+ + + 16 −

✰✲✱✛✳✢✴✶✵✷✱✸✳✍✹✻✺✽✼✿✾✄❀ ✹✥✼✿✹✥❁✄❂✢✱✸❂✢❃ ❄✛❁❅❄✄❆❈❇✮❉❊❇

C2 G3 C3 C1 G2 C0 G1 G0 Input

❋❊●■❍❑❏✸▲✛▼❖◆❊P✥P✥▼✶◗✕❘✷❙✛❚ ❙✛❯✩❙✛▲ ❱✻❲✕❳✝❨✽❩✝❨✝❬☞❭✁❪✝❫❵❴✝❛❜❫✁❝❞❴❢❡❞❡ ❨❣❝❞❭☞❤ ❫❞✐✄❝❵❴❢❥✝❨❢❬✍❦❢❡ ❨✄❧♠❬❢❤ ❫❞✐✁❦✸❬❢❤ ♥✸❤ ♦ ❦❢❡ ❦✝♣✝♣✝❡ ❴☞❦✝❝♠❳❣q rts✟✉✒✈①✇♠②❞③✄②❞④❢⑤⑥③✽⑤✍⑦ ⑧✒⑨ ⑩✁⑧✒⑨ ❶❵❷❢❸ ❹✛②♠⑩❞❸☞⑨ ❶❞❺✽⑨ ❶❞②♠⑩ ③✝❷✝❻✄④☞❼✛⑩❞❽✝③✛❾ ❿✕➀ ➁ ➂➃✇❞②❞③❣❻✶⑨ ❶ ✉✒➄❣✉➆➅ ➇✻➈❣➉✝➉✟➊✟➋ ➌➎➍❣➏ ➍❢➐⑥➍✟➑✛➒ ➓✁➔✁➓☞→♠➉✟➣❢➒ ➔❣➏☞➣❞➔♠➓❞➉➆↔♠↕➃➙✝➉✟➛ ➉✥➜❞➙✝➉✽➑❞➝✝➐✁➞✝➉✟➛⑥➍☞➟✄➊✝➔☞➜❵➔ ➓❞➠❢➐✁➞☞➍❣➏ ➓✍➔✟➑♠➊✄➜❞➙✝➉➡➑❞➝✝➐✍➞✝➉✟➛✢➍☞➟✛➛ ➉✟➊✟➝✝➑♠➊❢➔❢➑❞➜✢➓❞➠❢➐✍➞✝➍❣➏ ➓✥➒ ➓✁➔✄→❞➍✝↕✕➉✟➛⑥➍☞➟ ➢✒➤ ➥✻➦✕➧☞➨☞➩✥➨❵➫❢➭❢➯✝➲✁➳✝➵ ➯✥➵ ➫✟➸❢➧♠➲♠➺✢➺ ➫✽➸❢➧☞➵ ➲♠➺✢➯✟➵❞➵ ➫❢➵ ➲❢➻♠➼➃➩✒➽ ➨☞➩➡➽ ➲✸➺❞➩✝➯✥➺ ➾✝➚✟➽ ➨❵➳✟➪ ➶ ➽ ➹♠➭✄➫☞➘✸➯✟➵❞➵ ➫❢➵✍➼➎➯✄➘♠➳✝➨❵➯✒➴ ➷➮➬ ➱ ✃⑥❐✟➬ ❒ ❮ ❰ Ï ➱ Ð Ñ Ò Ó Ð Ò Ô Õ Ï ✃♠❒ Ö × Ò ❰ Ø Ù Ð ❰ Ú ÛÝÜ✸Þ✄Þ✄ß✥àâá✷ã✶ä å✸æ✲ç❊ß✥è✄ä é✍æ✢ß✥ê✍é ë❅ì✟í❢î✍ï☞ð♠ñ ò❢ó✍ô✥õ✒ö ÷♠ø☞ù ú➡û❵ü✝÷➆ý ü❢þ ÿ✁ ö ü✝÷✄✂✆☎✞✝✠✟☛✡✌☞ ✍✏✎✆✑✏✝☛✒ gL g1 g0 m j L − m j−1 m j State Input

• •

x j Encoded bits

x m g

j j i i i L

− =

∑

✓✕✔✞✖✞✗✘✔✚✙ ✛✞✜✄✢ ✔✚✖✞✣✤✙ ✓✕✔✚✥✧✦✩★ ✪✬✫✮✭✏✯✆✰✏✱✞✲ ✳✘✴✤✳✏✱✠✵ ✶☛✴✸✷✺✹✆✻✚✼✾✽ ✿✮❀ ❁ ❂✘❂✠❃✸❄❅✿☛❆✮❇ ❂ ❈❊❉✘❋✆●✠❍✆❋✏●✞■ ❏✘❑✤❏✏●✠▲ ▼☛❑✸◆✺❖✆P✩◗✏❘ ❙✾❚ ❯❲❱✘❱✠❳✸❨❅❙✆❩✮❬ ❱ ❭❊❪✘❫✆❴✠❵✆❫✏❴✞❛ ❜✤❝✠❞✸❡✄❵✆❫✆❴ ❢❤❣✌✐☛❥✞❴✠❦☛❢✩❝✠❞❤❧✠♠❲❞✮♥ ❫✆❴✆❛ ❞❤❧ ♦ ❦☛❢❤♣ ❢rqts✈✉ ✇✤①✠②✆③✤④✸⑤ ⑥✠⑦✌⑧ ⑨✏⑩✏❶✆⑥✄❷✠❸✸❹❅❺✆❻✮❼ ❽ ⑨✏❾✤❿✁➀❲➁ ➂❅➃✚➄❅➅ ➆❅➇➉➈☛➊✠➋✆➌ ➍ ➎❊➏➑➐☛➒✩➓✠➔❤→✠➣❲➔✮↔ ↕✆➙✆➛ ➔❤→❅➓✠➜✸→✤➝☛➒r➓❲➔✸➞✘➟✆↕✆➙ ➒❤➠✌➝✆➡✚↕✠➢✸➛ →✠➤✚➥✤➦✆➧✮➨ ➩✆➫✘➭ ➯❤➲❤➨ ➦✆➫ ➯❤➭ ➦

x m g

j j i i i L

− =

∑

SLIDE 6 ➳✕➵✞➸✞➺✘➵✚➻ ➼✞➽✄➾ ➵✚➸➚➳➪➵✚➶✧➹✩➘➷➴➮➬✃➱➪❐✤❒❰❮✚➻ ➹ ÏÑÐ✾Ò Ó✄Ô Õ✏Ó❅Ö ×✠Ø❲Ù ×✆Ú Û Ô✠Ü ×✠Ø✏Ý Þ❊ß✧à á✏â❲ã á✆ä å æ✠ç á✠â è✆ä✠à á✏é✏ê❅à è✠â✄ë✠ê✤ì ê✏í✏ì ê✆î ê✆â æ ê✏é✤ë✠ï✄æ ð✠ê✤ñ ò✏ó✠ô✄õ ö❅÷ ø ô☛ù ù ú ö✠û

00 11 11 00 10 01 01 10 Output Current state Next state 00 = a 01 = b 10 = c 11 = d a = 00 b = 01 c = 10 d = 11

( )

x m m m m m

j j j j j j

= ⊕ ⊕ ⊕

− − − 2 1 2 On 1 On 0 1101 becomes 11 01 01 00

üþý✩ÿ✁✄✂✆☎ ✝✟✞ ✠✡✄✝✟☛☞✄✌ ✍✟✎✏☎ ✄✝✟✑✁✌ ✠✒✟✂➪ý ✓✕✔✗✖ ✘✚✙✜✛ ✢✟✖ ✣✥✤ ✦✧✢✩★ ★ ✦✜★ ✪✚✫✬★ ✢✭✙✮★ ✢✬✪ ✢✬✤ ✯✱✰ ✲✕✳✵✴ ✴ ✶✜✴ ✷✚✸✬✴ ✹✁✺ ✶✬✴ ✴ ✹✩✺ ✻ ✹✬✼✁✽✮✾✏✻ ✿✮✹✁❀❂❁ ✻ ✹✜✴ ✽✵❁ ✸✜❃ ❄✮✶✜✴ ❁ ✻ ✿✜❅✥❆ ❇❉❈❋❊✮●☞❍✬■ ❏✮❑✜▲ ▼ ◆ ❊✩❖✡P✱●✮●✬◗✮❘❙❍✧❘

✮◆❙❑✮❚✥❯

❱✱❲✵❳ ❨ ❳ ❨ ❩ ❬✭❭✩❪✩❫ ❴✬❯✬❵✱❛❋❜✬❝✜❞ ❝✏❝✮❡✬❢ ❜✭❣ ❡✱❤ ❜✟✐ ❥ ❦♠❧✡♥ ❝✮♦✮❡ ♥ ❥ ❝✮♣✮q✱❝✬r✮❢ ❝✏s✬t✧❢ s✮r✮✉ s ♥ q ❤✮✐ s✮r✧❥ ❤ ❡✱❤ ❝✬❥ ❦✄✈ ❜✮❝✧✇✜①✩② ③☞④❙⑤⑥② ⑦ ⑧ ⑨ ⑩✥❶❋❷ ❸✬❹☞❸✬❺✬❻❙❻✥❼ ❽ ❾☞❿⑥❼ ➀ ❷ ❺✮❽✮➁ ❹✭➂✮❹✬❷ ➃❂❹✮❹✬❽✥❷ ❸✬❹✏➄✬➅ ❷ ➆✮➅ ❷ ➄✮➇✥❷ ❸✮❹✭➆ ❺✱❷ ❸✵➈✱❺✱❽✮❿☞❷ ❸✮❹✭➀ ➉✜❻❙➂✬➄✜➊ ➀✥➋ ❹✩➁ ❹✩❼ ➌ ❹✬❿✭➀ ➄✏➇ ❺✮➋ ➍❉➎❋➏✮➐✟➑ ➒✜➑ ➓✮➑ ➔✜→✱➣ ➐✮➓✏➑ ➣✚➓ ➏✬➐☞➣✮➑ ➒ ↔✩→ ➐☞↕✱➔✱➓ ➏✏➓ ➏✬➔✱➓❙➣ ➓ ➔✬➙ ➓ ➣✚➔✱➓✥➣ ➓ ➔✱➓ ➐✧➛❂➜ ➝➟➞➡➠✬➢✬➤✏➥ ➢✜➦ ➢✩➧ ➨✮➧ ➤ ➩✏➫ ➠✬➢☞➭ ➯✜➲❙➳✮➵✩➸ ➺❂➻✱➼ ➽✬➾☞➚ ➾✬➼❙➪✮➶✥➚ ➹✮➘ ➴✮➷ ➴✱➷ ➬ ➮✭➱ ✃✱➼ ➽✟➷ ➚✚➾✮❐✩➼ ➾✬➬✱❒✜➾✬❒ ❮✱❰ ✃✮❒✩❒✵➷ ➬ ➮✏✃✜Ï Ï✱➱✱➪✮➚ ➚✱➷ ❮ Ï ➾✁➷ ➬✱➱✮➹ ➼✥➚ ❰✜Ð❙❮ ➪✩Ï ➚❙➼ ➪✧➾✮✃✬Ñ ➽☞➱✱✃✱➼ ➽✩Ò Ó❉Ô❋Õ✮Ö✁×ØÖ✮Ù✱Ú Û Ü Ý❙Þ ß✬ÚØÙ Õ✬Ö☞à Ö✜á♠â✱ã✱Ù Õ✜Ý✚ã✬Ú Ö✭Ü ã✜ä Ü å✜ä ã✱Ù Ö✬æ✵ç èêé✜ë✧ì í✜î í✩ï ð✜ñ✱ò✱ð✱ó ô✬ì✧ï í✮ð✬õ ô☞ó ô✮í✭ì ð✬öØí☞ì ó ð ó í✵÷ ó ô✬í✏ø✬ù í☞úØû ó ô✏ó ô✬í✁ñ ø✮ú❂í✜ì ó öØí✮ó✱ï✱û õ ì✥ì ü✮ï î✱û î í✬ì ý➟þ➡ÿ✁✁✂☎✄ ÿ✁✆✝✂✟✞✡✠✁☛☞✄ ÿ✁✡✞✁✌✟✄ ✌✎✍ ✏✒✑ ✓✌✁✔ ÿ✁✁✞✖✕✓✗ ✁✁✘✒✠✓✂✝✙ ✚✆✄ ÿ✁✡✏ ✛✓✑ ✜✟✍ ✜✓✍ ✂ ✢✡✘✟✌✟✄ ÿ ✑ ✁✌✓✔ ÿ✣✍ ✂ ✢✆✌✟✄☎✏ ✄ ✌✟✄ ✒✤✦✥ ✧✩★✫✪ ✬✮✭ ✯☎✪✱✰☎✲✳✭ ✴✶✵ ✷✎✸✎✰☎✭ ✯☎★✺✹

01 11

00 11 00 00 11 11 10 01 11 00 10 01 01 10 2 3 3 2 5 2 3 4 4 4 1 1

11 Input:

1 1 1 1 1 1 1 1 00 = a 01 = b 10 = c 11 = d a = 00 b = 01 c = 10 d = 11 Scheme

✻✩✼✫✽ ✾✮✿ ❀☎✽✱❁☎❂✳✿ ❃✶❄ ❅✎❆✎❁☎✿ ❀☎✼✺❇❉❈❋❊✡❆✡●✎❀☞❍ ■

3 3 2 2 3 1 1 2 1 2 2 3 3 2 1 3 3 3 1 3 3 2 2 2 3 4 3 4 2 4 4 5 5 2 4 2 5 2

11 01 11 00 01 10 00 11 11 10 11 00 11 1 01 00 1 01 1 10 1 01 11 11 1 01 1 10 11 00

00 11 11 00 10 01 01 10 00 = a 01 = b 10 = c 11 = d a = 00 b = 01 c = 10 d = 11

Output:

Corrected:

Input:

❏▲❑◆▼ ❖✆P ◗✺▼ ❘❚❙❱❯✱❯◆❘✫❲✡❲❨❳✳P ❩◆❬✺❲❨❭◆❩◆❪▲❫◆❴✆❵✺❖✆❵◆❯◆❵◆▼ ❲ ❛❝❜✖❞ ❡✣❡✫❢ ❣✐❤✁❡✐❥✎❦✝❧✳♠ ♥ ♦✝♣✓❥✣q r s✣t✈✉ ❦✇♥ ♦✓❢✁① ❢ ❦✣① ❤✁❦✇♥ ♦✓❢ r ❥✣♥ ♦✓②✇♠ ❡✫③✒♥ ❞ ❡ t r ④✖t☞⑤ ❞ ❦ s✐⑥✖⑦✓s ❥✁❢ r ❥✝❜ s ❞ ❡ ⑥ ③✒♥ ❞ ❡✺❦✣❞✡⑧✒❡ ⑥ ♥ ⑨✐⑧✆⑩✖❡✣②✖❶✣❷✇① ♦✟❡✣❢✝❶ ③✒♥ ❞ ❡❸♠ ❡✐❥✓❥✣❶✁❡✣❢ ⑦✝❹ t r ⑦✝t✈❺ ③✒♥ ❢ ⑦ ❜✐❡ ⑥✳r ❡✣②✖❶✁❥✁③✒♥ ❢ ⑦ ❜✐❡ ⑥ ❷✇① ♦✟❡✣❢✝❶✐❻☎❛❝❼❽❡✖❢ ⑦✁t ❾ ❡✺❥✁❢ s ❞✟❢✆③✒♥ ❢✓❜✳❿✇➀ ➁✝➂✣➃✖➄✝➂✐➅✓➆✺➇ ➈ ➉✝➊✟➋✣➌✝➍◆➎✇➈ ➉✱➏✁➐✐➎✖➇ ➇ ➑✦➉✓➒✁➑✦➓ ➔✺→✐➣ ↔✝↕ ➙✣➣ ➛✩➜☞➝✝➝✁➛✣➞✓➞➠➟✐➡ ➢✝↔✟➢✐➝✁➢✣➣ ➤▲➥◆➦ ➧✆➨ ➩✺➦ ➫❚➭❱➯✱➯◆➫✫➲✡➲❨➳✮➵◆➸◆➧✆➺✡➵◆➦➠➻✖➤▲➭❱➳✮➼ ➽◆➺✆➵✺➧✆➵◆➯◆➵◆➦ ➲ ➾➪➚✫➶☎➹➴➘✐➷ ➬✐➮ ➬✣➱✓➬✇✃ ❐✣➱✟➬✝➬✣➷✓❒✦❮ ❰✟Ï✝➮ Ð✣Ñ✎➮✓➷ Ï✣❰✓Ñ✝Ò✱❮ Ñ✓Ñ✣❮ ➬✖❰✟Ñ✡Ó✐➷ ➬✣ÒÔ❒✦❮ Ó✝Ó✁Ð✖➷ Ð✇❰✓➮ Ñ✁➮ Ï✐➮✝❮ ➬✖❰✟Ñ✫❮ ❰✡➬✣➷✓❒✐Ð✖➷✡➮ ➬✺Ò✱❮ ❰✐❮ Ò✱❮ Õ✓Ð✖Ö✓Ï✝×✟➬✦❮ ❒✳➱✟➬✇✃ ✃ ❮ Ñ✣❮ ➬✖❰✟Ñ Ø➪Ù Ú✐Û❸Ü❝Ý✁Þ✖ß✝ß✁à✇á❝â✁Þ✖ã✟ä✝å ä✝å æ✐ß✣å ß✁ç✫è✫é☎ê➴ë✐ì í✣î í✣ï✟í✇ð ñ ò➪ó ô✖õ❸ö✦÷✖ø✁ù✖ú✐ûýü☎þ✁þ✁ÿ✁✂☎✄✝✆✟✞✡✠☞☛ ✌☞✍ ✌✁✎✏✌✒✑ ✓ ✔✖✕ ✗✙✘✛✚ ✜✣✢✥✤✁✦ ✧✙★✪✩✂✫✭✬✂✧✙✮✙✯✟✰✝✱✟✲✡✳☞✴ ✵☞✶ ✵✁✷✏✵✒✸ ✹ ✺✼✻✛✽✭✾✒✿ ❀✭❁☞❂✙❂✁❃ ❄✁❃ ❁✁❅✙❆✁❇❈❂✙❉❊❃ ❋☞❇❈●✁❃ ❍❈■✁❏ ❁❑❇❈▲✥❁✁❄✙❁✥❅✙❆✂❋✏❉✒❏ ❃ ▼✭❁✁▲

SLIDE 7 ◆P❖✡◗❙❘❚❘☎❯✝❱✡❲☎◗❙❳❈❨❬❩ ❨❬❩ ❭☎❘❚❩ ❘☎❪✼❫❵❴❛◆❝❜❚❳❬❭❚❨❬❭☎❞☎❭☎❱ ❡ ❢✖❣✟❤❥✐❧❦ ❣✟♠ ♥✟♦♣❤✟♠ q☞♠ r✁♠ s✥t✉✐✝✈✥✇ ①✭♠ ②✥✇ ♦✥③❑♠ t✂④✁⑤ ⑥✁⑦✙⑧☞⑨✁t✭t✏♦❊✇☞⑩❊♠ q☞♠ ⑩✁♦✥⑩♣♠ t✂① s✝❶ ①✭♠ ♥❷♦☎r✁✇ s☞① r✁❸✙s✥t✏♦✝②✙♦✥❹❈✈✂r✂♦✒❹✏❺✛♠ t✏♦☞❻✙❻✒♠ ⑦☞♠ ♦✒t✂①❈❼❷♠ ①✙⑧✡✇ s☞❼❽⑩✥✈✙①✏❾❚⑦✏❾✁⑦☞✇ ♦ ✈✙r✂♦✥❹ r✉⑨✁t✙⑩❚⑨✭①☎✇ ♠ ④✁⑧☞①☎✇ s✭⑨✁⑩✒❿ ➀➂➁❊➃❥➄❧➅ ➁✥➆ ➇✁➈✭➉✙➇✒➊✙➋✂➌➍➃✟➎ ➏☞➎ ➐✁➎ ➑✥➊✉➄❚➉✥➒ ➓✭➎ ➔✥➒ ➇✁→❑➎ ➊✂➣☞↔ ↕✭➙☞➆ ➇✁➈✭➉✙➇✒➊✙➋✂➌ ➐✙➉✁➛✁➜❑➎ ➏☞➎ ➜☞➇✥➜❊➝ ➞P➟✡➠❙➡❚➡☎➢✝➤✡➥☎➠❙➦❈➧❬➨ ➧❬➨ ➩☎➡❚➨ ➡☎➫✼➭✒➞✪➯❛➲❵➳❛➵ ➸➻➺❥➼✣➽❚➾❛➚ ➺❊➪✭➶✥➹➘➼✟➴ ➷☞➴ ➬☞➴ ➪☞➮P➽✝➱✭✃ ❐☞➴ ❒✁✃ ➹❮➾✟❰✙❰✙➹✁➬✂➬✂Ï Ð✭Ñ✁Ò❊Ó✁Ô Õ✒Ö × Ø✉Ù✙Ú☞Û Ü✁Ý✁Þ Ù✙Ú✭Ü☞ß✭à✂Û✂á✭âäã å❥æ✪ç✁è✉é❊ê❷ë❑ì✒í✙î✏ç✁ï❑ð í✂ñ❙ò✭î✭ó✭ì✒ô✟ì õ✼ö✁÷☞ø ù✭ö✙ú❚û ü✏ý✁þ☞ú✥ÿ✁✄✂☎✂✁ø ✆✁÷✏ú✥þ✞✝ ý☎ú✟☞ü✡✠❚ö✄✂✂ú☞☛✍✌✛ø ú✏✎☎✑✡✒✡✓☞✔✖✕☎✔✘✗✚✙✄✛✟✜✍✢✡✣ ✢✡✣ ✤☞✥✟✣ ✥☎✦ ✧✩★✁✪☎✫☞✬✮✭✰✯✡✪✄✱✡✲ ✳✮✴ ✵✷✶✰✸ ✹✍✺✼✻ ✺✘✽☎✽✿✾☞❀ ❁✡❂✟❃☞❄☎❂✄❅✄❆✚❄✄❇✟❂✘❈✡❈✍❉✏❊ ❅●❋ ❄☎❉❍❊ ❊ ■☞❊ ❂✘❀✄❏ ❅☎❂✟❆ ❉❍❊ ❊ ❑ ❆ ❉❍❏ ❉☞❆☎❄✄▲ ▼❖◆✷P P✄◗✄❘☎❙✼❚ ❘✚❘✡❯✟❱✟❚ ❙✞❲☎❯✡❙❨❳☎❩☞❬❪❭✖❫✡❴✍❭✟❵✟❛✄❭✘❜✄❝✡❞❍❡✘❢✟❣✡❤❪✐✟❥✟❦✡❧❨❣✄♠☎✐☞♥✷❧✟❥✄♠✚♦✡♣rq s t☞✉✘✈ ✇✡✇☞✈ q✄①✡②❨③✄④✟⑤✟⑥✄④✘q t ④✮⑦ ⑧ ⑨✏⑩✡❶☎❷✘❸✟⑨☞❹ ❺❼❻❍❽❍❾ ❿✟❿✘❾ ➀☎➁●➂☎➃✘➄✡➅✄➃✼➀✄➆✍➃➈➇ ❾ ➉☎➃✿➊✿➋❪➌✘➍✄➎✼➏✡➐✄➑☎➒✼➓❨➔ →✿➣☞↔✄↕✄➙✡➛☞➣✞➜✄➝✡➞❨➟✘➠ ➡✘➢✍➤☞➥ ➦➨➧☞➩✄➫✄➭✡➯☞➧✘➯➳➲✟➵ ➸✟➩✡➺☞➻☞➼●➽ ➾✘➚✄➪ ➶☞➪ ➹✍➘☞➴✄➷✘➪ ➶☞➹✍➘☞➴ ➬➱➮✃➽ ❐✄❒❍➪ ❮✟❮☞➪ ➹☎➶●➷☎❰✘Ï✡Ð✄❰✼➹✄❐☎❰☞➬ Ñ➨Ò☞Ó✘Ô✄Õ✡Ò➱Ö ×✄Ø❍Ù☞Ú Û✡Û✍Ü☞Ý☎Þ✟Ý ß✘à✘á✟â☎ã❪ß✡ä✚Ü❍Û✄â✍ß✘à✟Ü✼à✿å✘Ú æ✘Û✍ç✼è☎ç☞Û✄à✞â✡é❍Ú Þ✟Þ✘Ú Û☎æ å☎Ü✘ê✡á✄Ü✼Û✄â☎Ü✞ë Û✍ß✘ã Ü❍ì✡ã☎é✡Ü➈Ú Û✡Û✍Ü☞Ý☎Þ✟Ý ß✘à☞á✡â✄ã●Ú å✚ã✄é✡Ü❨å✄á✟í➳ß✡ä✿ã☎é✡Ü â✍ß✘í✷Þ✄ß☞Û✍Ü✼Û✄ã☎î ï✟ð✘î â✍ß☞í❪Þ✄ß☞Û✍Ü❍Û☎ã✷Þ✟Ý ß✘à✘á✟â☎ã å✡ñ ò❖ó✏ô✞õ✰ö✘÷☎ø❨ù➱ú✁û✮üþý➱ô✘ÿ✄÷✁✁✂☎✄✝✆ ✞✟✞✠✆ ✡☞☛✍✌☎ø✠✎☎✏✄ø✑✡✟✂✍ø✁✌✿õ✒✏☞✌✟✓✕✔✟ø✖✂☎✄✟ô✟✌☎ø✑✡ ô✘ÿ✗✓☞✄✟ô✁☛✄ô✠✡✍ö✠✘✟✓ ô✿ø✟ö✁✂✟✄✿ô✁✓☞✄✟ø☞ÿ✚✙ ✆ ✛ ø✑✛ ✠✆ ✡✟✡✍ø☞ÿ☞✞✟ÿ ô✢✜✢✏✁✂☞✓✕✣✕✤✝✥ ✦★✧✪✩✬✫✮✭✪✦★✯✱✰✳✲✴✧✶✵ ✷✚✵ ✸✕✵ ✯✱✹✺✩✬✻✱✼ ✽✒✵✗✾✿✼ ✲✴✫✶❀✱❀✍✲❁✸✕✸ ❂❄❃✚❅ ❅ ❆✁❇❉❈✕❊✁❋✁●✟❍✱❈☎■ ❋✁■✟❏ ❆✠❑✕■ ❆✱■☎▲ ❋✠❑✗❈✟▼✍❏ ■✒❆✁◆✗❊✠▲✚■☞❍✟❊✿❊✑❑☎■✟❏ ▲ ❊✿❖✁▲ ❊✢P✟◗☞❊✝❑☎●✗❘ ❈✟❙☎❊✠●☎■☞▲ ◗✁▼❚❋✠❅ ❅✟■☞❍✁❊✿■✟❏ ▼❯❊✑❱ ❲❄❳✿❨✠❩ ❬✟❭ ❪✠❩ ❫✿❴✢❭ ❵✒❨✠❩ ❬ ❛✢❜☞❫✁❝✁❨☎❴✕❬☞❞ ❛✠❜✗❴✟❵✍❭ ❴☞❴✢❭ ❝✠❜✗❴✚❛✢❞ ❫✱❴☎❫✠❪☎❛✁❞ ❛✟❬ ❫✑❡✿❨☎❴✢❭ ❜☞❢✿❣✗❝✢❡✝❭ ❜☞❢ ❬☞❤✁❫✁❝✢❞ ✐✠❥ ❦✺❧✠♠✑♥ ♥ ♦ ♣✝♦ q☞r✕s✁t ✉✢✈❯✇✁①✚✉✢t ✇✱✉✢♣✠♣✁✇✑♣②♥ ♦ q✗✇✁✉✢t✟♥ ③ ④✴⑤✢⑥✢⑦☎⑧✖⑨✝⑩ ❶✱⑩ ❷✱❸✝⑩ ❹✁⑩ ❸✁❺✑❸②⑩ ❻☞❶ ❼❁❽❾⑦☎⑧✝⑩ ❿☎❷✱➀ ➁✠➂✳➃✗➄ ➅✝➆✖⑦☎⑧✝⑩ ❿☎❷✍❿☎❺✠➇✍⑨✑⑩ ❶☞➈ ➉➋➊➍➌ ➎ ➏❯➐ ➑✍➒☞➓✢➔✚→☞➓✟➑☎➣✠↔✿➓✟↕✕➙✍➑✟→☎➣✠➒✢➐ ↕✠➐ ➒✕➒✟➛✑➐ →✁➜ ➑☎➝☞➞ ➣✢➙✁➔❾➟ ➔❯➙✟➑✁➠☎➡ ➢➋➤➍➥ ➦✝➧✒➨ ➩✍➫☞➭✁➯❁➲☞➳✢➵✚➸✢➺ ➯✑➵❯➯✑➻☞➫✒➳✟➼✍➫☞➭✁➯✖➵❯➽☎➩✁➾✚➳✟➼✱➥ ➚ ➪ ➶❄➹➴➘✁➷✱➷✢➬☎➬☎➷✠➮☎➱✟✃ ❐✗➷②❒✁❮✢❰☎Ï✠Ð❯✃ Ï✢➱☎➘②✃ Ñ✕Ò✟➬✍➱☞➘✁➷✿Ò✢Ó☞Ï✁➷✠Ó❯Ò✟➬ÕÔ Ö✟×ØÒ✟➬✱➱☞➘✁➷✿➬✟Ù✢Ú Ú Ñ✟Û☎➷✠➮☎➱☞Ó Ù✁× Ü★Ý✪Þ✬ß✮à✍á✿â✳ã ä✱å❄æ✚à✱ç②è❁éêè ë❄ì✟í☎î ï✚ð ñ í ñ☞ò ó☎ô❯ï☞í☞ð✒ò ñ ðõó☞ö✝ô❯÷✗ô☎ò ø☞÷✗ù✕î ï✁ò ú✒ð ù☎ø☞÷ ù✟ô☞î ù û✴ü☞ý☎þõÿ✁ ✂☎✄✝✆

✞✟

✠ ✡☞☛☞ÿ ÿ ✌✟✂✎✍✏✂☎✑✟✒✔✓✖✕✗✍✙✘✁✌☞þ ✠ ✚✖✍✟þ☎✌✗ÿ ✍☞✛ ✜ ✢ ✣ ✤✟✢ ✥✦✠ ý☞✧✝✍✖★ ý✟✠ ✍✩✞ ✚✔ ✄ ✪ ☛✖✆ ✌ ✍☎ÿ✫✛ ✬✭✣ ✢ ✥ ✓ ✮✰✯✝✱✳✲ ✴✟✵✷✶✎✸✟✹ ✺✻✱ ✼✖✽✎✸☞✹ ✾✁✵✝✿✟❀ ✱✖❀ ✿✫✹ ✲ ✸ ✲✟❀ ✼✖❁✻✱ ✼✝✽☎✹ ✵✝❁✁❂❃❀ ❁ ❄✏❅ ❆ ❇❈❀ ✹✎❉❃❉✔❉✭❆ ❆ ❉✭❆ ❆ ❊ ✵ ❊ ❀ ❋ ❋✖✽ ✵✖✾✖✽ ✵✖✹ ✵✝❁ ✲☞❀ ✲✳●✟❍✩■ ❏ ❆ ❏ ❆ ❏ ❆ ❑✖❆ ❑✟❆ ❏ ❆ ❑✟❆ ❑✟❆ ▲ ▼❖◆❈P ◗ ◗✟❘ ❙✝❚✖❘ ❙✖❯ ❙✖❱ ❲✫❲ ❳✖❙✏❨ ❳❃P ❚☞❩ ❙✝❨ ❲ ❬✖❘☎❭ ❬✖❘☎❯ ❲ ❪✁❲✁P ❬✖❱☞❫❈❴✁❪✟❱✁❵❛P ❲ ❯✫❱ ❙✟❜✟❪✁❲✟P ❬✟❱ ❝❡❞☎❢ ❢✖❣ ❤✔✐ ❥☞❦ ❧✖♠✟♥ ❧✝♦✟❣ ❧✝❦☎♣✖q ❧✏❥ ♣✝✐ q r✎✐ ❦ ❧☞s✖q t ❤✖s✁✉✟s✖♦ ♣✝❢ ✈✁t ❤✖♥✟❦☎✇☎① ②❃③✟④⑥⑤ ⑦✝⑧ ⑨❶⑩✭❷✟❸✏❹ ❺✖❻ ❼✎❽✝❾ ❿ ➀ ❸✝➁➂❿ ❹✁❹ ❸✔❻☎➃✖❻ ❺✟➁✔➄✟➅ ➆☎❺✖➇✫❽✟❹ ➈✏➅ ❷❃❿ ➃✙❿ ➉✻➊ ➋

−

= ≡

= i m i iT

S m T S 1 ) 1 ( 1 1

1 2 1

= ± = ≡

∑

= = m i i m i i

m S S m S S 1 ) 1 )( 1 ( 1 1

1 _ 1 _

− = − + = ≡

∑

= = m i i m i i

m S S m S S

➌➎➍➐➏➒➑➔➓✷→↔➣➙↕ ➛➂➜❡➝⑥➓➂→➂➛➂➞☞➟ ➠❡➡➤➢ ➥ ➦✁➥✟➧ ➨✟➩✻➢ ➫✖➩✁➭➂➧ ➥ ➢✻➯ ➲❃➧ ➳☞➢ ➫✖➵✟➸ ➫✖➩✟➯ ➫✏➺ ➨✝➻☎➼ ➽ ➾⑥➦✟➩✁➭➂➧ ➥ ➢✫➩✁➫✁➚✟➦✁➥✟➧ ➨✖➩✳➺ ➨✖➻✫➼ ➪✦➾ ➶❡➹➤➘✖➴✖➷✻➬ ➮ ➱✁➮✟✃ ❐✖➷✁➬☎➮✁❒ ➱✁➷✟➬ ❮✳✃ ➮✳➬✁✃ ❮☎❰✖Ï ➮ ➱✟➷ ➴✟❐✖❰✁➬✁Ï Ð✔Ñ✁➮ ➘✟➴❃✃ ❒☎➬✁✃ Ò✝➷ ➱✝Ï ➬✫➱✁Ó✔Ó➂Ï ✃ ➷ ➴✖➱✖❒ Ï Ð Ô➎Õ➐Ö➒×➔Ø✷Ù↔Ú➙Û Ü➂Ý❡Þ⑥Ø➂Ù➂Ü➂ß☞à á❶â✦ã✙ä å✔æ ã✖ç å✔ä✎è é✟å✷ê✔ë è✳ì è✁ä å✖í✖î➤ã✖ï✫í☞ì è í✁è✟ë ã✟ð✻ñ✦å✏ò✁ì å➂ë è ì✻æ é✔ë ó☞ì å✖ô✟ò å✖ð✖æ å õ✰ö✝÷✳ø ù✟ú✷û ú✝ü ú❃ý þ ú✖ÿ✁✔ý ø✄✂ ø✁û ú✆☎✞✝ ý ✂✠✟☛✡ ☞✍✌✠✎ ✏ ✑✒✏✞✓ ☞✞✔✖✕✘✗✙✓ ✏ ✚✜✛ ✢✤✣ ✏ ☞✍✌✠✥✧✦ ★ ✩✆✪✆✫✖✬ ✭✆✮✙✪✞✯✤✰✆✱✠✲✍✳ ✪ ✴✶✵✞✷✠✵✹✸ ✺✍✷ ✻✆✼ ✽✿✾❀✺❂❁✞✺✆✽ ❃✁❄✞❅✠❆ ❇✄❈ ✷ ✺✆❉ ✽✄❊ ❅ ❋

❃■❍

❅✠❆ ❇✄❈ ✷ ✺✆❉ ✽✄❊ ❏ ❋

❏ ❆ ❇✄❈ ✷ ✺✆❉ ✽✄❉ ❑✞✽ ▲ ❆ ❉ ❁

) 1 ( ) (

_ _ _

+ − + + =

+ + =

+ + = C D C C C B C A C D C B A C X D C B A X

SLIDE 8 ▼❖◆◗P❙❘❯❚✘❱❳❲❩❨ ❬✁❭❫❪❵❴☛❛✘❜❞❝❳❡ ❪ ▼❖◆◗P❙❘❯❢❣❬❳❚✘❱✁❲☛❪❵❤✘◆✐❪❵❚✘❱❳❲❩❪ ▼❖◆◗P❙❘✐❥❖❦❂❧♠❱✁♥✠♦✹❪❵❬✁❲☛❪❵♣❞❨ ❬✁❦❂❪❵♣✹q✘❪❵♣✹❪❵❬✁❚✘❪ ▼❖◆◗P❙❘❯r✧❚✁❱✁❬✁❦❂s ❲❩t ✉✙✈✠✇❵①③②✍④ ⑤⑦⑥✆⑧✧④✒⑨✍⑩ ⑧⑦❶⑦❷ ❸❫❹✤❺ ❻⑦❼ ❽✧❾✞❼✒❿✜➀✆❿✞❽✧❺ ❿✜➁✤❺ ❻✧➂➄➃ ➅✞❼✒❽✧❺ ➁✆❽✧❺ ❽❀➅✆❾✞❽✁➆✧➅✆➇❳➈ ➆✤➂✹➂✘➃ ➅✞➉ ➊ ➀✆❿✞❽✧➇❩➃ ➅✘➋③➋➍➌✤➌✧➎ ➏❫➐✤➑ ➒⑦➓ ➔✧→✞➓✒➣✜↔✆➣✞➔✧➑ ➣✜↕✤➑ ➒✧➙✶➑ ➛✤➜➞➝ ➒❳➙❂↔✧➟ ➓✍➝ ➐✞➛✤➓✞➠✁↕✆➛⑦➜➞➝ ➡✞➢ ➤➍➥✧➦ ➦ ➧✤➨✙➩✘➫❂➭✧➦ ➯✍➲ ➳✧➦ ➵❵➭✞➩✞➵❀➸ ➩✘➯ ➧❳➺ ➻✒➧✍➵✧➼➽➲ ➩✍➯✒➾✙➥✧➚✆➪❵➯✞➸ ➥⑦➚✒➩✍➫✘➲ ➯ ➩⑦➲ ➫❂➭⑦➦ ➯✒➥⑦➚✒➵✤➧✤➭✆➩⑦➦ ➶❳➨✖➲ ➯✞➹❵➫✘➲ ➚✤➲ ➫✖➥❀➦⑦➲ ➚✞➯ ➵✧➸ ➘✆➵✧➸ ➵➞➚✆➻✒➵➷➴ ➲ ➘❳➻✒➧⑦➪✤➵⑦➩✹➥⑦➸ ➵ ➺ ➧⑦➸✒➯✞➹✤➧✤➬✆➧✧➚✒➥❀➦ ➾ ➮ ➱❐✃✘❒✁❮❩❰❳ÏÑÐ✐Ò✘Ò✁Ó❵Ô✹ÔÖÕ❳×✹❰✁Ø❂❰❳Ò✘❰❳Ù Ô Ú❫ÛÝÜ✒Þ⑦ß✤à❵á✞â ã✧Ü✒ä✍å✘æ á ä✜ç⑦èêé✒ç⑦ë✆ì❀í✤î♠ï ð ñ➞ò✤ó✞ô✘õ❳ö✤÷✆ð ô⑦÷ ø❳ù✒ô✍ô⑦÷✞ú➞ð ó✒õ✍û✍ð ô✧ó õ✤ü✖ô✧ó✞ý❵ó✒ô⑦ú⑦ñ✤þ✍ÿ➞õ✤û✁✄✂✆☎ ☎✞✝✠✟✄✡☞☛✆☛✍✌✏✎✆✑☞✡✆✒ ✡✔✓ ✡✆✒ ✌✖✕✘✗ ✙✛✚✄✜✣✢✍✤✘✥✦✥☞✧✩★✞✥✪✧ ✫✭✬✍✥☞✮✄✫☞✯✩✰ ✱✠✲☞✳ ✳ ✴ ✵✪✶✪✷ ✸✆✹✻✺✆✼☞✽✔✾ ✼☞✹✻✾ ✿☞❀✍❁✄❂✩❃ ✹❄✿✆✹✩✾ ✿✪❀✠❅✄❆☞❂ ✹✆❃ ❂✁✼✄❁ ❇❉❈❋❊✄●✔❍✍■✪❏✠❑✪▲✄▼◆■☞❖✠❖✆P☞◗✻◗❙❘✔❚✞❯❙❱✄❲ ❳✄❨ ❳☞❩✍❳❭❬✠❪✆❱✠❫✪❩☞❴ ❵✪❴ ❫✄❪✣❛✆❳✄❜❝❨ ❳✔❞☞❫☞❨ ❫✪❩✠❨ ❩✍❳❭❬ ❬ ❴ ❪☞❴ ❳✪❡✍❪✩❢☞❡✠❞✖❛✆❳✄❜❝❨ ❳❣❲ ❫❭❩✍❳✄❤✍❫❭❲✁❵✄❲ ❳☞✐❥❨✻❛✄❫✪✐❧❦ ❤☞❴ ❢✔❞✄❫✏❬ ❢✠♠✆❫✪❞ ❲ ❫☞❨✻❲ ❢☞❡✍❪✄✐✦❴ ❪✻❪☞❴ ❳✪❡✍❪☞♥✠❵✠❳☞❲✁❫☞♦☞❢☞✐♣❱☞❬ ❫✪q rts✪✉☞✈☞✇♣①☞② ③✄④✩⑤✆⑥✣⑦ ✈☞⑧✠⑨☞⑤☞✇⑩✈✄❶✆❶✍③☞④✻④✦❷✖❸❺❹❻①✆⑦ ⑤✄❼ ⑤☞❶✻⑤❭② ④☞❽ ❾ ✈✄❿❋➀❺➁✄➂✩➃❋➃❺s✏➄❝❸✁➁✄➂✦➅❄❸ ❾ ➆ ❿✘❸✁➁✄➂✦➅❄❸ ❾ ❶✠❿✘❹➇➀❋❷✖❸❝✈☞⑧✠⑨❣❹➇➀❺❷❣❸✞➈✠❹✘➄ ➉➋➊ ➌✣➍❄➍❄➎❣➏➑➐◆➊ ➌✔➒✭➓ ➔❉→✞➣ ↔✞↕❻➣ ➙✦➛✏➣ ➜✄➣ ➛✄↕✪➛❻➣ ➝✠➞ ➟✦↕☞➠✆➡✠➢✪➤✠➙☞➣ ➥✻↕✔➙☞➤ ➟✄➞ ➙✣➦ ➧♣➨✆➡✪➤ ➤✆➩✠➢☞➫✆➭✻↕☞➞❄➙☞➣ ➥✠↕✪➯ ➲✛➳❣➵✍➸☞➺✁➻ ➼✣➳✄➽✻➽✆➾ ➚✄➾ ➵✻➪✦➶✠➹ ➳✆➹✆➾ ➘✪➵♣➹✠➽ ➳✪➵✍➶✆➴✦➾ ➹ ➶✩➳✣➹✻➷✄➸✖➬✄➸☞➪❭➾ ➵✆➵✄➾ ➵✻➪✦➘✆➮✦➹✻➷✄➸ ➵✍➸☞➱❭➹✁➶☞➻ ➘✄➹ ✃❒❐ ❮✔❰✍Ï❭Ð Ð ❐ Ñ☞❐ Ï✪Ò❄Ï☞❰✆❰✻Ó✄Ô Ñ✦Õ Ö✆Ñ✻Ñ✠Ó✄×✁Ø❣❰✆Ù✆Ö✪Ò✆Ò✍Ø➇Ð✠❮✠Ø✄Ø❭Ú❭Û✆Ö☞❰✆Ü☞Ý✠Ø☞Þ✣ß✻Ù✆Ø✖Ô Ø✪❰✻Ø➇❐ à✍Ø✪Ô ❐ Ò✻❮✠Ï☞Ô✍×✁Ñ✦ß✻Ù✄Ø✣Ñ✠Ï✄Ó✆Ô✻❰✻Ø✣Ï✆❮✦Ö✔❰✍Ï❭Ð Ð ❐ Ñ☞❐ Ï✪Ò✠á Ý✠ß✻Ù✄Ø✔Ñ✻Ï✄Ó✄Ô✻❰✍Ø✖Ô Ø✪ß✻Ô Ö☞Ò✍Ñ✆×✦❐ ß Ñ ß✻Ù✄Ø✖â✻Ö☞❰✆Ü✻Ø☞ß❄Ö✆ß❄Ø✄Ö✄❰✆Ù✣Ñ☞Ð Ï✄ß♣ã✁❐ ß✻Ù✖â✆Ô Ï✪Û✄Ö☞Û➇❐ Ð ❐ ß ä✔å☞Ý✠Ó☞Ò✻ß✆❐ Ð✻Ñ✆Ó✆❰✆❰✍Ø✄Ñ✠Ñ✻❮✆Ó☞Ð æ ç❉è❋é✆ê✆ê✍ë☞ì✻ì✦í è❺î ï✆ð✪ñ❭ò ò ó ì☞ó ñ✪ô✦í ð➇î ï✔õ➇ö♣÷✠ø ù❣í õ❭î➇ì☞ò ñ✄ø ì ú❉û❺ü ý✁þ✄ÿ✁✁ý✄✂ ☎✝✆✟✞✟✠☛✡✟✡✌☞✎✍✟✏✒✑✓✂ ✍ ✂ ✔✕✠✓✑✟✂ ✖☛✡✗☞✓✘✒✘☛✂ ✆✓✂ ☞✙✡✕✑✌✚✛✂ ✑✝✂ ☎✗✘✟✏☛✍ ✍ ✜ ✢ ☞✙✆✌☞✙✡✕✑✒✣ ✠✙✍ ✂ ✔✒☞ ✢✎✤

SLIDE 9 ✥✧✦ ★✁✩✪✩✪✫✭✬✯✮✰✦ ★✲✱✴✳✵✫✭✶✝✶✝✷ ✸✁✷ ✫✭✹✁✸✻✺ ✼✓✽✲✾✄✿✒❀ ❁✟❀✟❂ ❃☛❄✌✿✝❅✓❁✓❆✌❇✭❈✒❁✓❉✓❊✕❇❋❀ ✿✝❀ ❃✝✿✕❇✎❄✒●✎❍✒❁❋❄✒●✲❇✓❁❋❉✒❅✲❀✕■ ❁❋❄✌✿✟❏✝❂ ❀ ✿✭❂ ❄ ❇✓❁❋❉✒❅✁✿❋❑ ❃❋❀✪▲▼❂ ❀✕❅✭❈✓■ ❃☛◆✓❁❋◆✎❂ ❑ ❂ ❀ ❖◗P❙❘✟❚✕❯✓❱✭❲✓❳ ❨☛❩✟❬☛❩✙❭ ❪ ❭ ❚ ❫✝❨✟❴◗❵✟❛✟❜✟❜✌❱✓❵✕❵✒❴✟❛❋❪ ❚✕❳ ❬❋❝✌❵✟❞✝❭ ❵✕❵❋❭ ❨☛❝✝❡❣❢ ❤❋✐ ❥✓❦❋❧▼♠✲♥✒♠✓❧✌♦✟❢ ♣✒q☛r ♠✓❧◗s✌❦❋t❋✉✎✈✓✇✻①✪②✭③ ④✒⑤ ②❋⑥ ⑦ ⑧✎⑨ ⑩ ❶ ❷✓❸❋❹▼❺❋❻✗❺✓❹✒❼✎❽ ❾✕❹ ❺❋❹ ❿➀❻✌❸❋➁✓➂✲❸✟➃✝❾✕➄✓➂➀➅✁➆ ➇➉➈✪➊✟➋ ➌☛➍✭➎ ➌☛➏✓➐ ➑✝➌✙➏✌➒✲➓✕➋ ➔☛➏✌→✟➣✝↔ ➓ →✓↕➛➙◗➜❣➝➀➞ ➟✕➠ ➝❋➡ ➢ ➤❙➥ ➦ ➧ ➨◗➩✟➫✟➭ ➯▼➲✙➳✒➵✌➲✙➳ ➸✒➺✁➻✟➼✲➽❋➾✲➽✝➚✲➪ ➶✓➹ ➘✓➻❋➴▼➺☛➷❋➲✓➯✗➩☛➳ ➺✎➬☛➭ ➼✲➹◗➚✓➮✎➬✓➱✻➚✁✃ ❐ ➘✓➻❋➴✗➹❒➵✌➺☛➴ ❮➀➳ ➲❋➴✌❰✒➺✲➻☛Ï✌➺✲➼☛➭ Ï✒Ð❋Ñ✝➱➛➚✲➪ ➶✕➺➀Ò ➲✓➩✓➩✓➴ ➻✓➷❙➭ ➯▼➲✓➫ ➺✎➳ ❮✙➬❋✃ Ó❋Ô❙Õ Ö✁×✁Ø✪ÙÛÚ ×✁Ü✁Ý◗Þ ß✲à✪à▼Ù➀á â✄ãåä✭æèçéã êìë▼í î✓ï✌ï ð✙ñ✭ò▼ó✓ô✝õ✪ò➉ö ð❋÷✟ø☛ù ö ð✓ú◗ú❋í î✓ï✪ú✕û☛ü✒ý✒þ☛ö î☛ü✓ù ÿ✁✟ï✟ù î☛ü ✂☎✄✝✆✟✞ ✠☛✡✟☞ ✌✎✍✑✏✒✌✎✍ ✆✟✞ ✓✕✔✗✖✗✡✁✘✗✍ ✌✙✄✛✚✟✜✣✢✤✄☛✖✗✥✗✓✦✌✗✆✧✔✒✓✗★✩✍ ✌✕✪✁✘✕✞ ✍ ✌✧✆✟☞ ✓✗★✒✆ ✫☎✬✮✭✒✯✟✰✗✱✳✲✵✴ ✶✕✭✒✷✦✸✣✹ ✲ ✷✣✺✤✹ ✲✁✻✦✯✗✼✦✲✑✶✦✺✽✶✕✹ ✲✦✹ ✭✵✾✩✿✦✯✟✴✑✲✵✻✗✱✙❀✗✱✟✾✎✹ ✭✦✭✗✹ ✭✵✾✣✯✦✿✩✶✣✷✟❁ ✯✗✲ ❂❄❃✕❅✎❆ ❆ ❇ ❈✟❇ ❅✕❉✣❊✗❋ ❅✕●✗❍✟●■❇ ❆ ❇ ❏ ❑✙❇ ❉✁▲✁❋ ▼✗❍✦❈✵▼✗❈❖◆ ❊✁❍✗▲✦P✵▼✟❏✩▲✒❍✕❉✩▲✵❅✎❆ ❆ ❇ ◗✗▼✳❘✤❇ ❏✵❙❖❅✗❏✁❙✦▼✎❋ ❊✁❍✗▲✦P✵▼✕❏ ❈✩❘❚❙■❇ ▲✦❙❖❍✗❋ ▼✳❏✵❋ ❍✟❉✒❈✦❯✣❇ ❏✒❏ ▼✕◗✳❘✤❇ ❏✵❙✎❇ ❉✑❍❖❘✤❇ ❉✁◗✗❅✗❘✝❏✒❘✤❇ ▲✵▼✧❍✁❈ ❆ ❍✟❋ ❱✦▼✧❍✁❈✧❇ ❉✩❲❚❳ ❨✑❆ ❅✟❙✦❍✟❩ ❬☎❭❫❪✕❴ ❵✟❛✁❜✟❪✟❝✦❛✦❞✣❡ ❢✣❴ ❣✕❤✕❛✦✐✵❣✕❤❦❥✦❧❖❵✕♠✒❣✳❪✗♥✕♦ ♣✕q✟❡ ❣sr❚t✧✉ ✈✦✇ ①✟❣✕② ③⑤④✙⑥⑧⑦⑨③❶⑩❸❷❦❹☛❺❖❻❖❼✧❷❾❽✧❻❖❿➁➀✎❽✧❻❖❹✑➂ ➃✣➄❖➅ ➆✩➇ ❺✧❿✑❿✑➂✳➅ ➈ ➉ ➉ . ➊ ➋ . ➌ ➍ . ➎ ➏ . ➐ ➑ ➑ . ➒ ➓ ➓ . ➔ → → . ➣ ↔ G (number of attempts per packet time) S ( throughputper frame time ↕⑤➙✙➛⑧➜⑨↕❶➝☛➞✣➟❾➠✳➡⑨➠✳➝⑧➝✩➢✣➡⑨➡⑨➤❖➥✑➦ ➧✳➠✳➨ ➩➭➫➲➯ ↕❶➳ ➩ ➤❖➥✑➥☛➦ ➠✳➥ ➫ ➠✳➵❖➝☛➠ ➯ ➢❖➸ ➺✑➦ ➻✧➸ ➠➼↕⑤➞❖➞✣➠✳➝☛➝✩➽ ➾➪➚■➶✤➹✧➘✩➴✎➷ ➬ ➮✁➱ ✃■❐✣❒✗✃✗❮✁❰✟Ï ✃✳➱✵Ï Ð✟❐✒➮✦Ñ✣➬ ➱✁Ò✵Ó✗❮✧Ô✁Õ✗Ð✟❐✦❐✒✃Ö➷✟➬ ➮☛➮✵✃■❐✒➮✵✃✕×❦❒✟Ø✵➮✵Ù✎Ú ×✗✃✟❮✁✃✕Ï✑➱✵Ï Ð✕❐✒➮✦Ñ✣➬ ➮✵➮✟➬ ❰✕❐ Û❄Ü✁Ý✕Þ✒ß✗à ß✁á✒Ý✟â✁á❸ã■ä❚å✳æ☛ç✟è é✟ê✵è ë✙ì í☛í✤é✕î■ì ï✦ê éÖð ë❖ñ❚ò✗é✎ó✩ô✦ò✦ï✕ó✦ó✒é■ð✟õ✦é✎ô✒ö✟í✤é✗÷ ì îÖð é✙ø ê✵ò✎ì ÷❖í✛ï✦ë✧ô✒ï✗ù✁÷✵é❦ì ó✒÷✁ê ï✕õ✎ì ð ì ê ë✟ú û☎ü☛ý✗þ ÿ ✁✄✂✆☎✞✝ ☎✠✟✆✁ þ ✟☛✡✌☞✎✍✑✏✓✒✄✔ ✕✄✖✠✔ ✗✙✘✛✚✜✖✆✕✢✔✣✔ ✘✄✤✛✥✄✦✄✧✩★ ✤✠✖ ✕✢✔✆✪✆✘✢✫ ✬✮✭✰✯✞✱ ✲✴✳✄✵✆✯✷✶ ✶ ✸ ✹✄✸ ✯✷✺✆✹✙✻✎✼✛✽✾✹✛✱✜✸ ✶ ✶✠✲✄✿❀✸ ✹✛✱✜❁✛✹✄✸ ✺✛✵✆✲❂✱✆❃❀✯✾✹✛✱ ✼✜✱✜✸ ✯✢✺✆✹✾✻✎✼✛✽✙✹✠✲✌✺✆✹✠✲ ✱✠❄✞✲☛✵✛❄✞✼✄✺✜✺✆✲✌✶✢✸ ❅✴✶ ✲✑✼✜✱✣✱✠❄✜✲✑✹✠✼✄✻✎✲✑✱✞✸ ✻✎✲☛❆✌✯✄❇✙❈✜✲✄✱✠✱ ✲✢❇✜❁✛❃✰✸ ✱✠❄✌✸ ✺✣✼ ❉ ❊✠❋ ✶ ✺✆✲✷❇ ✼✢❈✷✶ ✲✄●❍❃✎✸ ✺✛❅✄✯✞❃❏■✙❇ ✯ ❋ ✺✛❅✑✱✠❇✜✸ ❑✾❅✞✲✌✶ ✼✛✽✄▲ ▼❖◆✷P✙◗✆❘✛❙✠❚✑❯✜❱✑◗✆❯✷❲ ❲ ❳ ❙✄❳ ❯✢P✞❨✛❩✠❬✞❚✑❚✷P✠❩✜❳ ❭ ❚❂❪✄❫✛❩✰❩✛❭ ❘✢P✆❙✜❴✙❳ ❙✠❙✢❳ ❯✢P✓❩✜❳ ❴✎❚❵❳ ❙ ❛ ❘✛❙✜❩ ❚✢❜ ❝❡❞✩❢❤❣❥✐✙❦✑❧ ❧ ♠ ♥✣♠ ❦✑♦✾♥

SLIDE 10 ♣❡q✩r❤s✉t✙♣❡✈①✇✢♣❡②✾③ ③ ④ ⑤✓④ ②✾⑥⑦✈✉⑧❂⑨✰⑧❂⑩✙⑨✰④✆②✾⑥✾❶ ❷❖❸✌❹✎❺✑❻❽❼✛❸❿❾✎➀✄➁✆➂✄➃✆➃✜➄ ➅✢➃✎➆✠➅✌➇✆➆✄➄ ➇✠➈✙➂✢➇✛➉❂➉✄➅✞➊✛➅✢➃✠➃ ➂✢➋✢➋ ➄ ➌✆➅❵➄ ➇✣➍✌➎❍➏❂➐✰➑✄➒✢➓✛➔✞→ ➁✆➣✷➋ ➋ ➄ ➆✄➄ ➣✢➇✆➆✓➂✞➃ ➅❂➉✄➅✄➔ ➅✷➁✠➔ ➅✢➉❂↔✎➄ ➔✠↕✷➄ ➇✰➂✙➊✛➅✢↔➛➙✌➄ ➔✣➔✜➄ ➜❽➅✄➆✞➑ ➝✮➞❿➟ ➠✄➡✆➢✜➤✙➥ ➢✠➢✄➥ ➦✢➡✾➥ ➢✓➧✠➨✞➩✷➡✣➠✄➫✞➦✄➟✆➧ ➩✢➭✌➯✞➟ ➩✢➭✄➲✞➳✞➥ ➡✠➵✾➧✠➨✞➩❂➳✜➨✜➠✢➡✜➡✆➩✌➸✜➺❀➠✛➢✛➧ ➠✞➵✛➩ ➳✆➦✢➡✆➢✢➥ ➭✞➩✷➟ ➠✢➫✷➸ ➻✄➼ ➽✮➾✴➚✄➪✄➶ ➹✆➘✷➴ ➴ ➚✷➷✴➬✜➮✢➱ ✃✞❐ ✃✠❒✆➮✢❮✛❒✓❰ Ï✢Ð✠❰ Ñ✄Ò✆Ó✜Ô✙Õ Ó✠Ó✄Õ Ö✢Ò✑Õ Ó❂Õ Ô✣×✢Ø Ï✢Ô✎Ï✌Ò✠Ð Ï✢Ù Ú⑦Û✢Ü✷Ý Ý Þ ß✄Þ Ü✢à✙á✞â✄ã✆â✢ä✠ã✞Þ Ü✢à✑Þ ß✓å✞æ✄ç✠èêé ë❵ì✎é í✆å✞îêï✞ð✰ñ✣ç✙ò ó✢ô✢õ✄ö✷÷ ø✆ó✢ù✠ú û✄ü✆ý✄ø þ ó✞ý✜ÿ✁✄✂ ó✑ÿ✆☎ ô✄ø✆ý✞✝✛ÿ✛ù✟✂ ó✷ø✠ô✞ù✟✠☛✡✢ø✓ù✟✠✜ó☞✝ ☎ ø✆ó✌õ✁✡✆✂✣ü✌✡✞✍✞ó✏✎✑☎ ✡✒✝ ý✞ù✄☎ ✡✢ø✠ÿ✄õ✟✡✆✂ ü✌✡ þ✔✓ ý✑✂ ó❂ù✌✕❂ý✄ø✁✍✖✂ ó✢ü✠ó✗☎ ✎✆ó✑ÿ✆☎ ô✄ø✆ý✒✝ ÿ ✘✚✙✞✛✒✜ ✜ ✢ ✣✆✢ ✛✞✤✦✥✑✧✆★✌✧✞✩✟★✑✢ ✛✞✤✔✪✁✫✞✬✄✬✁✭✄✮✰✯✞✱✳✲✞✭✑✬✁✱✵✴ ✬☞✶✷✴ ✸✌✱✒✹ ✱✑✺✟✺✼✻✑✽✷✾✔✺✦✿ ❀✟❁✑❂ ❃ ❂✞❄✟❂✗❅ ❆✌❂ ❃ ❅ ❇✔❇✄❁✆❈✄❀❊❉✄❋✁❋☛●❍❁✒❅ ■ ❂✏❀ ❃ ❏✆❑ ❇✄▲✦❅ ❀✌❀✄❅ ❑✟▼✞◆ ❀ ❉ ❏ ❆✌❉✒❅ ❖✖❖ ❏ ▲ ❏✄▼ ❅ ❑✟▼ ❅ ❀

❊❅

❀✟❁☛❂✆P✒❄✟❂✑❇✟❇☛◗✟❉✆●❘❂ ❃✟❙ ❚✚❯✗❱❍❲✏❳❩❨✁❯❘❬❪❭✟❫✆❴✔❫✑❵✑❵✑❛ ❜✄❫✆❭✁❝✏❭✄❝✄❫✞❴✄❴✌❞✗❡✄❢✁❣✑❤ ❡ ❤ ✐✟❫✑❣✄❤ ❜✞❴✦❥✑❦✷❤ ❴✦❧✑❳❊♠✷♥☛♦ ❡ ❜✑♣ ❛ ❫✄❣✄❤ ❜✦❜✄qr❵✑❛ ❜✆❵✁❫✄s✄❫✄❣✄❤ ❜✞❴✷❜✑t✟❞✞❛✔❵✁❫✑❭✑✉✌❞✞❣✷❣✟❛ ❫✞❴✌♥✄✈✦❤ ♥✟♥✆❤ ❜✞❴✔❣✑❤ ✈❊❞✞✇ ①❪②④③⑥⑤⑧⑦⑩⑨ ❶✷❷⑥①✼❸r❹ ❹ ⑨ ❺✔⑨ ❸r❻✚❼❾❽✏❶✷❽✏❿☛❶✷⑨ ❸☛❻ ➀ ①❪②④③⑥⑤➂➁✦①❪❼❾➃ ➄➆➅✷➇✄➈✆➉✌➊✔➊✟➉ ➋✆➌✌➍✄➎✦➏ ➍✟➍✆➏ ➈✞➌r➏ ➐r➑✌➈✒➒ ➒ ➏ ➍✆➏ ➈✞➌✷➈✆➑✄➑✟➓✑➉ ➍ ➔④→✷➣✖↔✌↕✑↕✞➙✏➛ ➣r➛✟➜ ➝✆↔✌➞✄➟✦➠ ➛✷➛✟➡✑↕✏➢❍➡✑➣✒➤ ↕r➥✑➜ ➝✆➟❊↕r➢❩➡✄↕✗↔✦➦✑↔✌➣✑➢❊➠ ↔✟➧✖➠ ➛✷➢❊➠ ➤ ➤ ↔✌➣✑➛✷➝✑➜✟➜✄➠ ➨✌↕✖➩❊➫✑↕✆➛✌➛ ↕✒➜✔➭✁➡✑➝✆↔✄↔✌↕➯➤✁➲✄➛✄➠ ➤ ➠ ➳✁➝✄➛✑➠ ➣✞↔ ➵➺➸✒➻✆➼✄➽✄➽✁➾✞➚✁➪✄➾✞➶ ➹✑➾✏➘ ➴➬➷✑➮✟➱✆✃ ➱✆❐✟❒ ❮✆❮✞❰r➱✁Ï✄❒ ❮✒✃❊➴✟Ð✆Ñ❊❮☞➘ ❐✑➘ ❒✄➘ ➱✒Ò✆Ó✟Ô✑Õ➯Ö ×✆Õ➯Ö Ø Ô✑Õ Ù ×✑Ú✄Ø Ô✆Û Ü➆ÝßÞ✑à✏á✟â✞ã✟ä à✒ã✟ä✑å â✞ã✦æ✟à✒ç✁å â✆è☞å é✦ä✌ê❊å á✟à✏ä✟Þ✄à✖æ✑ç â✆æ✟ë✑ì✁ë✑ä✄å â✞ã✦è✑à✗í ë✁î ï➺ð✞ñ ò✑ó❊ô✖ó✷õ✁ö✁÷✔ø✑ò✄ù✟ô☛òró✦ú û✑ú ó✷õ✑ó④ü ô✗û✟ý✄÷✟ø☛þ✁ÿ✆ñ✷ö✟ô✒û✁✑ô✒ñ✷÷ ÿ✂✑ô✆÷ ô☎✄✟÷ ✄✌ÿ✒ü ü ú ö✆ú ÿ✞û

τ−ε τ

✆✞✝✠✟☛✡✌☞✎✍ ✏✒✑☛✆✔✓✖✕ ✕ ✍ ✗✘✍ ✓✖✙✛✚✢✜✂✏✒✜✂✣✤✏✒✍ ✓✤✙

(Tanenbaum)

✥✞✦✠✧☛★✪✩✫✥✞✬✮✭✫✯✖✰ ✰ ✱ ✲✘✱✳✯✤✴✛✵✷✶✂✸✒✶✂✭✤✸✒✱ ✯✤✴

(Tanenbaum)

✹✻✺✎✼✫✽✖✾ ✿✤❀❁✺✎❂✤❃✒✿✖❄✘❅✠❆☛❇✪❈❊❉✂❃✒❋✖●✒❋✤❍✤❋✤■ ❄ ❏❁❑▼▲✫◆✁❖◗P✒❘▼❙❯❚❱❖❳❲✳❙✖❨❩❙❳❙❭❬✘❪❩❚❳❖❱❪✒❫◗❴❱❵◗❛❱❛❱❜❞❝❢❡✁❵❞❣✳❤❱✐ ❤❱✐ ❥❳❛◗✐ ❛✁❦✖❧❯♠❢♥ ♦❳♣ q◗r q◗s✳q☎t ✉✤✈ ✇②① ❧④③◗⑤ ① ❧✢⑥◗⑦❱⑧✖♥ ① ❧❯♠②⑨ s ⑥◗⑦ ✉❱⑩ ⑥ ♣ ❶✂r❩⑩❱❶❯s❱⑩ ⑥❞⑦❱⑦ ❶❭t ❷ ⑥❞❸ ♣❱t ❹❳❺✻❻❳❼❱r ⑥ ✉ ❸ ⑦❩❽ t ❶✖✉✁r ⑥ r ❸ q ⑦ s ⑥❞⑦❱⑦ q❳r✘❼❩✉❩❶ ❸ r ⑥ t t ❾✛❿❭➀◗➁❱➂❞➃❳➄➅➀◗➆✁➆✁➇◗➈❩➈✤➉✂➊②➋④➌❳➍ ➎❳➏ ➎◗➐✳➎☎➑ ➒➔➓❞➑ ➑ ➎❳→✔➓✫➒◗➣ ↔❩↕❞➑ ➙✂➛✁➒❩➙❞➍✒➜❱➛◗➑ ➑ ➐✁➝❳➓◗↔❱↔❩➙❭➑❱➍ ➓❳➏ ➙◗➞✻➟◗➛✁➏➔➐✳➓❞↔❱↔✳➎❳➏➠➒❳➝❱➓◗➍ ➙✂➏❩➝❳➙❯➐✁➝❳➓◗↔❱↔✳➙✻➑❩➜✁➓☎➣ ➍❱➑ ➡✖➢ ➣ ↔✒➜✁➓◗➐❩➏❱➤ ➥✁➦❞➧❱➨❩➩❱➫ ➭✷➯ ➲➔➳❱➵❱➸ ➺☎➻✘➳❞➼❱➲❩➺☎➽ ➾❩➺❞➚❞➪ ➶❁➹✘➘ ➴❩➷✤➬✁➮❱➱☎✃ ➱✖❐◗✃ ➱✂❒ ➬✳❐◗❮◗❰ Ï❩Ð✤➬✳Ñ❳✃✁Ï✳➴✁Ò❢Ó❳✃ ➷❳➬ ➷◗Ô❩➷☎➘ ➴❳Õ Õ Õ

SLIDE 11 Ö✻×✎Ø✫Ù✖Ú Û✤Ü❁×✎Ý✤Þ✒Û✖ß✘à✠á☛â✪ã❊ä✂å✒æ✖ç✒æ✤è✤æ✤é ê ëíì❢î◗ï❞ð ñ✁ò✔ì②ó❱ô✳ñ✁õ✞ö✂÷②ø④ù❳ú û❳ü û◗ý✳û☎þ ÿ✁❳ý✄✂✆☎ ✝✟✞✠✝☛✡❳û❳ü☞✂✍✌✎✏☎ ú✎✑✠✝❳ÿ❩ÿ✒✟✑✎✓✔✌✄✕❞þ þ ú ❱ü ✝✗✖☞❳ü✒ü☞✂✘✝✔✝✟✙☎ù✎✝✏✑✳ÿ✎✝✤û✄✌✫ÿ❩û✟✚✛✝✔✝✟✙❞ü✁ú ✖ý❩û✜✑❩ü❩ú û☎þ❩û✘✞✠✝☎ú☞✂✄✝✘✟✓ ✢ ✣✟✤✦✥✄✧✟★ ★ ✩ ✪✎✫✭✬✯✮✔✰✍✮✄✱✎✲ ✳✜✴✵✱✎✲ ✮✄✲✄✶ ✷✜✸✵✷✏✸✵✮✔✹✘✺✛✻✼✶ ✸✒✲✠✽✘✴✎✸✁✾ ✶ ✸☞✿✘✶ ✲ ✳✘✱✎❀ ✲☞❁✘✳✔✱✟❂ ✮✄✿✠✳✔✱✎✲ ✮✘✲✄✶ ✷✜✸✠✱✦✲ ✷✔✲☞✴ ✮✟✸✠✱✄❃✦✶ ✲✵✲☞❁✘✳✆✶ ✴✁❄✎✮✘❅✄❆☞✳✜✲ ✱✦❇ ✽✘❄✦✲ ✷✍✮✔✰✍✮✄❈✆❉ ❊ ❋ ✴ ✷✜●✏❂ ✳✏❃✛✱✟❍✟■✜✳✟❏✄✽✎✳✘✱✎✲✁✲ ✷▲❑✗✳✆✸✎▼✟◆✎❖P❂ ✳✟✮✘✴✵✲ ✷▲❑P✳✏✸✎▼✔✷✘✿✠✳✜✴☞❁✘✳✘✮✘▼✗◗✟❂ ✮✘✲ ✳✏✸✎❅☞❘✏◗ ✱✟✶ ✸☞❙✜❂ ✳❚❄✎✷✏✶ ✸☞✲✵✷✄❯✒❯✎✮✏✶ ❂ ✽✄✴ ✳❚❇ ✰✍✮✄✱✎✲ ✳✜✴☞❉ ❱ ❲✜❳✒❨❬❩✘❭✄❪✟❫❵❴✄❛✟❜☞❜✘❝ ❫✄❞✏❡✘❢☞❣✘❤▲✐☞❥✜❦☞❢☞❧ ❥✏♠☞♥☞♦✘♣✎q✜rts ✉✦✈✎✇✎✉☞✉✎①✜②✔③✘④ ⑤✜⑥⑦⑤✜⑧✠① ⑧✠⑤✟②✘①▲⑨ ⑤✔⑨☞⑩✘①❚⑧✠①✜❶✜⑨✵✉☞①✟❷✄❸☞①✆⑧☞⑨✄s ✇✏❹ ❹ ❺✜❻✎❼✜✇✜⑧✵✇✜❹ ❹ ①✟❽✘s ✇✄⑨ ①▲⑨☞⑩✘①❾❹ ✇✄⑨ ①✆⑧✎❿✠❺✦✇✜⑧✎② s ⑥✁✈✘④ ⑤✘❽✠①✔③✎✇✄❸✜❹ ⑨✁⑨ ⑤✏❹ ①✜④ ✇✜⑧✎❿✠①❚➀ s ⑧✁✇✍⑨ ⑤✜➁☞①✏⑧✦➂✟❸✎✉✦❿☞⑤✜⑧✠③✜s ➃✘❸✄④ ✇✘⑨✄s ⑤✜⑧✎➄ ❻✘➅P⑨✘s ❹ ❹ ➆ ①✆❹ ✇✜➂✄⑤✜④ ✇✘⑨ ①❚✈✄④ ⑤✟❿☞①✜②✟❸✘④ ①✘✉✦⑨ ⑤✔④ ①✜❿☞⑤✘❽✠①✜④✛③✟④ ⑤✟⑥➈➇ ➉✄➊☞➋❚➋☞➉✘➌✎➍✜➎✜➏P➐✟➑☞➒✘➓ ➔▲→↔➣➙↕✵➛▲➜✍➝☛➞✍➟✔➠ ➟✔➡✔➢ ➛▲➤ ➥➧➦▲➨✯➩☛➫✘➭ ➯✘➲ ➯✟➳☞➯✏➵ ➸✒➺✎➸☞➻✜➼❾➽ ➾✒➚✘➨✛➪✵➸✟➶✄➲ ➯▲➳✠➯✜➾☞➲☞➭ ➯✏➵✎➹✘➳✄➳✠➻✘➸☞➸✦➲ ➯✔➲☞➘✄➻ ➳✎➘✘➹✟➾✄➾☞➻✆➵ ➴➬➷❬➮✘➱✎✃✜❐❵❒✭❮ ❐✎❰✄Ï✟Ð✄Ñ✏Ò✆Ò✗Ò☛Ó✜Ô✗Õ✆Ö ×❚Ø Ñ✆Ù✜ÚÜÛ Ý✜Þ☞ß✏à✦á✄â à☞ã✘ä å✎æ✎Ý✟á✁ç☞Ý✟è✁é✎ê✄Û ß✏á á Ý✄Ý✟è✦å☞Ý✟á✍ë✗ß✜é✎ì✘á✠Û☞è✛ß✏à☞Û✒ç✠Ý✜à✄à✠ß✏ç☞Û✄â í✘â Û✠î✜å✄ê✘é✦Û Ý❚ï ð✏Ú☛ñ✟é✎ò✎ó✗ô✆ë✯ë✗Ñ Ø ô✆â ñ✄ß✏á✦ë✯â ò✎Û✎á✎â ñ✘ê✄Û ß✏õ☛ë✗ì✘Û ì✦Ñ✏à☞Û ß✜á æ✎ì✟ç✠ß✜ä å✎æ✎Ý✟á✵ö✜ì✟è✁é✎ê✎ò✒ì✟à✎õ❚Ú✍ß✟Û✎á Ý ç✠Ý✜à✄à☞ß✜ç☞Û✄â í✘â Û✠î✜å✄ê✘é✦Û Ý▲Õ✜Ô✆Ô❚ò✎Û ì✄Û✄â Ý✜à✠ò✟å✎ì✄Û✍ï Ô✏Ô✗Ú❚ñ✜é✎ò✘Ö ÷➧ø✜ù✄ú✄û✜ü✠ý✎û✟ù✠þ✟ÿ✁✄✂✆☎✞✝ ✟✁✠☛✡✌☞✁✎✍✑✏✓✒✎✔✖✕✗✍✙✘✚☎✁✛ ✟✜✡ ✟✞✢✌✟✄✝ ✣✙✤ ✥✦✒★✧✩☎✌✪✬✫ ✭✄✮✑✮✑✮ ✯ ✥✦✰✑✱ ✲✩✳ ✴✞✵✜✶✗✪✗✡✷✮✄✸ ✹✺✞✡✻✫ ✤ ✥✄✥✦✒★✧✩☎✗✪✁✳ ✴✗✼✾✽ ✿✗✶✎✮✄✸ ✹✺✞✡✻✫ ✤ ✴ ✥✑✥✄✥❀✒❁✧✞☎✗✪✁✳ ✣✦✧✜✠ ❂ ✶✜✛✆✡✌☞✁★✂❃✟✁✪✗✡✻☎✗✟✞☎✗❄✩✝ ✶✞✛✆❅✜✔❃❆❇✡ ✩✢✗☞✄✹✺✟✄✝ ✟✜✿✁✠