3rd International Symposium on Quality Electronic Design: Proceedings 2002 March 18-21, 2002, San Jose, California 9780769515618, 0769515614

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3rd International Symposium on Quality Electronic Design: Proceedings 2002 March 18-21, 2002, San Jose, California 9780769515618, 0769515614

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Trading off Reliability and Power-Consumption in Ultra-Low Power Systems Wayne Burleson ✁✄✂✆☎ Russell Tessier Atul✝✟Maheshwari ✞✡✠☞☛✍✌✏✎✒✑✓✞✕✔✆✎✗✖✙✘✛✚✗✜✢✞✤✣✕✎✒✌✏✥✦✣✤☛✍✜✧☛★✔✪✩✬✫✭✖★✑✮✠✰✯✱✎✡✞✕✌✛✚✗✔✳✲✄✥✴✔✰✞✤✞✕✌✏✥✴✔✳✲ ✵✶✔✆✥✴✷★✞✕✌✤✸✤✥✴✎✺✹✻✖✼✘✾✽✿☛★✸✤✸❀☛❁✣❃❂✱✯❄✸✕✞❀✎✺✎✦✸✤❅✧❆✛✑❇❂☞✞✕✌✤✸✏✎✦❅❈✽❉❆❋❊❁●✄❊❁❊✍❍ ✚✗■✡✑✓☛★✥✴✜✢❏✮❑✱☛★✑✓☛▲❂☞✞❀✸▼❂❄◆❖❅✒P✕✯✱✌✏✜✢✞❀✸❀✖✍✔☞❅◗✎✡✞✏✸✤✸✏✥✦✞✕✌✤❘❚❙❯✞✤✣✏✸✕❱❲✯✱✑✓☛❳✸✤✸✕❱✴✞❃✩✍✯

Abstract

✫❖✌✏✥✴✎✒✥✦✣✤☛★✜❖✸✏✹❳✸✏✎✡✞❀✑✟✸❨✜❩✥✢❬❁✞❭✠✆☛✄✣✤✞✕■✡✑❪☛❫❬✄✞✕✌✤✸✤❅✛✩✄✞✒❴❵P✕✌✏✥✴✜✴✜✢☛★✎✡✖★✌✤✸✤❅❯◆❛✞✤☛★✌✏■ ☛✄P✕✜✢✞❪✣✤✖★✑✮✠✰✯✱✎✡✞❀✌✤✸✟☛✍✔✰✩✻✖✍✎✴❂✆✞❀✌❜✞❀✜✢✞✤✣✕✎✒✌❃✖★✔✆✥✦✣❝✲✳☛✄✩▲✲❁✞✕✎✦✸❭❂✆☛★✷★✞❜✎❞✖❉P✤✞ ✩✄✞❀✸✏✥❡✲✍✔✪✞❃✩❢✔✪✖★✎❨✖✍✔✆✜❩✹❪✘❀✖★✌❣✌▼✞✕✜❩✥✦☛✄P✕✥✴✜❩✥✴✎✺✹❤P✕✯✱✎❇☛★✜✐✸✕✖❪✘❀✖✍✌❉✯✱✜❩✎✺✌▼☛✍■✡✜✢✖★◆ ✠☞✖✍◆❛✞❀✌❤✣✤✖★✔✆✸✤✯✱✑✮✠✰✎✺✥✦✖★✔❥✩✍✯✆✞❦✎❞✖❧✜❩✥✴✑❜✥✴✎✡✞❃✩♠P✤☛✍✎✒✎✡✞❀✌✏✹❧✜❩✥ ✘❀✞❫❱♦♥✪❂❄✥♣✸ ✠☞☛✤✠☞✞✕✌❣✞❃q❀✠✰✜✢✖✍✌▼✞❀✸❣☛★✌▼✣✤❂❄✥✴✎✡✞✤✣❀✎✺✯✱✌▼✞❀❅❭✜❲✖▼✲✄✥✦✣✿☛★✔✪✩r✣✕✥✴✌▼✣✕✯✱✥✴✎✾✜✢✞✕✷❳✞✕✜s☛✤✠✰■ ✠✰✌▼✖❫☛✄✣✤❂☞✞❀✸❤✎❞✖t✎◗❂❄✥♣✸❦✎✺✌▼☛✄✩❁✞❃✖✙✉✮❱✇✈✶☛★✯✱✜❩✎①✎✡✖★✜❲✞❀✌▼☛✍✔✰✣✤✞❤✎✡✞✤✣❃❂✱✔✆✥✦②✕✯✆✞✏✸ ☛★✎❇✎◗❂☞✞③☛★✌▼✣✤❂❄✥✴✎✡✞✤✣❀✎✺✯✱✌▼✞④✜✢✞✕✷★✞❀✜✮✣✤☛★✔⑤P✤✞✿P✕✌▼✖❫☛✄✩❄✜❡✹⑥✣❀✜✢☛★✸✤✸✤✥ ❴✗✞✤✩❦✥✴✔✆✎✡✖ ✸✺✠☞☛✍✎✒✥✦☛✍✜s✖✍✌①✎❞✞✕✑✮✠☞✖✍✌▼☛★✜❵✌▼✞✤✩★✯✱✔✰✩❁☛★✔✪✣❀✹✄❱⑦✵⑧✸✏✥✴✔✳✲❢☛★✔♠✞▼q❄☛✍✑❯✠✪✜✢✞✬✖✼✘ ✣✤✖★✯✱✔✆✎✡✞✕✌✤✸✟⑨✦⑩❶✥✴✔✪☛★✌✏✹✻☛✍✔✰✩④❷s✌▼☛✍✹✤❸❪◆❛✞✾✸▼❂☞✖★◆♠✎◗❂☞☛✍✎✭✎✡✞❀✑✮✠☞✖✍✌▼☛★✜⑧✌▼✞❀■ ✩★✯✱✔✪✩✄☛★✔✪✣❀✹r✥♣✸❉P✤✞✏✸✏✎❭✸✏✯✱✥✴✎❞✞✤✩✟✘❀✖★✌✻✎◗❂☞✞❀✸✕✞❣✯✱✜❩✎✺✌▼☛★■✡✜✢✖✍◆❹✠✆✖★◆❛✞✕✌❣☛★✔✪✩ ✜✢✖★◆✻✠✆✞❀✌◗✘❀✖✍✌✏✑❪☛✍✔✰✣✤✞✗✸✏✹❳✸✏✎❞✞✕✑❨✸❵☛★✸❵✥✴✎❺✣✤✖★✔✆✸✤✯✱✑✓✞❀✸❵❍❁❊☞❻♠✜✢✞✏✸✤✸❼✠✆✖★◆❛✞✕✌ ✎✴❂✆☛★✔♠☛★✔♠☛★✌▼✞✤☛③✌▼✞✤✩★✯✱✔✪✩✄☛★✔❚✎❝✎❞✞✤✣✤❂❄✔✆✥✦②✕✯✆✞❫❱♠✫❖✥✴✌▼✣✕✯✱✥✴✎❭✎✡✞✤✣❃❂✱✔✆✥✦②✕✯✆✞✏✸ ☛★✜✴✜✢✖✍◆❽✠☞✖✍◆❛✞❀✌✏■✡✌❃✞❀✜❩✥✦☛❁P❀✥✴✜❡✥✴✎✒✹❾✎✺✌▼☛❁✩✄✞✤✖✼✉s✸✬✖✼✘✬☛✄P✤✖✍✯✱✎✟❿✄❊☞❻✇✥✴✔⑤✞✤☛✄✣✤❂ ✑❪✞✤☛★✸✤✯✱✌❃✞▲❱➀❆♦✑✓✞❀✎◗❂☞✖❫✩✄✖✍✜✢✖▼✲✄✹♠✥♣✸❦✩❁✞❀✷★✞✕✜✢✖❃✠✆✞✤✩➁P✤☛❳✸✕✞✤✩➂✖✍✔⑦✜✢✖★◆❈■ ✜✢✞✕✷❳✞✕✜✶✘❀☛✍✯✱✜❩✎❇✸✏✥✴✑❜✯✱✜✢☛★✎✺✥✦✖★✔❽✯❄✸✏✥✴✔✳✲❦➃☞➄❈➅★✫⑧✚❵❅✟◆✶❂❄✥✦✣✤❂⑤☛✍✜✴✜✢✖★◆❖✸r✩❁✞❀■ ✎❞☛✍✥✴✜✢✞✤✩❾✣✕✥✴✌▼✣❀✯✱✥✴✎❨✑❪✖❫✩✄✞✕✜✐✸❭✘❀✖✍✌✿P❃✖✍✎✴❂✿✠✆✖★◆❛✞✕✌✬✣❃✖✍✔☞✸✏✯✱✑✮✠✰✎✺✥✦✖★✔⑤☛★✔✪✩ ✌▼✞✕✜❩✥✦☛✄P✕✥✴✜❩✥✴✎✺✹✻✥✴✔❢✣✕✯✱✌✏✌▼✞✕✔✆✎❵☛✍✔✰✩✛✘✤✯✱✎✒✯✱✌❃✞✓✫✧✽❤➆❵➃r✎❞✞✤✣✤❂❄✔✰✖✍✜✢✖❃✲✍✹✄❱

1. Introduction ➇❵➈❃➉❡➊❃➉❲➋ ✁✍➌⑧➍▼➎✱➍ ➊❃➏✕➐ ➍ ➈ ✁✄✂☞➑ ➉ ✂☞➑❜➒ ➈❃➓✄➐➔➐❪➏ ☎ ➉❲➋ ✁✍➌⑧✁✄→☞→☞➌ ➉❲➋ ✁ ➊❃➉✢➓ ✂✆➍ ➉➌ ❲➣✄➏ →✆✁ ➋✕➏❀↔❞➐ ✁ ➣✄➏▲➈ ➍❤✁✄✂✆☎↕☎ ➏❀➙❚➛☞➈▼➉ ➌❲➌❲✁ ➊▼➓✄➈ ➍ ➊❃➓⑦➊▼➜☞➏➁➏✕➐❪➏✕➈ ➑ ➉ ✂☞➑ ➝ ➏ ✁ ➈ ✁ ➛ ➌ ➏ ➝ ➈❃➉ ➍ ➊✙↔ ➝ ✁ ➊❃➋✤➜❇➋✕➓✄➐ →☞➞ ➊❃➏✕➈ ➍ ➞ ➊▼➉ ➌ ➉❲➟✕➏✗➏✕➐✟➛❚➏ ☎☞☎ ➏ ☎ ➛ ✁ ➊▼↔ ➊▼➏▲➈▼➉❲➏ ➍▲➠❉➡✛➞ ➏❪➊▼➓✿➊▼➜☞➏ ➌ ➉✢➐❪➉✢➊▼➏ ☎ ➛ ✁ ➊▼➊▼➏✕➈ ➎③➌ ➉ ➒ ➏ ✁✍➌ ➓ ✂☞➑ ➝ ➉✢➊▼➜❦➊❃➜☞➏ ➒✦✁ ➋❀➊❉➊❃➜ ✁ ➊④➉ ✂ ➐ ✁✍✂❄➎ ➓ ➒ ➊▼➜✆➏ ➍ ➏ ➍▼➎✱➍ ➊❃➏✕➐ ➍ ➛ ✁ ➊✙➊❃➏✕➈❃➉✢➏ ➍ ➋ ✁✍✂☞✂ ➓✍➊ ➛❚➏❤➈❃➏ →✆➌❲✁ ➋❀➏ ☎ ➓✄➈✬➈❃➏▲➋✤➜ ✁ ➈ ➑ ➏ ☎ ➊▼➜✆➏❾➋❀➉❲➈❃➋ ➞ ➉❡➊ ➍✬➞✆➍ ➏ ☎ ➉ ✂ ➊❃➜☞➏ ➍ ➏ ➍✙➎✱➍ ➊▼➏▲➐ ➍❝➍ ➜☞➓ ➞✆➌❲☎ ➛❚➏❪➏✕➢✳➊❃➈▼➏▲➐❪➏ ➌❲➎✬➌ ➓ ➝ ↔ → ➓ ➝ ➏✕➈ ➠❇➤ ➊❝➊▼➜☞➏ ➍❃✁ ➐❪➏ ➊▼➉❲➐❪➏s➊▼➜☞➏❯➋✕➈▼➉✢➊▼➉♣➋ ✁✄➌ ➉✢➊ ➎ ➓ ➒ ➊▼➜✆➏ ➍ ➏ ➍▼➎✱➍ ➊❃➏✕➐ ➍ ➝ ✁ ➈❃➈ ✁✄✂ ➊ ➍ ➊▼➜☞➏ ➞✆➍ ➏❶➓ ➒ ➒✦✁✍➞☞➌ ➊✙↔✺➊▼➓ ➌ ➏▲➈ ✁✄✂ ➋❀➏①➊▼➏▲➋✤➜ ✂ ➉❲➥ ➞ ➏ ➍ ➊❃➓③➏ ✂✆➍✙➞ ➈▼➏❉➈▼➏ ➌ ➉ ✁ ➛ ➌ ➏ ➒◗➞☞✂ ➋✏➊▼➉❲➓ ✂ ↔ ➉ ✂✆➑✆➠ ➇✗➦r➧❝➨✾➊❃➏▲➋✤➜ ✂ ➓ ➌ ➓ ➑✄➎❇➍ ➋ ✁✄➌ ➉ ✂☞➑ ➊▼➈❃➏ ✂✆☎✆➍❈✁ ➈❃➏ ✁✄➌❲➍ ➓✛➈❃➏ ➍▼➞☞➌ ➊▼➉ ✂☞➑ ➉ ✂ ➋❀➉❲➈❃➋ ➞ ➉❡➊ ➍ ➝ ➉✢➊▼➜✾➜☞➉ ➑ ➜✆➏✕➈ → ➓ ➝ ➏✕➈⑧➋✕➓ ✂✆➍▼➞ ➐ → ➊▼➉❲➓ ✂❇✁✄✂✆☎✾➌ ➓ ➝ ➏▲➈❼➈▼➏✕↔ ➌ ➉ ✁ ➛✆➉ ➌ ➉❡➊ ➎❁➠❈➩ ➜☞➉ ➍❛→✆✁✍→ ➏✕➈ ➞✆➍ ➏ ➍✭➫ ↔✺➛☞➉✢➊❛➈❃➏ ✁✄➌ ↔✺➊▼➉❲➐❪➏❯➋❀➓ ➞✆✂ ➊❃➏✕➈ ➍✭✁✄➍❵✁✍✂ ➏❀➢ ✁ ➐ →☞➌ ➏✾➊❃➓ ➍ ➊ ➞✆☎✱➎❣➒✦✁✄➞☞➌ ➊▼↔✒➊❃➓ ➌ ➏✕➈ ✁✍✂ ➋✕➏❝➊▼➏❫➋✤➜ ✂ ➉♣➥ ➞ ➏ ➍❭✁ ➊ ➍ ➏✕➭❁➏✕➈ ✁✍➌ ➌ ➏▲➭✄➏ ➌❲➍✓✁✄✂✆☎ ➉ ➌❲➌✢➞❚➍ ➊❃➈ ✁ ➊▼➏④➊▼➜✆➏④➊▼➈ ✁✄☎ ➏▲➓✍➯➂➛✰➏❀➊ ➝ ➏✕➏ ✂❹→ ➓ ➝ ➏▲➈①➋❀➓ ✂ ↔ ➍✙➞ ➐ → ➊▼➉❲➓ ✂✬✁✍✂✆☎ ➈❃➏ ➌ ➉ ✁ ➛☞➉ ➌ ➉✢➊ ➎ ➓ ➒❈✁❪➍✙➎✱➍ ➊▼➏✕➐ ➠ ➩ ➈ ✁❁☎ ➉✢➊▼➉❲➓ ✂✆✁✄➌☞➒✦✁✍➞✆➌ ➊❵➊▼➓ ➌ ➏✕➈ ✁✍✂ ➋❀➏ ➍ ➋✤➜☞➏✕➐❪➏ ➍❛➌ ➉❲➣✄➏ ➩ ➈❃➉ →✆➌ ➏❭➦✬➓ ☎ ↔ ➞☞➌♣✁ ➈✶➲❯➏ ☎✱➞☞✂❚☎☞✁✍✂ ➋ ➎❜➳✒➩ ➦✿➲✮➵ → ➈❃➓★➭✳➉ ☎ ➏ ✁ ➜✆➉ ➑ ➜ ☎ ➏ ➑ ➈▼➏▲➏✭➓ ➒❄➒✦✁✍➞✆➌ ➊▼↔ ➊▼➓ ➌ ➏▲➈ ✁✄✂ ➋❀➏ ➝ ➜✆➉ ➌ ➏✮➐ ✁ ➉ ✂ ➊ ✁ ➉ ✂ ➉ ✂☞➑✟→ ➏▲➈ ➒ ➓❁➈▼➐ ✁✍✂ ➋❀➏ ✁ ➊❛➊▼➜✆➏❭➋✕➓ ➍ ➊❵➓ ➒ ➐❪➓✄➈❃➏❶➊▼➜ ✁✄✂ ➊ ➝ ➓✾➊▼➉❲➐❪➏ ➍ ➊▼➜☞➏ ✁ ➈❃➏ ✁❨✁✍✂✆☎✓→ ➓ ➝ ➏✕➈❵➋✕➓ ✂✆➍▼➞ ➐ → ➊❃➉✢➓ ✂❺➠ ➦✬➓ ➍ ➊❈➓ ➒ ➊▼➜☞➏ ✁ ➛✰➓★➭✄➏❵➐❪➏ ✂ ➊▼➉❲➓ ✂ ➏ ☎✟➍▼➎✱➍ ➊❃➏✕➐ ➍❈✁ ➈❃➏✗➈▼➏ ➌❲✁ ➊▼➉❲➭✄➏ ➌❲➎❝➌ ➓ ➝

→ ➏✕➈ ➒ ➓✄➈❃➐ ✁✄✂ ➋❀➏✮➛ ➞ ➊ ✁ ➈▼➏ → ➓ ➝ ➏✕➈❛➋✕➈▼➉✢➊▼➉♣➋ ✁✄➌❚✁✄✂✆☎ ➜☞➏ ✂ ➋❀➏✮➐❪➓✄➊▼➉❲➭ ✁ ➊▼➏ ➊▼➜✆➏ ➍ ➊ ➞✆☎✱➎ ➓ ➒ ➊▼➜✆➏❇➉✢➐ →✆✁ ➋✏➊❯➓ ✂✬→ ➓ ➝ ➏✕➈❯➋✕➓ ✂✆➍▼➞ ➐ → ➊▼➉❲➓ ✂✬☎✱➞ ➏✾➊▼➓ ➉ ✂ ➋❀➓❁➈ → ➓✄➈ ✁ ➊❃➉✢➓ ✂ ➓ ➒✧➒✦✁✍➞✆➌ ➊▼↔✒➊❃➓ ➌ ➏✕➈ ✁✍✂ ➋✕➏ ➠ ➩ ➜✆➏❯➈▼➏▲➐ ✁ ➉ ✂✆☎ ➏✕➈❈➓ ➒✰→❚✁✍→ ➏✕➈✭➉ ➍ ➓✄➈ ➑❁✁✄✂ ➉❲➟✕➏ ☎❜✁✄➍❈➒ ➓ ➌❲➌ ➓ ➝ ➍▲➸ ➨❄➏❫➋✏↔ ➊▼➉❲➓ ✂⑥➺✿☎ ➉ ➍ ➋ ➞❚➍▼➍ ➏ ➍ ➊ ➝ ➓ ➌ ➓ ➑ ➉♣➋❪➉❲➐ →✆➌ ➏▲➐❜➏ ✂ ➊ ✁ ➊❃➉✢➓ ✂✆➍ ➓ ➒ ➋❀➓ ➞✆✂ ➊❃➏✕➈ ➝ ➜☞➉♣➋✤➜ ➝ ➏▲➈▼➏✬➋❀➓ ✂✆➍ ➉ ☎ ➏▲➈▼➏ ☎❾➒ ➓❁➈✓➊▼➜✆➉ ➍①➍ ➊ ➞❚☎✱➎✄➠ ➨❄➏▲➋❀➊▼➉❲➓ ✂♠➻❦☎ ➉ ➍ ↔ ➋ ➞❚➍▼➍ ➏ ➍ ➊▼➜☞➏❣➐❪➏❀➊▼➈❃➉♣➋ ➍❨✁✄✂✆☎ ➐❪➏❀➊❃➜☞➓ ☎ ➓ ➌ ➓ ➑❁➎r➞❚➍ ➏ ☎ ➊▼➓③➐❪➏ ✁✄➍▼➞ ➈▼➏ ➒✦✁✍➞✆➌ ➊▼↔✒➊❃➓ ➌ ➏✕➈ ✁✍✂ ➋✕➏ ✁✄✂✆☎❨→ ➓ ➝ ➏✕➈ ➠ ➨❄➏❫➋✏➊▼➉❲➓ ✂❜➫❝☎ ➉ ➍ ➋ ➞❚➍▼➍ ➏ ➍ ➐❪➏❀➊❃➜☞➓ ☎☞➍ ➓ ➒ ➉❲➐ → ➈▼➓★➭❄➉ ✂☞➑ ➊▼➜✆➏ ➍ ➏✮➋❀➓ ➞☞✂ ➊▼➏✕➈ ➍ ➛ ➎ ➐❪➏ ✁✍✂✆➍ ➓ ➒❺✁✄☎☞☎ ➉ ✂☞➑ ➈❃➏ ☎☞➞☞✂ ↔ ☎☞✁✄✂ ➋ ➎④➳✦✁ ➈❃➋✤➜☞➉✢➊▼➏❫➋✏➊ ➞ ➈▼➏ ➌ ➏▲➭✄➏ ➌ ➵ ✁✄✂✆☎ ➛ ➎ ➈❃➏ ☎ ➏ ➍ ➉ ➑❁✂ ➉ ✂✆➑❇➍ ➓❁➐❜➏✛➋❀➉❲➈✙↔ ➋ ➞ ➉❡➊✾➛ ➌ ➓✱➋✤➣ ➍❜➳ ➋✕➉✢➈✤➋ ➞ ➉❡➊ ➌ ➏▲➭✄➏ ➌ ➵ ➠❇➼ ➉ ✂✆✁✄➌✢➌❲➎ ➨❄➏❫➋✏➊❃➉✢➓ ✂❢➽❉☎ ➉ ➍ ➋ ➞❚➍▼➍ ➏ ➍ ➍ ➓✄➐❪➏✾➋❀➓ ✂ ➋ ➌❲➞✆➍ ➉❲➓ ✂❚➍❶✁✍✂✆☎✻➒◗➞ ➊ ➞ ➈▼➏ ➝ ➓✄➈❃➣ ➠

2. Counters ➾ ✂ ➊▼➜✆➉ ➍s➍ ➏▲➋✏➊❃➉✢➓ ✂ ➝ ➏ ☎ ➉ ➍ ➋ ➞✆➍❃➍ ➊▼➜☞➏❭➉✢➐ →☞➌ ➏✕➐❪➏ ✂ ➊ ✁ ➊❃➉✢➓ ✂ ➓ ➒✧➚ ➉✢↔ ✂✆✁ ➈ ➎④✁✍✂✆☎r➪ ➈ ✁❳➎ ➋❀➓ ➞✆✂ ➊❃➏✕➈ ➝ ➜☞➉❲➋✤➜ ➝ ➏✕➈❃➏❨➋✕➓ ✂✆➍ ➉ ☎ ➏✕➈❃➏ ☎❣➒ ➓✄➈✮➊▼➜☞➉ ➍ ➍ ➊ ➞✆☎✱➎❁➠✧➼❚✁✍➞☞➌ ➊ ☎ ➏❀➊❃➏▲➋✏➊❃➉✢➓ ✂ ➊▼➏❫➋✤➜ ✂ ➉♣➥ ➞ ➏ ➍⑧➒ ➓✄➈✶➊▼➜☞➏ ➍ ➏✗➋❀➓ ➞☞✂ ➊▼➏✕➈ ➍⑧✁ ➈▼➏ ✁✍➌♣➍ ➓ ☎ ➉ ➍ ➋ ➞✆➍❃➍ ➏ ☎❼➠✟➚ ➉ ✂✆✁ ➈ ➎✬✁✍✂✆☎❦➪ ➈ ✁❳➎ ➋✕➓ ➞☞✂ ➊❃➏✕➈ ➍❭✁ ➈▼➏ ➍ ➊ ➞✆☎ ➉❲➏ ☎ ➉ ✂ ➊▼➜☞➉ ➍❯→❚✁✍→ ➏✕➈✮➛ ➞ ➊❯➊▼➜✆➏ ➍❃✁ ➐❪➏❝➊▼➏❫➋✤➜ ✂ ➉♣➥ ➞ ➏✟➋ ✁✄✂ ➛❚➏✟➏❀➢❄➊▼➏ ✂✆☎ ➏ ☎ ➊▼➓ ✁✄➌ ➐❪➓ ➍ ➊ ✁✄✂❄➎ ➋❀➉❲➈❃➋ ➞ ➉❡➊ ➠ ➇❵➓ ➞☞✂ ➊▼➏▲➈ ➍ ➝ ➏▲➈▼➏❛➊ ✁ ➣✄➏ ✂❜✁✄➍❖✁✍✂ ➏❀➢ ✁ ➐❜↔ →☞➌ ➏ ➒ ➓❁➈❶➊▼➜☞➉ ➍❭➍ ➊ ➞✆☎✱➎④✁✄➍ ➊❃➜☞➏ ➎✬✁ ➈❃➏ ✁✍✂ ➉ ✂ ➊▼➏ ➑ ➈ ✁✄➌❺→✆✁ ➈✙➊✮➓ ➒ ➊▼➜☞➏ ➍ ➏ ➍▼➎❄➍ ➊▼➏▲➐ ➍✟✁✄✂✆☎ ➐ ✁❳➎ ➛❚➏ ➞✆➍ ➏ ☎⑥✁❁➍❨✁ ➊▼➉❲➐❜➏▲➈❪➓✄➈ ✁❁➍✟✁r✁✄☎☞☎ ➈▼➏ ➍▼➍ ➑ ➏ ✂ ➏✕➈ ✁ ➊❃➓✄➈ ✁❁➍ ➊▼➜✆➏ ➎❣→ ➈▼➓★➭❄➉ ☎ ➏❝➊ ➝ ➓ ☎ ➉❡➯✪➏✕➈❃➏ ✂ ➊ ➍ ➊ ✁ ➊▼➏❇➏ ✂ ➋❀➓ ☎ ➉ ✂☞➑ ➓ ➒❈✁ ➋❀➓ ➞☞✂ ➊▼➏✕➈ ➠

2.1. Binary Counter ➩ ➜✆➏ ➚ ➉ ✂✆✁ ➈ ➎ ➋✕➓ ➞☞✂ ➊▼➏▲➈✾➉ ➍ ➊❃➜☞➏ ➍ ➉✢➐ →☞➌ ➏ ➍ ➊ ✁✍✂✆☎ ➐❪➓ ➍ ➊❨➋❀➓✄➐❜↔ ➐❪➓ ✂☞➌❲➎✾➞✆➍ ➏ ☎ ➋❀➓ ➞✆✂ ➊❃➏✕➈ ➠✧➪ ➓ ➞ ➊▼➉ ➍ ➉ ✂❣➶❡➹✕➘❄→ ➈▼➓ → ➓ ➍ ➏ ☎❇✁ ➊❃➏▲➋✤➜ ✂ ➉❲➥ ➞ ➏ ➒ ➓✄➈❈➐ ✁ ➣✳➉ ✂☞➑ ➊▼➜☞➏ ➚ ➉ ✂✆✁ ➈ ➎ ➋❀➓ ➞☞✂ ➊▼➏✕➈ ➒✦✁✄➞☞➌ ➊ ➍ ➏▲➋ ➞ ➈❃➏ ➠✶➤t→ ➈❃➓ → ➏✕➈▼➊ ➎ ➓ ➒ ➊▼➜☞➏ ➩❦➴ ➉ → ↔ ➴ ➓ → ➝ ✁✄➍✶➞✆➍ ➏ ☎❝➒ ➓❁➈ ☎ ➏❀➊▼➏❫➋✏➊❃➉ ✂☞➑ ➏✕➈❃➈❃➓✄➈ ➍✕➠❺➼ ➉ ➑✄➞ ➈❃➏ ➹ ➍ ➜☞➓ ➝ ➍ ➊❃➜☞➏❭➋✕➉✢➈✤➋ ➞ ➉❡➊✗➉✢➐ →☞➌ ➏✕➐❪➏ ✂ ➊ ✁ ➊▼➉❲➓ ✂ ➓ ➒⑧✁❨➩t➴ ➉ → ↔ ➴ ➓ → ➛ ✁✄➍ ➏ ☎ ➋❀➓ ➞☞✂ ➊▼➏▲➈ ➝ ➉❡➊❃➜ ➒✦✁✄➞☞➌ ➊ ☎ ➏❀➊❃➏▲➋✏➊❃➉✢➓ ✂④➌ ➓ ➑ ➉♣➋ ➠ ➩❵➎❄→ ➉♣➋ ✁✍➌❲➌❲➎ ➉ ✂ ➇✗➦r➧❝➨ ➚ ➉ ✂✆✁ ➈ ➎ ➋✕➓ ➞☞✂ ➊▼➏▲➈ ➍t✁ ➈❃➏⑤➉❲➐ →☞➌ ➏❀↔ ➐❪➏ ✂ ➊▼➏ ☎♠✁✄➍①➍ ➜☞➓ ➝ ✂ ➉ ✂❹➼ ➉ ➑✄➞ ➈❃➏ ➺ ➈ ✁ ➊▼➜✆➏✕➈❪➊▼➜ ✁✍✂♠➞✆➍ ➉ ✂✆➑❾✁❤➩ ➴ ➉ → ↔ ➴ ➓ →❺➠ ➨❄➉ ✂ ➋❀➏✓➊❃➜☞➉ ➍ ➉✢➐ →☞➌ ➏✕➐❪➏ ✂ ➊ ✁ ➊❃➉✢➓ ✂❤➞✆➍ ➏ ➍✾✁✬➡ ↔ ➴ ➉ →❦➴ ➓ → ➳ ➓❁➈ ✁❝➌♣✁ ➊❃➋✤➜✰➵ ✁✍✂✆☎❜✂ ➓✄➊ ➩ ↔ ➴ ➉ →❜➴ ➓ → ➊▼➜✆➏ ✁✍➌❲➑ ➓✄➈❃➉✢➊▼➜☞➐ → ➈▼➓ → ➓ ➍ ➏ ☎ ➉ ✂❦➶✢➹❀➘ ➋ ✁✍✂✆✂ ➓✍➊❶➛✰➏ ☎ ➉✢➈❃➏▲➋❀➊ ➌❲➎✻✁✍→✆→☞➌ ➉❲➏ ☎ ➊▼➓❪➊❃➜☞➉ ➍ ➋❀➓ ➞☞✂ ➊▼➏✕➈ ➠❈➷ ➓ ➝ ↔ ➏✕➭❁➏✕➈ ✁✍✂❣✁✍➌ ➊▼➏▲➈ ✂✆✁ ➊▼➏ ➍ ➋✤➜✆➏✕➐❪➏✾➋ ✁✍✂ ➛❚➏ ➞✆➍ ➏ ☎ ➝ ➜☞➏▲➈▼➏✛➊▼➜☞➏ →✆✁ ➈▼➉✢➊ ➎ ➓ ➒ ➊❃➜☞➏❢➏ ✂✆✁ ➛ ➌ ➏ ➍ ➉ ➑✄✂❚✁✍➌♣➍✿➳✦➬❇➮❪➱ ➬❇➮❨✃⑥➠✢➠❲➠❐➬❨➮❨❒ ➵①➉ ✂✆☎ ➉♣➋ ✁ ➊▼➏

Proceedings of the International Symposium on Quality Electronic Design (ISQED’02) 0-7695-1561-4/02 $17.00 © 2002 IEEE

✆

PARITY

ENABLE

T

Q

T

TFF

Q

T

TFF

Q

T

TFF

Q TFF

CLOCK

a) Binary Counter using T−Flip Flop T1 T2 T3 T4

PREDICTED PARITY D

Q1 Q2 Q3 Q4

Q

Q’

CLOCK

b) Parity prediction logic

➼ ➉ ➑❁➞ ➈▼➏ ➹❁➸ Binary counter with fault detection using T-Flip flop ➜ ➏❀➊❃➜☞➏✕➈❛➊▼➜☞➏ →✆✁ ➈❃➉❡➊ ➎ ➓ ➒ ➊▼➜✆➏ ✂ ➏❀➢❄➊ ➍ ➊ ✁ ➊▼➏ ➝ ➉ ➌❲➌ ➋✤➜ ✁✄✂☞➑ ➏s➓✄➈ ✂ ➓✍➊ ➠ ➝ ☞ ➷ ➏ ✂ ➋❀➏r➉ ✂✆➍ ➊▼➏ ✁✄☎ ➓ ➒ ➊▼➜✆➏ ➱ ✃⑥➠✢➠❲➠ ❒⑤➍ ➉ ➑✄✂✆✁✄➌❲➍ ➉ ✂ ➙ ➑✄➞ ➈❃➏ ➹❁➳ ➛❚➵ ➍ ➉ ➑❁✂✆✁✍➌♣➍s➬❇➮❜➱ ➬❇➮❨✃❜➠❲➠✢➠✭➬❨➮❨❒ ➋ ✁✍✂ ➛❚➏ ➞✆➍ ➏ ☎ ➊▼➓ ☎ ➏✕➊▼➏▲➋❀➊ ✁❪➒✦✁✍➞✆➌ ➊ ➠ ➾ ➊✛➋ ✁✄✂ ➛❚➏ ➍ ➏▲➏ ✂ ➊❃➜ ✁ ➊ ➼ ➉ ➑✄➞ ➈▼➏ ➹✟✁✍✂✆☎✬➼ ➉ ➑✄➞ ➈❃➏ ➺✓✁ ➈▼➏ ➍ ➉❲➐❪➉ ➌♣✁ ➈✾➉❲➐ →☞➌ ➏✕➐❪➏ ✂ ➊ ✁ ➊▼➉❲➓ ✂✆➍ ➓ ➒ ➊▼➜☞➏ ➚ ➉ ✂✆✁ ➈ ➎ ➋❀➓ ➞☞✂ ➊▼➏▲➈❇➏❀➢☞➋❀➏ → ➊ ➒ ➓✄➈s➊❃➜☞➏✾➐❪➏✕➐❪➓✄➈ ➎ ➏ ➌ ➏✕➐❪➏ ✂ ➊ ➠✂✁ ➏ ✁ ➈▼➏ ➑ ➓❁➉ ✂✆➑ ➊❃➓①➋❀➓ ✂❚➍ ➉ ☎ ➏✕➈✗➊❃➜☞➏ ➉✢➐ →☞➌ ➏✕➐❪➏ ✂ ➊ ✁ ➊❃➉✢➓ ✂③➍ ➜✆➓ ➝ ✂ ➉ ✂❢➼ ➉ ➑❁➞ ➈▼➏ ➺❪➒ ➓✄➈✛➊▼➜✆➉ ➍❝➍ ➊ ➞✆☎✱➎✬✁❁➍ ➉✢➊ ➉ ➍✮✁✟→ ➓ →✆➞☞➌❲✁ ➈❯➉❲➐ →✆➌ ➏▲➐❜➏ ✂ ➊ ✁ ➊❃➉✢➓ ✂✬✁✍✂✆☎④✁✍➌♣➍ ➓✟➐ ✁ ➣❁➏ ➍ ➉✢➊✮➏ ✁❁➍✙➎ ➊▼➓ ➋❀➓❁➐ →❚✁ ➈❃➏ ➚ ➉ ✂✆✁ ➈ ➎ ➋❀➓ ➞☞✂ ➊▼➏▲➈ ➍ ➝ ➉✢➊▼➜ ➪ ➈ ✁❳➎ ➋❀➓ ➞✆✂ ➊❃➏✕➈ ➍✕➠

➍ ➏❪➓ ➒❶➪ ➈ ✁❳➎ ➋✕➓ ☎ ➏❜➋✕➓ ➞☞✂ ➊▼➏▲➈ ➍ ➜ ✁❁➍ ➛❚➏▲➏ ✂❢→ ➈❃➓ → ➓ ➍ ➏ ☎ ➊❃➓ ➍❃✁ ➭✄➏ ➓ → ➝ ➏▲➈✛➉ ✂ ➊❃➜☞➏❜➋✕➓ ✂ ➊▼➈❃➓ ➌✶→✆✁ ➊❃➜✿➓ ➒ ➏✕➐❨➛✰➏ ☎✆☎ ➏ ☎③→ ➈▼➓✱➋✕➏ ➍❃➍ ➓❁➈ ➍❇➶ ➺❳➘❞➠ ✁ ➓✄➈❃➣✿➜ ✁✄➍ ➛✰➏✕➏ ✂❢☎ ➓ ✂ ➏❜➊▼➓ → ➈❃➓★➭✄➏❇➊❃➜☞➏ ✁✄☎ ➭ ✁✄✂ ➊ ✁✍➑ ➏ ➍ ➓ ➒s➪ ➈ ✁❳➎ ➋❀➓ ☎ ➏ ✁✄☎✆☎ ➈▼➏ ➍▼➍ ➉ ✂☞➑ ➉ ✂ ➊❃➜☞➏④➋❀➓ ✂ ➊❃➏❀➢❄➊❜➓ ➒ ➛☞➉✢➊①➋✤➜ ✁✍✂☞➑ ➏ ➍ ➓ ✂ ➊▼➜☞➏ ✁✄☎✆☎ ➈▼➏ ➍▼➍①➌ ➉ ✂ ➏ ➍✻✁✍✂✆☎ ➜☞➏ ✂ ➋❀➏ ✁ ➈▼➏ ☎✱➞ ➋✏➊❃➉✢➓ ✂ ➓ ➒❇➍ ➝ ➉✢➊❃➋✤➜✆➉ ✂☞➑❾✁ ➋✏↔ ➊▼➉❲➭❄➉❡➊ ➎ ➛ ➎① ✞✝➻ ↔ ✟➽ ✝✡✠ ☎✱➞ ➈❃➉ ✂☞➑❨✂ ➓❁➈▼➐ ✁✄➌❚→ ➈❃➓ ➑ ➈ ✁ ➐ ➏✕➢✱➏▲➋ ➞ ➊▼➉❲➓ ✂①➞✆➍ ↔ ➉ ✂☞➑r✁❢➪ ➈ ✁❳➎ ➋❀➓ ☎ ➏❣➋❀➓ ➞✆✂ ➊❃➏✕➈ ➶ ➻★➘✺➠❦➷ ➓ ➝ ➏✕➭❁➏✕➈ ➉❲➐ →☞➌ ➏✕➐❪➏ ✂ ➊▼➉ ✂☞➑ ✁❾➪ ➈ ✁❳➎ ➋❀➓ ➞☞✂ ➊▼➏✕➈✓➉ ➍❪✂ ➓✄➊ ✁✄➍①➍ ➉✢➐ →☞➌ ➏ ✁✄➍✓☎ ➏ ➍ ➉ ➑❁✂ ➉ ✂✆➑❦➚ ➉ ✂✆✁ ➈ ➎ ➋❀➓ ➞☞✂ ➊▼➏▲➈ ➍▲➠①➤↕➍ ➉ ➑✄✂ ➉❡➙❚➋ ✁✍✂ ➊ ✁ ➐❪➓ ➞✆✂ ➊✾➓ ➒✗➌ ➓ ➑ ➉❲➋❜➉ ➍ ➈▼➏❫➥ ➞ ➉✢➈❃➏ ☎ ➊▼➓ ☎ ➏✕➊▼➏✕➈❃➐❪➉ ✂ ➏✟➊❃➜☞➏ ✂ ➏❀➢❄➊ ➍ ➊ ✁ ➊❃➏❪➓ ➒ ➊❃➜☞➏✓➋❀➓ ➞✆✂ ➊❃➏✕➈ ➠✟➩ ➜☞➉ ➍❭➌ ➓ ➑ ➉♣➋❨➉ ➍ ➵ ➑✳✁ ➊❃➏ ➍✮☎ ➏✕➏ →✿➒ ➓✄➈ ✎ ➞✆➍▼➞✆✁✍➌❲☞☛➌❲✍ ➎❦ ♠➹✌ ➳ ✁ ☛ ↔✺➛✆➉❡➊❝➋❀➓ ➞✆✂ ➊❃➏✕➈ ✁✍✂✆☎✿☎ ➏❀↔ → ➏ ✂✆☎☞➍ ➓ ✂❹✁✍➌❲➌ ➊▼➜☞➏④➛☞➉✢➊ ➍ ➓ ➒ ➊❃➜☞➏ → ➈▼➏▲➭❄➉✢➓ ➞✆➍❪➍ ➊ ✁ ➊▼➏ ✁✄✂✆☎ ➊❃➜☞➏✕➉❲➈ ➋❀➓❁➐ →☞➌ ➏▲➐❪➏ ✂ ➊ ➍▲➠ ➤✮➌✢➌ ➊▼➜✆➉ ➍❉➌ ➓ ➑ ➉♣➋ ✁✄➌ ➋❀➓❁➐ →✆➌ ➏✕➢❄➉✢➊ ➎ ➐❪➉ ➑ ➜❁➊❣➏ ✂✆☎ ➞☞→ ➐ ✁ ➣❄➉ ✂☞➑ ➊▼➜✆➏ ➪ ➈ ✁❳➎ ➋❀➓ ➞✆✂ ➊❃➏✕➈❇➐❪➓❁➈▼➏ → ➓ ➝ ➏▲➈✾➜ ➞✆✂☞➑ ➈ ➎✄➠❣➤✮➍ ➍ ➜☞➓ ➝ ✂ ➉ ✂❹➼ ➉ ➑✄➞ ➈▼➏ ➻ ✁r➍ ➏ ➑ ➐❪➏ ✂ ➊▼➏ ☎t➪ ➈ ✁❳➎ ➋❀➓ ➞☞✂ ➊▼➏✕➈ ➶ ➫❳➘ ➋ ✁✍✂ ➛✰➏ ➞✆➍ ➏ ☎ ➊❃➓❦➈▼➏ ☎✱➞ ➋❀➏❉➊▼➜✆➏ ✁ ➐❪➓ ➞☞✂ ➊❪➓ ➒❭➌ ➓ ➑ ➉♣➋✻➈❃➏▲➥ ➞ ➉❲➈▼➏ ☎ ➝ ➉✢➊▼➜ ✏ ➞✆➍ ➊ ✁❪➍✙➌ ➉ ➑ ➜✳➊❶➉ ✂ ➋✕➈▼➏ ✁✄➍ ➏✛➉ ✂ ➊▼➜☞➏ ➍ ➝ ➉✢➊❃➋✤➜☞➉ ✂☞➑✓✁ ➋❀➊▼➉❲➭✳➉✢➊ ➎✄➠❈➡ ➏❀➊❃➏▲➋✏➊▼↔ ➉ ✂☞➑❪➒✦✁✍➞☞➌ ➊ ➍ ➉ ✂✬✁✓➪ ➈ ✁❳➎ ➋❀➓ ➞✆✂ ➊❃➏✕➈❶➉ ➍ ➭✄➏▲➈ ➎ ➏ ✁✄➍▼➎✻✁✄➍ ➝ ➉✢➊▼➜④➏▲➭✄➏✕➈ ➎ ➍ ➊ ✁ ➊❃➏✮➋✤➜ ✁✄✂☞➑ ➏s➊❃➜☞➏ →✆✁ ➈▼➉✢➊ ➎ ➓ ➒ ➏ ✁ ➋✤➜ ➍ ➏ ➑ ➐❪➏ ✂ ➊✭➣❁➏✕➏ →❚➍ ➊▼➓ ➑✄➑✄➌ ➉ ✂☞➑✆➠ ➤ ➋❀➉❲➈❃➋ ➞ ➉❡➊✗➉✢➐ →☞➌ ➏✕➐❪➏ ✂ ➊ ✁ ➊❃➉✢➓ ✂ ➓ ➒ ➊❃➜☞➏ ➪ ➈ ✁❳➎ ➋✕➓ ➞☞✂ ➊❃➏✕➈✗➉ ➍✗➍ ➜✆➓ ➝ ✂ ➉ ✂④➼ ➉ ➑✄➞ ➈❃➏ ➫✆➠ 4 − bit Gray counter

overflow

overflow

4 − bit Gray counter

.....

4 − bit Gray counter

overflow

a) Segmented Gray counter using 4−bit Gray counters

ENABLE

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

1

0

0

0

1

1

0

0

0

31

0

0

1

1

0

0

0

32

..... EN 0

EN 1

EN 2

EN 3 0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

.. .

CLOCK

b) Output of a Segmented Gray counter

DFF

DFF

BIT 0

DFF

BIT 1

➼ ➉ ➑✄➞ ➈❃➏ ➻☞➸ Segmented Gray counter

DFF

BIT 2

BIT 3

➼ ➉ ➑✄➞ ➈❃➏ ➺✱➸ Binary counter using a D-Flip flop

2.2. Gray counter

☎✄❪➏ ↔ ➚ ➉ ✂✆✁ ➈ ➎ ➋❀➓ ➞✆✂ ➊❃➏✕➈ ➍✛✁ ➈▼➏ ✂ ➓✍➊❝➉ ✂ ➊ ➞ ➉✢➊▼➉❲➭✄➏ ➌❲➎ ➭❁➏✕➈ ➎❣→ ➓ ➝ ➏✕➈❭ ➋❀➉❲➏ ✂ ➊ ➍ ➉ ✂ ➋❀➏❝➊▼➜✆➏✕➈❃➏ ✁ ➈❃➏❝➐ ➞☞➌ ➊▼➉ →☞➌ ➏✾➊▼➈ ✁✍✂✆➍ ➉✢➊▼➉❲➓ ✂✆➍ ➝ ➜✆➏ ✂✿➍ ➝ ➉❡➊✤➋✤➜✱↔ ➉ ✂✆➑✓➒ ➈▼➓❁➐ ➓ ✂ ➏ ➍ ➊ ✁ ➊❃➏✾➊▼➓①➊▼➜☞➏ ✂ ➏❀➢❄➊ ➠❯➩ ➜☞➏ ➪ ➈ ✁❳➎ ➋❀➓ ➞✆✂ ➊❃➏✕➈✮➋ ✁✍✂ ➛❚➏ ➌ ➓ ➝ ➏✕➈▼↔ → ➓ ➝ ➏✕➈ ➍ ➉ ✂ ➋✕➏❈➊▼➜☞➏▲➈▼➏❛➉ ➍ ➊▼➈ ✁✍✂✆➍ ➉❡➊❃➉✢➓ ✂ ➉ ✂ ➓ ✂☞➌✢➎ ➓ ✂ ➏ ➴ ➉ → ↔ ➴ ➓ → ➝ ➜☞➏ ✂❤➍ ➝ ➉✢➊❃➋✤➜☞➉ ✂☞➑✬➍ ➊ ✁ ➊❃➏ ➍▲➠①➩ ➜☞➉ ➍ ➈▼➏ ☎✱➞ ➋❀➊▼➉❲➓ ✂ ➉ ✂❤➍ ➝ ➉❡➊✤➋✤➜✱↔ ➉ ✂✆➑①✁ ➋✏➊❃➉✢➭❄➉✢➊ ➎ ➋ ✁✍✂✬➍▼✁ ➭❁➏ ✁❜➍ ➉ ➑✄✂ ➉✢➙❚➋ ✁✄✂ ➊ ✁ ➐❪➓ ➞☞✂ ➊❯➓ ➒✧→ ➓ ➝ ➏▲➈ ✁✍➌ ↔ ➊▼➜☞➓ ➞☞➑ ➜❢➉ ✂ ➊❃➏✕➈❃➐❪➏ ☎ ➉ ✁ ➊❃➏ ➌ ➓ ➑ ➉❲➋❜➐ ✁❳➎ ➜ ✁ ➭❁➏✟➐❪➓❁➈▼➏✟➊▼➈ ✁✍✂✆➍ ➉✢➊▼➉❲➓ ✂✆➍▲➠

3. Fault model and fault sensitivity analysis methodology ➼❚✁✍➞☞➌ ➊ ➍ ➋ ✁✍✂ ➛❚➏❝➛☞➈❃➓ ✁❁☎✱➌❲➎ ➋ ➌♣✁✄➍❃➍ ➉✢➙✆➏ ☎ ➉ ✂ ➊❃➓ ✠✆✞❀✌✏✑✓☛★✔✪✞❀✔❚✎ ✁✍✂✆☎ ➏✕➈❃➐ ✁✍✂ ➏ ✂ ➊ ➒✦✁✄➞☞➌ ➊ ➍❨✁ ➈▼➏ ➞❚➍✙➞✆✁✄➌✢➌❲➎ ➋ ✁✍➞❚➍ ➏ ☎ ✺✎ ✌▼☛★✔✆✸✤✥✦✞✕✔✆✎ ➒✦✁✍➞☞➌ ➊ ➍▲✍✑ ➠ ❃ ➈ ➉ ▼ ➊ ☞ ➜ ✻ ➏ ➐ ❀ ➋ ☎✱➞ ✂☞➑ ✁✄✂❄➞✱➒✦✁ ➊ ➞ ➈❃➉ ✂✆➑④➍ ➊ ✁✄➑ ➏ ➝ ➜☞➉ ➌ ➏❪➊❃➈ ✁✄✂✆➍ ➉✢➏ ✂ ➊ ➒✦✁✄➞☞➌ ➊ ➍ ➈✁ ❃➏❨➋ ✁✍➞✆➍ ➏ ☎ ➉ ✂ ➊❃➜☞➏❇➙✆➏ ➌❲☎❺➠ ➲❶➏ ✁✄➍ ➓ ✂✆➍s➒ ➓❁➈✮➊❃➈ ✁✄✂✆➍ ➉✢➏ ✂ ➊ ➒✦✁✍➞☞➌ ➊✛➉ ✂ ↔ ➋ ➌❲➞✆☎ ➏✬➈ ✁✄☎ ➉ ✁ ➊▼➉❲➓ ✂✆➍ ➋✕➈▼➓ ➍▼➍ ➊ ✁✄➌ ➣ ✁✍✂✆☎❧→ ➓ ➝ ➏✕➈❪➊❃➈ ✁✄✂✆➍ ➉✢➏ ✂ ➊ ➍✕➠ ➾ ➊ ➜ ✁❁➍ ➛❚➏▲➏ ✂❦➍ ➜☞➓ ➝ ✂ ➊▼➜ ✁ ✓ ➊ ✒ ✝✔✠ ➓ ➒✗➍▼➎✱➍ ➊❃➏✕➐ ➒✦✁ ➉ ➌❲➞ ➈❃➏ ➍ ➉ ➍✾☎✱➞ ➏❜➊▼➓ ➊▼➈ ✁✍✂❚➍ ➉❲➏ ✂ ➊ ➒✦✁✄➞☞➌ ➊ ➍r➶ ➽ ✖✕ ➘❞➠ ➷ ➏ ✂ ➋❀➏ ➒ ➓✄➈✻➊▼➜☞➉ ➍❉➍ ➊ ➞❚☎✱➎ ➝ ➏ ✁ ➈▼➏ ➋❀➓ ✂✆➍ ➉ ☎ ➏▲➈▼➉ ✂☞➑ ➓ ✂✆➌✢➎ ➊❃➈ ✁✄✂✆➍ ➉✢➏ ✂ ➊ ➒✦✁✄➞☞➌ ➊ ➍✕➠ ➨✱➏✕➭✄➏▲➈ ✁✄➌❈➒✦✁✍➞✆➌ ➊❨➐❪➓ ☎ ➏ ➌❲➍❇➒ ➓✄➈✾➊❃➈ ✁✄✂✆➍ ➉❲➏ ✂ ➊ ➒✦✁✄➞☞➌ ➊ ➍ ➜ ✁ ➭✄➏✓➛✰➏✕➏ ✂ ❃ ➈ ➓ → → ➓ ➍ ➏ ☎t➶ ✗ ✒ ➘❞➠❪➼ ➓✄➈❝➊❃➜☞➏ →☞➞ ➈ → ➓ ➍ ➏❪➓ ➒ ➊▼➜✆➉ ➍✾➍ ➊ ➞✆☎☞➎ ➝ ➏ ✁ ➈▼➏ ➞✆➍ ➉ ✂✆➑ ➊❃➜☞➏❦➐❜➓ ☎ ➏ ➌❝→ ➈▼➏ ➍ ➏ ✂ ➊▼➏ ☎ ➉ ✂❐➶ ✗❳➘ ➝ ➜☞➉♣➋✤➜⑤➐❪➓ ☎ ➏ ➌♣➍④✁✍✂❄➎

Proceedings of the International Symposium on Quality Electronic Design (ISQED’02) 0-7695-1561-4/02 $17.00 © 2002 IEEE

➩ ➜✆➏ ✂❄➞ ➐✟➛❚➏▲➈④➓ ➒ ↔ →❚✁ ➈▼➊▼➉♣➋ ➌ ➏ ➍ ➜☞➉❡➊▼➊▼➉ ✂☞➑♠✁ ➋✕➉✢➈✤➋ ➞ ➉❡➊④➉ ➍④☎ ➉✢↔ ➈❃➏▲➋✏➊ ➌✢➎✓→ ➈▼➓ → ➓❁➈✙➊❃➉✢➓ ✂✆✁✍➌ ➊▼➓✟➊▼➜☞➏ ✁ ➋❀➊▼➉❲➭✄➏ ✁ ➈❃➏ ✁ ➓ ➒ ➊❃➜☞➏❭➋✕➉✢➈✤➋ ➞ ➉❡➊ ➳ ↔ →✆✁ ➈✙➊❃➉❲➋ ➌ ➏ ➍ ➜✆➉❡➊ ☎ ➓❄➏ ➍✟✂ ➓✍➊①➋❀➈❃➏ ✁ ➊▼➏ ➒ ➈▼➏▲➏④➋✤➜ ✁ ➈ ➑ ➏❉➋ ✁ ➈❃➈▼➉❲➏✕➈ ➍ ➉ ➒ ➉❡➊ ➜☞➉✢➊ ➍❭✁✓✂ ➓ ✂✿✁ ➋✏➊❃➉✢➭❁➏ ✁ ➈❃➏ ✁✬➶✢➹ ✝★➘ ➵ ➠✮➷ ➏ ✂ ➋❀➏ ➊❃➓✻➋❀➓❁➐ →❚✁ ➈❃➏ ☎ ➉❡➯✪➏✕➈▼↔ ➏ ✂ ➊❭➉✢➐ →☞➌ ➏✕➐❪➏ ✂ ➊ ✁ ➊▼➉❲➓ ✂❚➍ ➓ ➒ ➊▼➜☞➏❜➋❀➓ ➞✆✂ ➊❃➏✕➈ ✁ ➋✏➊▼➉❲➭✄➏ ✁ ➈❃➏ ✁ ➓ ➒ ➊▼➜☞➏ ➋❀➓ ➞☞✂ ➊▼➏▲➈ ➍ ➜☞➓ ➞✆➌❲☎ ➛✰➏✛➊ ✁ ➣❁➏ ✂ ➉ ✂ ➊▼➓ ✁ ➋✕➋✕➓ ➞☞✂ ➊ ➠✧➷ ➏ ✂ ➋✕➏ ➝ ➏ ☎ ➏✕➙ ✂ ➏ ➵ ✁✄➍ ✁❪✂ ➏ ➝ ➐❪➏❀➊❃➈▼➉♣➋✾➋ ✁✄➌✢➌ ➏ ☎❣➼✆✁✄➞☞➌ ➊ ❈➞✆➌✢✂ ➏▲➈ ✁ ➛☞➉ ➌ ➉✢➊ ➎③➳

BIT0 BIT0 BIT1 BIT1 . . . . BIT3

Logic to generate the bit for next state Similar for other bits

✱ ✏✹✸❙ ✹✸❙ ✘ ✵✸✷✺✹❯❚ ❃ ✕☛ ✞✡✠❲❱❳✎✂✄✝✆✒✎✟✄❩❨❭❬❪☛✛✠☞✆✟☛✕❫☎✠☞✞ ➓❢➐❜➏ ✁✄➍▼➞ ➈❃➏ ✵✸✷✺✹ ✁✄✂✆❴✹ ☎ ✸❙ ✁③➍ ➋❀➈❃➉ → ➊▼➏ ☎⑥➍ ➏❀➊❪➓

CLOCK

DFF

DFF

BIT 0

DFF

BIT 1

➩ ➒ ➍ ➉✢➐ ➞ ↔ ✛ ➊ ▼ ❲ ➉ ➓ ✕ ➏ ❃ ➈ ➏ ➏ ▼ ➊ ➓ ✕ ➏ ➈ ➓ ✄ ❃ ➈ ➐ ➏ ✕ ✱ ➢ ➜ ▼ ➊ ❲ ➉ ✄ ➭ ➏ ➉ ➌♣✁ ✂ ➍ ➝ ❚ ➞ ➍ ☎ ✆ → ➒ ✍✁ ➞✆➍ ✁✄✂✆✁✍➌❲➎✱➍ ✕➍ ➠s➩ ➜☞➏ ➓★➭✄➏▲➈ ✁✄✢➌ ➌ ➊❃✳ ➓ ➓ ➌✪➴ ➓ ➝ ➉ ❯ ☞ ➜ ➓ ➉ ➉ ➈ ▼ ➏ ➍ ➍ ➝ ✂ ✬ ✂ ➼ ❁ ➑ ➞ ➽☞➠

DFF

BIT 2

BIT 3

➼ ➉ ➑✄➞ ➈❃➏ ➫✆➸ Implementation of a Gray counter ➊▼➈ ✁✍✂✆➍ ➉❲➏ ➊▼➉❲➭✄➏ ✂ ➓ ✁✄➍❶✁❪☎ ➓

INPUTS

✂ ➊ ➝ ➜☞➉♣➋✤➜❜➈❃➏ ▼➍ ➞☞➌ ➊ ➍ ➉ ✂ ➋❀➓ ➌✢➌ ➏▲➋❀➊▼➉❲➓ ✂ ➓ ➒ ➋✤➜ ✁ ➈ ➑ ➏s➓ ✂✓✁✍✂✓✁ ➋❀↔ ➵ ➠❖➩ ➜☞➏s➊▼➈ ✁✍✂✆➍ ➉❲➏ ✂ ➊❛➉ ➍ ➐❪➓ ☎ ➏ ➌ ➏ ☎ ☎ ➏ ➳ ➏ ➑✆➠ ✌ ➛ ✾ ➏ ❀ ➏ ➢ ➓ ➏ ❃ ➊ ➉ ➉ ❫ ➏ ➞ ➌ → ✂ ✂ ✁✄➌ ✂ ✏ ➋✏➊❃➉✢➓ ✂ ➋ ➞ ➈❃➈▼➏ ✂ ➊ ➑ ➉❲➭✄➏ ✂ ➛ ➎r➸

✂✁☎✄✝✆✟✞✡✠☞☛✍✌✏✎✒✑

➌ ➍ ✂ ✂❚➍ ✁✍✂ ➠ ➍ ➉ ✂☞➑ ➊❃➜☞➉ ➍①➒✦✁✄➞☞➌ ➊④➐❪➓ ☎ ➏ ➌❝✁❤➒✦✁✄➞☞➌ ➊ ➍ ➏ ✂✆➍ ➉❡➊❃➉✢➭❄➉✢➊ ➎❹✁✄✂✆✁✍➌❲➎✱➍ ➉ ➍ ➛✰➏ ☎ ➓ ✂ ➏❉➊▼➓❤➋❀➓❁➐ →✆✁ ➈❃➏①➊ ➝ ➓③➊ ➎❄→ ➏ ➍ ➓ ➒ ➋❀➓ ➞☞✂ ➊▼➏✕➈❜➉❲➐ →✆➌ ➏✕↔ ➊ ✁ ➊▼➉❲➓ ✂✆➍▲➠ ➲❯➏▲➋❀➏ ✂ ➊ ➝ ➓✄➈❃➣ ➶ ★➘ ➜ ✁✄➍❭➍ ➜☞➓ ➝ ✂ ➊▼➜ ✁ ➊✮➊❃➜☞➏ ➒✦✁✍➞☞➌ ➊ ➉❡➊❃➉✢➭❄➉✢➊ ➎❣✁✄✂✆✁✍➌❲➎✱➍ ➉ ➍s➒ ➓✄➈ ✁✍✂ ↔ →❚✁ ➈▼➊▼➉♣➋ ➌ ➏❇➉ ✂❚☎✱➞ ➋❀➏ ☎ ➊▼➈ ✁✍✂❚➍ ➉❲➏ ✂ ➊ ➛✰➏ → ➏✕➈ ➒ ➓✄➈❃➐❜➏ ☎❉✁ ➊ ✁✍✂ ➏ ✁ ➈ ➌❲➎✻➍ ➊ ✁✄➑ ➏❝➉ ✂ ➊❃➜☞➏ ☎ ➏ ➍ ➉ ➑✄✂ ➋ ➎ ➋ ➌ ➏ ➨ ➾ ➋✕➉✢➈✤➋ ➞ ➉✢➊ ➍▲➠ ➐❪➏✕➊▼➈❃➉❲➋✬➋ ✁✍➌❲➌ ➏ ☎ ➊❃➜☞➏ ✑ ➈▼➓❁➛ ✁ ➛☞➉ ➌ ➉❡➊ ➎ ➓ ➒❝➼❚✁ ➉ ➌✢➞ ➈▼➏ ➳ ➵ ➛✰➏✕➏ ✂④→ ➈▼➓ → ➓ ➍ ➏ ☎ ➉ ✂❦➶ ✍➘✺➠✭➩ ➜☞➏ ➉ ➍s➑ ➉❲➭✄➏ ✂ ➛ ➎

✰

✲✱✴✳

✰

❒

➝

✵✸✷✺✹ ✘ ✻ ✽✔ ✼ ✔✯➬ ❀ ✔❂❁ ➱✿✾ ➜☞➏✕➈❃➏ ❃✴❄✦❆ ✔ ➉ ➍ ➊❃➜☞➏ ✁ ➈❃➏ ✁ ➓ ➒ ➬

➊▼➜☞➏ ✂ ➓

✔ ✘ ❇ ❒ ❃❅❄✦❆ ✔ ✔ ❈✔ ✼ ➱ ❃ ❄✦❆ ✾ ☎ ➏ ✤✠ ➠ ➬ ❀ ✔ ➉ ➍s➑ ➉✢➭❁➏ ✂

➹ ✻ ❀✔ ✘ ❋ ❉ ✽✔ ✼ ❊ ➱ ➬ ✔●❁

✁

◆✆

➬

✝

➹

➳✒➺ ➵ ➛ ➎

❉ ✘ ✁■❍❑❏▲❍▼✆

❒ ➝ ➜☞➏✕➈❃➏ ➉ ➍ ➊▼➜☞➏ ✂❄➞ ➐❨➛✰➏✕➈✧➓ ➒✆➍ ➊ ✁ ➊▼➏ ➍▲➳✺➺ ➒ ➓✄➈ ✂ ➝ ➜☞➉♣➋✤➜③➊❃➜☞➏ ➍ ➉❲➐ ➞✆➌❲✁ ➊▼➉❲➓ ✂ ➝ ✁❁➍✛→ ➏✕➈ ➒ ➓✄➈❃➐❪➏ ☎ ➓ ➒ ➉ ✂ ✏ ➏❫➋✏➊❃➉✢➓ ✂t➌ ➏✕➭❁➏ ➌♣➍ ➋❀➓ ✂❚➍ ➉ ☎ ➏✕➈❃➏ ☎❧✁✍✂✆☎ ➉➍ ➊▼➉❲➐❪➏✻➉ ✂✆➍ ➊ ✁✍✂ ➋✕➏ ➍✟✁ ➊ ➝ ➜☞➉♣➋✤➜ ➒✦✁✍➞✆➌ ➊ ➍ ➝ ➏✕➈❃➏✓➉ ✂ ➓ ➞ ➊✤➋❀➓❁➐❜➏❝➓ ➒❖✁✟➒✦✁✍➞✆➌ ➊❯➉ ✂ ✏ ➏▲➋❀➊▼➉❲➓ ✂ ➏❀➢ → ➏✕➈❃➉✢➐❪➏ ✂

✔ ✘P◗ ❘❖

✶✵✸✷✺✹

✵✸✷✺✹

❏

➳✦➻ ➵

↔❞➛☞➉❡➊❈➋❀➓ ➞☞✂ ➊▼➏▲➈✤➵ ➒ ➓❁➈ ➉ ➍ ➊▼➜☞➏ ✂❄➞ ➐✟➛❚➏▲➈ ➊▼➜✆➏ ✂✳➞ ➐❨➛✰➏✕➈✓➓ ➒ ➊❃➜☞➏ ✏ ➏▲➋✏➊❃➏ ☎❼➠r➬ ➊❶➉ ➍❶➑ ➉❲➭✄➏ ✂ ➛ ➎

➉ ➒ ➊▼➜✆➏✾➉ ✂ ✏ ➏❫➋✏➊❃➉✢➓ ✂ ➉ ✂ ➊▼➓ ✂ ➓ ☎ ➏ ✁✟➒✦✁✍➞☞➌ ➊ ➎ ➓ ➞ ➊ →☞➞ ➊ ➓✍➊❃➜☞➏✕➈ ➝ ➉ ➍ ➏

✔

✠

1. Create a list of nodes

SPICE wirelist

✓✕✔ ❒✟✖ ✗➳ ✞ ➵✙✘ ✓✛✚ ✏➳ ✎✢✜☎✣✏✤✦✥★✧ ✌✩✎✪✜✫✣✏✤✦✥✭✬ ➵ ➳✼➹ ➵ ➝ ➜☞➏✕➈❃➏ ✓ ✚ ➉ ➍ ➊❃➜☞➏❪➐ ✁ ➢✱➉✢➐ ➞ ➐✇➋ ➞ ➈❃➈❃➏ ✂ ➊ ✯✮ ➱ ➉ ➍ ➊▼➜☞➏✓➋❀➓ ➌✢➌ ➏▲➋❀➊▼➉❲➓ ✂ ➊▼➉❲➐❪➏r➋❀➓ ✂✆➍ ➊ ✁✍✂ ➊ ➒ ➓❁➈ ✁ ✏ ➞☞✂ ➋❀➊▼➉❲➓ ✂⑤✁✄✂✆☎ ✃ ➉ ➍ ➊❃➜☞➏③➉❲➓ ✂ ➊❃➈ ✁ ➋✤➣ ✮ ➏ ➊ ➛ ➉ ➜☞➐❪➏ ➊s➊▼➉❲➐❜➏✟➋❀➓ ➊ ➊ ➍ ✁ ✆ ➋ ✁✄✂ ➐❪➏ ✂ ➍ ➏ ✂✆➍ ➋ ✁✄✂ ➓ ➒ ➤ ➜ ✁✄➍

➳✺➽ ➵

➈❃➏ ➍▼➞☞➌ ➊ ➍ ➉ ✂ ➳◗➫ ➵

2. Run SPICE simulations with fault at one node

Inputs (States)

OUTPUTS RELIABILITY

3. Repeat step 2 for various charge generated , inputs (states), time instances

Charge Generated Time instance of fault

( POF, FV ) POWER

4. Compare the outputs to detect errors.

➼ ➉ ➑❁➞ ➈❃➏ ➽✱➸ Tool flow for measuring Reliability and Power

4. Improving fault tolerance of counters

❵

➢✱➜ ✁✍➞✆➍ ➊▼➉❲➭✄➏ ➍ ➉✢➐ ➞☞➌❲✁ ➊▼➉❲➓ ✂✆➍s➍ ➜☞➓ ➝ ✂ ➉ ✂ ➊▼➜☞➏❭➊▼➓❄➓ ➌❚➴ ➓ ➝ ➳✦➼ ➉ ➑ ↔ ❃ ➈ ➏ ➞ ➽ ➵ ➝ ➏▲➈▼➏ → ➏✕➈ ➒ ➓✄➈❃➐❪➏ ☎❪➞✆➍ ➉ ✂✆➑ ➊▼➜☞➏ ✁ ➛✰➓★➭✄➏s➐❪➏ ✂ ➊▼➉❲➓ ✂ ➏ ☎❪➒✦✁✍➞✆➌ ➊ ➏➍ ✂✆➍ ➉❡➊❃➉✢➭❄➉✢➊ ➎r✁✄✂✆✁✍➌❲➎✱➍ ➉ ➍ ➐❜➏✕➊▼➜☞➓ ☎ ➓ ✂❤✁❢➹✄➠✐➺ ➇✗➦r➧❝➨ → ➈▼➓✱➋✕➏ ➍❃➍✕➠ ❃ ➊ ☞ ➜ ➏ ➓ ➏ ➓ ▼ ➊ ☞ ➜ ❇ ➏ ✕ ➋ ➓ ▼ ➊ ▲ ➏ ➈ ▲ ➏ ▼ ➈ ❝ ➏ ❀ ➋ ➓ ➉ ➤❯➌❲➌ ✂ ☎ ➍ ➒ ➞☞✂ ✂✆➍ ☎ ➏▲➈▼➏ ☎①➒ ➓❁➈ ✁❪➍ ➉ ✂ ↔ ➝ ➏ ➊ ❃ ➊ ☞ ➜ ➏ ➓ ❲ ➉ ➛ ➏ ➊ ▼ ➊ ➏ ➑✄➌ ➒✦✁✍➞☞➌ ✁✍✂❚☎r✁✄➌✢➌ → ➍▼➍ ➌ ➍ ✁ ➍ ➓ ➒✗✁❣➫ ↔❞➛☞➉✢➊❇➋❀➓ ➞✆✂ ➊❃➏✕➈ ✕ ➏ ❃ ➈ ❭ ➏ ✕ ➋ ★ ➓ ✄ ➭ ✕ ➏ ❃ ➈ ➏ ❄ ➨ ▲ ➏ ✄ ➭ ✕ ➏ ➈ ☎❺➠ ✁✍➌ ➉ ✂ ✏ ➏▲➋❀➊▼➉❲➓ ✂❣➌ ➏▲➭✄➏ ➌♣➍ ➝ ➏▲➈▼➏ ✁✍➌♣➍ ➓❜➋❀➓ ✂✆➍ ➉ ☎ ↔ ➝ ➏✕➈❃➏ ☎❺➠ ➨✱➉✢➐ ➞☞➌❲✁ ➊▼➉❲➓ ✂ ➈❃➏ ➍▼➞☞➌ ➊ ➍ ➓ ➒ ➊❃➜☞➏④➋❀➓ ➞✆✂ ➊❃➏✕➈ ➍ ➝ ➉✢➊▼➜✆➓ ➞ ➊ ✁✍✂❄➎ ➓ → ➊▼➉❲➐❜➉❲➟ ✁ ➊▼➉❲➓ ✂ ➉ ➍❶➍ ➜☞➓ ➝ ✂ ➉ ✂ ➊ ✁ ➛ ➌ ➏ ➹✄➠

✒❛

➇❵➓ ☞ ➞ ✂ ➊▼➏✕➈ ➚ ➉ ✂❚✁ ➈ ➎ ➪ ➈ ✁❳➎

✑ ➧ ✝✆➠✢➹ ✝✆➠ ✝

➼

✗ ✒ ✒ ✝

❜✱

➼ ➹❫✡✗➺ ❄➠ ✕ ✕ ➠✕

✰

✑ ➓ ➝ ➏✕➈ ✝☞➠ ✝❁➽✄➺ ➐ ✁ ✝☞➠ ✝✄➻ ✒✄➐ ✁

➩✧✁ ➛ ➌ ➏ ➹✄➸ Comparison of counter without any optimization ➩ ➝ ➓ ✁✍→☞→ ▼➈ ➓ ✁ ➋✤➜☞➏ ➍ ➝ ➏✕➈❃➏s➋❀➓ ✂❚➍ ➉ ☎ ➏✕➈❃➏ ☎❨➒ ➓✄➈❈➉❲➐ → ➈❃➓★➭✳➉ ✂☞➑❭➒✦✁✍➞✆➌ ➊ ➊▼➓ ➌ ➏▲➈ ✄✁ ✂ ➋❀➏❦➓ ➒ ➊❃☞ ➜ ➏❾➋❀➓ ➞☞✂ ➊▼➏✕➈ ➠➀➼ ➉✢➈ ➍ ➊✿➐❪➏✕➊▼➜☞➓ ☎ ➉ ✂ ➭❁➓ ➌ ➭✄➏ ➍ ➉ ✂ ↔ ➋❀➓❁➈ → ➓✄➈ ✁ ➊❃➉ ✂✆➑ ➈❃➏ ✱ ☎ ➞✆✂✆☎☞✁✍✂ ➋ ➎ ➉ ✂ ➊▼➜☞➏✻➋✕➓ ➞☞✂ ➊❃➏✕➈❝➊▼➓④➐ ✁ ➣❁➏❜➊▼➜☞➏▲➐

Proceedings of the International Symposium on Quality Electronic Design (ISQED’02) 0-7695-1561-4/02 $17.00 © 2002 IEEE

➒✦✁✍➞☞➌ ➊✙↔✺➊▼➓ ➌ ➏▲➈ ✁✄✂ ➊ ✶ ➠ ➩ ➜✆➏ ➍ ➏▲➋✕➓ ✆ ✂ ☎ ➐❪➏❀➊❃➜☞➓ ☎✟➌ ➓❄➓✄➣ ➍❖✁ ➊❈➈❃➏ ☎ ➏ ➓➍ ❁➐❪➏❭➓ ➒ ➊❃➜☞➏✾➛ ➌ ✱ ➓ ➋✤➣ ➍ ➊❃✓ ➓ ➐ ✁ ✄➣ ➏❭➊▼➜✆➏❇➋❀➓ ➞✆✂ ➊❃➏✕➈ ➒✦✁✍➞✆➌ ➊▼↔✒➊❃➓

➍ ➉ ✄➑ ✂ ➉ ✂☞➑ ➌ ➏✕➈ ✁✍✂ ➊ ➠

RESET Error Detection Circuit

Counter data

Counter

4.1. Incorporating redundancy in the counters ➾ ✂⑦➑ ➏ ✂ ➏▲➈ ✁✄➌❇➍✙→✆✁ ➊▼➉ ✁✍➌❞➳✦✁ ➈▼➏ ✁ ➵❉➓✄➈④➊❃➏✕➐ → ➓❁➈ ✁✄➌✺➳ ➊▼➉❲➐❪➏❫➵④➈❃➏ ☎✱➞✆✂ ↔ ☎☞✁✍✂ ➋ ➎ ➋ ✁✍✂ ✁✍→☞→☞➌ ➉❲➏ ☎ ➊▼➓ ✁ ➋❀➉❲➈❃➋ ➞ ➉❡➊④➊❃➓t➐ ✁ ➣✄➏❢➊▼➜☞➏▲➐ ➒✦✁✍➞✆➌ ➊▼↔ ➊▼➓ ➌ ➏▲➈ ✁✄✂ ➊ ➠❋➤ ➈❃➏ ✁ ➈▼➏ ☎✱➞☞✂✆☎☞✁✄✂ ➋ ➎ ➋ ✁✍✂ ➛✰➏ ✁✍→☞→✆➌ ➉❲➏ ☎ ➊▼➓❹➋❀➓ ➞✆✂ ↔ ➊▼➏▲➈ ➍ ➉ ✂⑤✁ ➭✄➏▲➈ ➎t➍ ➉❲➐ →☞➌ ➏ ➒ ➓✄➈❃➐ ➓ ➒❇➡✮➞❚✁✍➌ ➦✬➓ ☎✱➞☞➌♣✁ ➈❉➲❯➏ ☎✱➞☞✂ ↔ ☎☞✁✍✂ ➋ ➎❼➳✦➡ ➦✿➲✮➵ ➳✒➼ ➉ ➑❁➞ ➈▼➏ ✕ ➵❢➓✄➈ ➩ ➈❃➉ →☞➌ ➏➂➦✬➓ ☎✱➞☞➌♣✁ ➈❾➲❯➏ ☎✱➞☞✂ ↔ ☎☞✁✍✂ ➋ ➎❼➳✦➩ ➦✿➲✛➵ ➝ ➜☞➏✕➈❃➏✕➉ ✂ ➈❃➏ ☎☞➞☞✂✆☎☞✁✄✂ ➊✿➋✕➓ ➞☞✂ ➊▼➏▲➈ ➍④✁ ➈▼➏ ✁✄☎✆☎ ➏ ☎ ✁✍✂✆☎ ➊❃➜☞➏❶➙ ✂✆✁✄➌ ➓ ➞ ➊ →☞➞ ➊❛➉ ➍ ➊▼➜☞➏✮➐ ✁ ✏ ➓✄➈❃➉❡➊ ➎ ➭✄➓✍➊❃➏❶➓ ➒ ➊▼➜☞➏ ➍ ➏✛➋❀➓ ➞✆✂ ↔ ➊▼➏▲➈ ➍▲➠ ➇ ➌ ➏ ✁ ➈ ➌✢➎r✁✄☎☞☎ ➉ ✂☞➑✬✁✍✂❄➎ ➊ ➎❄→ ➏✓➓ ➒❶✁ ➈❃➏ ✁ ➈▼➏ ☎✱➞☞✂✆☎✆✁✍✂ ➋ ➎ ➉ ✂ ↔ ➋❀➈❃➏ ✁❁➍ ➏ ➍❈→ ➓ ➝ ➏✕➈❵➋❀➓ ✂❚➍✙➞ ➐ → ➊❃➉✢➓ ✂✻➍ ➉ ➑❁✂ ➉❡➙✰➋ ✁✍✂ ➊ ➌✢➎④➳ ➛ ➎❪✁✾➒✦✁ ➋❀➊▼➓❁➈❛➓ ➒ ➺ ➓✄➈ ➻ ➵ ➠

ERROR Counter clock Counter load

OUT1

Counter LOAD DATA

OUT

with enable

Correct Data DATA

➼ ➉ ➑❁➞ ➈▼➏ ✗✱➸ Architecture of time redundant counter ➇❵➓ ☞ ➞ ✂ ➊▼➏▲➈ ➤ ➈❃➏ ✁ ➲❶➏ ☎☞➞☞✂✆☎☞✁✄✂ ➊ ➚ ➩ ➉❲➐❜➏❇➲❯➏ ☎✱➞☞✂❚☎☞✁✍✂ ➊ ➚ ➤ ➈▼➏ ✁ ➲❯➏ ☎✱➞☞✂❚☎☞✁✍✂ ➊ ➩ ➉✢➐❪➏❇➲❶➏ ☎✱➞☞✂✆☎☞✁✄✂ ➊

ERROR

CLOCK

2:1 MUX

Error Detection Circuit

2−1 MUX

Control Logic

CLOCK

CLOCK RESET

OUT Regi− ster

LOAD

➩❛➎❄→ ➏ ➉ ✂✆✁ ➈ ➎ ➉ ✂❚✁ ➈ ➎ ➪ ➈ ✁❳➎ ➪ ➈ ✁❳➎

✑ ➓ ➝ ✝☞➠❲➹✄➹❫➺✄➻ ✝☞➠ ✝ ✒ ➺❁➺ ✝☞➠ ✝ ✒ ✝ ✕ ✝☞➠ ✝ ✕ ➺✄➻

➇❵➓ ➞✆✂ ➊❃➏✕➈ ➇❵➓ ➞☞✂ ➊▼➏▲➈ ➇❵➓ ➞☞✂ ➊▼➏▲➈ ➇❵➓ ➞☞✂ ➊▼➏✕➈

➏✕➈ ➐ ✁ ➐ ✁ ➐ ✁ ➐ ✁

➩✧✁ ➛ ➌ ➏ ➺✱➸ Power comparison of area and time redundant counters

OUT2

Redundant Counter

4.2. Circuit-level fault tolerance ➼ ➉ ➑❁➞ ➈▼➏ ✕ ➸ Architecture of area redundant (DMR) counter ✁ ➏ → ➈❃➓ → ➓ ➍ ➏❪➊▼➓③➉ ✂ ➋✕➓✄➈ → ➓❁➈ ✁ ➊▼➏ ✎✺✥✴✑❪✞✕■✡✌▼✞✤✩★✯✱✔✪✩✄☛✍✔✰✣✕✹ ➉ ✂ ➊❃➜☞➏ ➋❀➓ ➞☞✂ ➊▼➏✕➈ ➍▲➠♦➩ ➜☞➉ ➍❦✁✍→☞→ ➈❃➓ ✁ ➋✤➜ ➌ ➉❲➐❪➉❡➊ ➍ ➜ ✁ ➈ ☎ ➝ ✁ ➈▼➏⑥➓★➭✄➏✕➈❃➜☞➏ ✁✄☎ ➌ ➏ ✁✄☎ ➉ ✂☞➑ ➊▼➓③➈❃➏ ☎☞➞ ➋❀➏ ☎❤→ ➓ ➝ ➏✕➈❪➋❀➓ ✂✆➍▼➞ ➐ → ➊▼➉❲➓ ✂❺➠ ➾ ✂ ➓ ➞ ➈ ✎✒✥✴✑✓✞❀■ ✌▼✞✤✩★✯✱✔✪✩✄☛★✔❚✎ ➊❃➏▲➋✤➜ ✂ ➉❲➥ ➞ ➏ ✁✍✂ ➏▲➈▼➈ ✁✍✂ ➊❨➓ ➞ ➊ →☞➞ ➊❜➉ ➍ ➈❃➏▲➋✕➓✄➐ →☞➞ ➊❃➏ ☎ ➉ ✂✬✁✄✂❣✁ ➊✙➊▼➏▲➐ → ➊❶➊▼➓✓➈❃➏▲➋✕➓★➭✄➏✕➈ ➒ ➈❃➓✄➐↕➊❃➈ ✁✄✂✆➍ ➉❲➏ ✂ ➊ ➒✦✁✍➞✆➌ ➊ ➍✕➠ ➼ ➉ ➑✄➞ ➈❃➏ ✗ ➉ ➌❲➌❲➞✆➍ ➊❃➈ ✁ ➊▼➏ ➍ ➓ ➞ ➈❵➉❲➐ →☞➌ ➏✕➐❪➏ ✂ ➊ ✁ ➊▼➉❲➓ ✂ ➓ ➒ ➊❃➜☞➏ ✎✒✥✴✑✓✞❀■ ✌▼✞✤✩★✯✱✔✪✩✄☛★✔❚✎ ➊▼➏▲➋✤➜ ✂ ➉❲➥ ➞ ➏ ➠ ➡✛➞ ➈❃➉ ✂☞➑❽✂ ➓❁➈▼➐ ✁✍➌ ➓ → ➏▲➈ ✁ ➊▼➉❲➓ ✂ ➊❃➜☞➏ ➋❀➓ ➞☞✂ ➊▼➏✕➈❛➓ ➞ ➊ →☞➞ ➊❵➉ ➍❛➍ ➊▼➓❁➈▼➏ ☎ ➉ ✂①✁✄✂ ➏ ✂✆✁ ➛ ➌ ➏ ☎ ➈❃➏ ➑ ➉ ➍ ➊▼➏▲➈ ➠ ➾ ✂ ➋ ✁✄➍ ➏ ➓ ➒☞✁✍✂ ➏▲➈▼➈❃➓✄➈ ➊❃➜☞➏ → ➈▼➏▲➭✳➉❲➓ ➞❚➍✙➌❲➎ ↔ ➍ ➊▼➓❁➈▼➏ ☎ ➋✕➓✄➈❃➈▼➏❫➋✏➊❺➭ ✁✍➌❲➞ ➏✭➉ ➍❺➌ ➓ ✁❁☎ ➏ ☎ ➉ ✂ ➊❃➓✓➊▼➜☞➏❜➋❀➓ ➞☞✂ ➊▼➏✕➈ ➠❶➩ ➜☞➏❨➋✕➓ ➞☞✂ ➊▼➏▲➈✮➉ ➍ ➊❃➜☞➏ ✂✿➑ ➉✢➭❁➏ ✂✬✁ ➋ ➌ ➓✱➋✤➣❉➊▼➓ ➈▼➏❫➋❀➓❁➐ →✆➞ ➊▼➏❶➊❃➜☞➏ ✂ ➏✕➢❄➊ ➍ ➊ ✁ ➊❃➏ ➠❖➩ ➜☞➏ ✁❁☎☞☎ ➉✢➊▼➉❲➓ ✂✆✁✄➌ ➜ ✁ ➈ ☎ ➝ ✁ ➈❃➏s➈▼➏✕↔ ➥ ➞ ➉✢➈❃➏ ☎ ➉ ✂ ➋ ➌❲➞✆☎ ➏ ➍✾✁✍✂ ➏ ✂✆✁ ➛ ➌ ➏ ☎ ➈▼➏ ➑ ➉ ➍ ➊❃➏✕➈ ➐ ➞☞➌ ➊▼➉ →☞➌ ➏❀➢✱➏✕➈ ➍ ✁✍✂✆☎ ➋❀➓ ✂ ➊❃➈▼➓ ➌❚➌ ➓ ➑ ➉❲➋ ➒ ➓✄➈ ➌ ➓ ✁❁☎✻✁✍✂❚☎ ➋ ➌ ➓✱➋✤➣ ➍ ➉ ➑❁✂✆✁✍➌♣➍✕➠ ✑ ➓ ➝ ➏✕➈❛➉ ➍❶➍❃✁ ➭✄➏ ☎ ➍ ➉ ✂ ➋✕➏❉➏▲➈▼➈❃➓✄➈❇➈❃➏▲➋✕➓★➭✄➏▲➈ ➎❢➌ ➓ ➑ ➉♣➋✓➉ ➍✟➞❚➍ ➏ ☎ ➓ ✂✆➌✢➎ ✂✁☎✄✝✆✟✞ ✁✄✂ ➏✕➈❃➈❃➓✄➈ ➜ ✁✄➍ ➛✰➏✕➏ ✂❉☎ ➏✕➊▼➏▲➋❀➊▼➏ ☎❼➠✭➩ ➜ ➞✆➍ ➊❃➜☞➉ ➍ ➊❃➏▲➋✤➜ ✂ ➉❲➥ ➞ ➏❭➉ ➍s✁✄→☞→ ➈❃➓ → ➈❃➉ ✁ ➊▼➏ ➒ ➓✄➈ ➞☞➌ ➊▼➈ ✁ ↔ ➌ ➓ ➝ → ➓ ➝ ➏✕➈ ✁✄✂✆☎❉➌ ➓ ➝ → ➏▲➈ ➒ ➓❁➈▼➐ ✁✍✂ ➋❀➏ ➍✙➎✱➍ ➊▼➏✕➐ ➍▲➠ ➼ ➓✄➈ ➍ ➉ ✂☞➑✄➌ ➏ ➒✦✁✄➞☞➌ ➊ ➍ ✁ ➈▼➏ ✁➂✁✍✂❚☎ ➊▼➉❲➐❪➏t➈❃➏ ☎☞➞☞✂✆☎☞✁✄✂ ➊r➊▼➏❫➋✤➜✱↔ ♣ ➉ ➥ ✂ ➞ ➏ ➍❝☎ ➉ ➍ ➋ ➞✆➍▼➍ ➏ ☎③✁ ➛✰➓★➭✄➏❇➈❃➏ ➍▼➞☞➌ ➊❭➉ ✂❾➹ ✝✞✝✡✠ ➈❃➏ ➌ ➉ ✁ ➛☞➉ ➌ ➉✢➊ ➎✄➠❝➩ ➜☞➏ → ➓ ➝ ➏✕➈s➋❀➓ ✂✆➍▼➞ ➐❪➏ ☎ ➛ ➎ ➊▼➜✆➏ ➍ ➏✛➉❲➐ →☞➌ ➏▲➐❪➏ ✂ ➊ ✁ ➊▼➉❲➓ ✂✆➍ ➉ ➍✗➍ ➜☞➓ ➝ ✂ ➉ ✂ ➊ ✁ ➛ ➌ ➏ ➺☞➠

➤ ➋✕➓ ➞☞✂ ➊❃➏✕➈✭➋❀➓ ✂✆➍ ➉ ➍ ➊ ➍ ➓ ➒❼✁❝➍ ➏✕➊❈➓ ➒ ➐❜➏▲➐❪➓✄➈ ➎ ➏ ➌ ➏✕➐❪➏ ✂ ➊ ➍✮➳✴➴ ➉ → ↔ ➓ ➴ ✆ → ➍ ➵ ➝ ➜☞➉♣➋✤➜❉➜✆➓ ➌♣☎☞➍ ➊❃➜☞➏✾➋ ➞ ➈❃➈❃➏ ✂ ➊ ➍ ➊ ✁ ➊▼➏❭➓ ➒ ➊❃➜☞➏✾➋❀➓ ➞✆✂ ➊❃➏✕➈ ✁✍✂✆☎ ➓➌ ➑ ➉♣➋ ➝ ➜☞➉♣➋✤➜ ☎ ➏❀➊▼➏▲➈▼➐❪➉ ✂ ➏ ➍ ➊❃➜☞➏ ✂ ➏✕➢✳➊ ➍ ➊ ✁ ➊▼➏s➛ ✁❁➍ ➏ ☎ ➓ ✂ ➊❃➜☞➏ → ➈❃➏❀↔ ➭❄➉✢➓ ➞✆➍❶➍ ➊ ✁ ➊❃➏ ➠ ➨❄➉ ✂ ➋✕➏ ➴ ➉ → ↔ ➴ ➓ →✆➍❶✁ ➈❃➏✛➛✆➉ ➍ ➊ ✁ ➛ ➌ ➏❝➏ ➌ ➏▲➐❜➏ ✂ ➊ ➍ ➊▼➜☞➏ ➎ ✁ ➈❃➏❣➐❜➓❁➈▼➏ ➍ ➏ ✂✆➍ ➉❡➊❃➉✢➭❁➏✻➊❃➓③➊❃➈ ✁✄✂✆➍ ➉✢➏ ✂ ➊ ➍ ➊▼➜ ✁✄✂ ➊▼➜✆➏ ➌ ➓ ➑ ➉❲➋ ➑❁✁ ➊▼➏ ➍✕➠ ➷ ➏ ✂ ➋❀➏ ✁✍✂❄➎❹✁ ➊▼➊▼➏✕➐ → ➊❣➊▼➓⑥➈▼➏ ☎ ➏ ➍ ➉ ➑❁✂ ➋❀➓ ➞☞✂ ➊▼➏✕➈❉➋❀➓✄➐ → ➓ ✂ ➏ ✂ ➊ ➍ ➍ ➜☞➓ ➞☞➌♣☎④➍ ➊ ✁ ➈▼➊ ➒ ➈▼➓❁➐❋➊❃➜☞➏ ➴ ➉ → ↔ ➴ ➓ →❺➠❵➤❥➩ ➈ ✁✍✂❚➍ ➉❲➏ ✂ ➊ ✑✭➞☞➌♣➍ ➏ ➩ ➓ ➌ ↔ ➏✕➈ ✁✍✂ ➊ ⑧✁ ➊✤➋✤➜ ➳✦➩ ✑❵➩ ➵ → ➈▼➓ → ➓ ➍ ➏ ☎ ➉ ✂❽➶❡➹❁➹✏➘ ➋ ✁✍✂ ➛✰➏ ➞❚➍ ➏ ☎ ➊▼➓ ➉❲➐ → ➈▼➓★➭❁➏❵➊❃➜☞➏ ➒✦✁✄➞☞➌ ➊❛➊▼➓ ➌ ➏✕➈ ✁✍✂ ➋❀➏s➓ ➒ ➊▼➜☞➏ ➴ ➉ → ↔ ➴ ➓ →✓✁✍✂✆☎ ➜☞➏ ✂ ➋❀➏❶➓ ➒ ➊▼➜✆➏❜➋✕➓ ➞☞✂ ➊▼➏▲➈ ➠ ➲❯➇❽➋❀➉❲➈❃➋ ➞ ➉❡➊❭➜☞➏ ➌❲→✆➍ ➉ ✂ ➙ ➌ ➊❃➏✕➈❃➉ ✂✆➑ ➓ ➞ ➊✮➊▼➜✆➏✟➜☞➉ ➑ ➜ ➒ ➈❃➏▲➥ ➞ ➏ ✂ ➋ ➎ ➊❃➈ ✁✄✂✆➍ ➉❲➏ ✂ ➊ ➍▲➳✒➼ ➉ ➑✄➞ ➈▼➏ ✒❁➵ ➠ ➨❄➏▲➭✄➏▲➈ ✁✄➌ ➲❯➇❦➭ ✁✄➌✢➞ ➏ ➍ ➝ ➏▲➈▼➏ ➓✄➜☞➐ ➞✆➍ ➏ ☎♠➳ ➈ ✁✄✂☞➑ ➉ ✂☞➑④➒ ➈❃➓✄➐ ➽ ↔ ➺✟✡✠✝ ✗✍➽ ➯❚↔ ➻ ✝✞✝ ➯❛➵✛➊▼➓ ➍ ➏✕➏①➊▼➜☞➏ ➏❀➯✪➏▲➋❀➊❵➓ ➒⑧➩ ✑❛➩ ➓ ✂❪➒✦✁✍➞☞➌ ➊✙↔✺➊▼➓ ➌ ➏▲➈ ✁✄✂ ➋❀➏ ✁✄✂✆☎❪→ ➓ ➝ ➏✕➈ ➳✦➩✧✁ ➛ ➌ ➏ ➻ ➵ ➠ ➲❯➏ ➍▼➞☞➌ ➊ ➍✻➍ ➜☞➓ ➝ ➊▼➜ ✁ ➊ ➝ ➉❡➊❃➜➂➉ ✂ ➋❀➈❃➏ ✁❁➍ ➏④➉ ✂ ➈▼➏ ➍ ➉ ➍ ➊ ✁✍✂ ➋✕➏ ✁✍✂✆☎ ➋ ✁✄→✆✁ ➋✕➉❡➊ ✁✍✂ ➋✕➏✓➊▼➜✆➏❉➈❃➏ ➌ ➉ ✁ ➛☞➉ ➌ ➉✢➊ ➎ ➓ ➒ ➊▼➜☞➏❣➋❀➓ ➞☞✂ ➊▼➏✕➈❜➉ ✂ ➋❀➈❃➏ ✁❁➍ ➏ ➍❇✁ ➊ ➊▼➜✆➏❣➋✕➓ ➍ ➊✟➓ ➒ ➉ ✂ ➋✕➈▼➏ ✁✄➍ ➏ ☎❦→ ➓ ➝ ➏▲➈ ➳✒➼ ➉ ➑✄➞ ➈▼➏ ➍ ③✁✄✂✆☎♠➹ ✝ ➵ ➠❦➩ ➜☞➏ ➑❁✁ ➉ ✂ ➉ ✂ ➊▼➏▲➈▼➐ ➍ ➓ ➒ ➈▼➏ ➌ ➉ ✁ ➛☞➉ ➌ ➉❡➊ ➎ ➜☞➓ ➝ ➏▲➭✄➏▲➈ ➍▼✁ ➊ ➞ ➈ ✁ ➊❃➏ ➍❶✁ ➊ ✁ ➛✰➓ ➞ ➊ ➹ ☛ ✝ ✠ ➓✄➜☞➐ ✁✄✂✆☎✻✁✄✂❄➎✟➒◗➞ ➈✙➊❃➜☞➏✕➈s➈❃➏ ➍ ➉ ➍ ➊ ✁✄✂ ➋❀➏✛➉ ✂ ➋✕➈▼➏ ✁✄➍ ➏✮➈❃➏ ➍▼➞☞➌ ➊ ➍ ➉ ✂ ✁✄☎✆☎ ➉❡➊❃➉✢➓ ✂✆✁✍➌❼→ ➓ ➝ ➏✕➈❯➋❀➓ ➍ ➊ ➠ ➤✮✂ ➓✍➊❃➜☞➏✕➈r➊▼➏❫➋✤➜ ✂ ➉♣➥ ➞ ➏ ➝ ➜☞➉♣➋✤➜❥➐❪➉ ➑ ➜✳➊ → ➈❃➓★➭✳➉ ☎ ➏❾➉❲➐ → ➈❃➓★➭✄➏❀↔ ➐❪➏ ✂ ➊❇➉ ✂③➒✦✁✄➞☞➌ ➊▼↔✒➊❃➓ ➌ ➏✕➈ ✁✍✂ ➋✕➏✟➉ ➍ ➊▼➓④➉ ✂ ➋❀➈❃➏ ✁❁➍ ➏✟➊▼➜✆➏ ➍ ➉❲➟✕➏❪➓ ➒ ➊▼➈ ✁✍✂ ↔ ➍ ➉ ➍ ➊▼➓❁➈ ➍r➶❡➹❳➺❫➘✺➠ ➾ ✂ ➋❀➈❃➏ ✁❁➍ ➉ ✂☞➑ ➊❃➜☞➏ ➍ ➉❲➟✕➏✿➓ ➒ ➊▼➜☞➏③➊▼➈ ✁✍✂✆➍ ➉ ➍ ➊▼➓❁➈✻➈❃➏❀↔ ☎✱➞ ➋✕➏ ➍ ➊❃➜☞➏✓➐ ✁✍➑✄✂ ➉❡➊ ➞✆☎ ➏❜➓ ➒ ➊❃➜☞➏✓➓✍➯ ➍ ➏❀➊ ✂ ➓ ☎ ➏❪➭✄➓ ➌ ➊ ✁✄➑ ➏❜➓ ➒ ➊▼➜☞➏

Proceedings of the International Symposium on Quality Electronic Design (ISQED’02) 0-7695-1561-4/02 $17.00 © 2002 IEEE

✳

✳

✳

✂✰

0.075

Clk

0.07

Clk

Power consumed (in mW)

R,C

Clk R,C

Binary Counter Gray Counter

0.065 0.06 0.055 0.05 0.045 0.04 0.035

Clk

0

5

10 Resistance (in K−ohms)

15

20

➼ ➉ ➑❁➞ ➈❃➏ ➹ ✝☞➸ Effect of resistance on power ➼ ➉ ➑❁➞ ➈▼➏ ✒ ➸ Transient Pulse Tolerant Latch (TPTL) ➇❵➓ ✆ ➞ ✂ ❃➊ ➏✕➈ ➓ ➈▼➐ ✁✍➌ ❁ ➚ ➉ ✂✆✁ ➈ ➎ ➽ ✠ ➓✄➜☞➐ ➹ ✝✡✠ ➓✄➜☞➐ ➺✟✝ ➣✓➓✄➜☞➐ ➈ ➓❁➈▼➐ ✁✍➌ ➪ ✁❳➎ ➽ ✠ ➓✄➜☞➐ ➹ ✝✡✠ ➓✄➜☞➐ ➺✟✝ ➣✓➓✄➜☞➐

✑ ➧ ➼ ✝✆➠✢➹ ✗ ✒

✝✆➠✢➹❳➽✄➺ ✝✆➠✢➹ ✄ ✝ ➻ ✝✆➠✢➹ ✝ ✝ ✝ ➠✝ ✒ ✆ ✝✆➠ ✝ ✕ ➺ ✝✆➠ ✳ ✝ ➽✍➻ ✝✆➠ ✳ ✝ ➽✄➺

➼ ✱ ❜ ➹❫✡✗➺ ❄➠ ✕ ➹ ✝✢☞➠✰ ✝ ✗✍➻☞➠ ✒ ✗✱➹✄➠ ✗ ✰ ✕ ➠✕ ✗★➫✆➠ ✰ ✕ ➫✆➠ ✝ ✒ ✕ ➺✱➠

✑ ➓ ➝ ➏✕➈

✝☞➠ ✝❁➽❁➺ ➐ ✒ ➐ ✝☞➠ ❁ ✝ ➽ ✍ ✝☞➠ ✝ ✕ ➽ ➐ ✝☞➠ ✝✡✍➻✗ ➐ ✒ ➐ ✝☞➠ ✄ ✝ ➻ ✍ ✝☞➠ ✍ ✝ ➫❁➫ ➐ ✝☞➠ ❁ ✝ ➽☞➹ ➐ ✝☞➠ ✝ ✕ ➹ ➐

✁ ✁ ✁ ✁ ✁ ✁ ✁

Binary Counter Gray Counter 120

Fault Vulnerability

110 100 90 80 70

5

10 Resistance (in K−ohms)

15

➊▼➓ ➺ ✝✡✻➠ ✠ ✑ ➧ ➼ ✝✆➠✢➹ ✗ ✒ ✝✆➠✢➹▲✔✗➫ ✝✆➠ ✝ ✒ ✝ ✝✆➠ ✄ ✝ ✞✝➫ ✝ ➠✝ ✒ ☞

✝✆➠ ✝✳➽✄➽ ✝✆➠ ✳ ✝ ❭✰➺ ✝✆➠ ✆ ✝ ➹❫➽

➼ ✱ ❜ ➹❳✞✗➺ ❄➠ ✕ ➹❁➹✄➹✄➠ ✗ ✕ ➫✆➠✐➺ ➻❁➻☞➠ ✒ ✰ ✕ ➠✕ ✗✟☞➠✝ ➻ ➻✢☞➠✰ ✐➺ ➺☞➹✄➠ ➻

✑ ➓ ➝ ➏✕➈

✝☞➠ ✝❁➽❁➺ ➐ ✝☞➠ ✝ ✕✞✕ ➐ ✝☞➠ ✝ ✒ ➺ ➐ ✒ ➐ ✝☞➠ ✝✪✰ ✍ ✒ ➐ ✝☞➠ ✝✄➻ ✍

✁ ✁ ✁ ✁ ✁

✝☞➠ ✝❁➽❁➽ ➐ ✁ ✝☞➠ ✝✡✄➺✗ ➐ ✁ ✝☞➠ ✝ ✒✞✍➐✒ ✁

➩✧✁ ➛ ➌ ➏ ➫✆➸

Comparison of counters using various transistor sizes

➲❯➏ ➍▼➞☞➌ ➊ ➍❇➍ ➜☞➓ ➝ ➊❃➜ ✁ ➊✾➊❃➜☞➏✓➈❃➏ ➌ ➉ ✁ ➛☞➉ ➌ ➉✢➊ ➎ ➓ ➒ ➊▼➜☞➏❉➋❀➓ ➞✆✂ ➊❃➏✕➈✾➉ ✂ ↔ ➋❀➈❃➏ ✁❁➍ ➏ ➍ ➝ ➉✢➊▼➜❇➉ ✂ ➋✕➈▼➏ ✁✄➍ ➏✭➉ ✂ ➊▼➜☞➏ ➍ ➉❲➟✕➏✭➓ ➒ ➊▼➜☞➏❵➊▼➈ ✁✍✂❚➍ ➉ ➍ ➊❃➓✄➈ ➍ ✁✍➑✳✁ ➉ ✂ ✁ ➊✛➊▼➜☞➏❜➋❀➓ ➍ ➊✮➓ ➒ ➉ ✂ ➋✕➈▼➏ ✁✄➍ ➏ ☎❣→ ➓ ➝ ➏▲➈ ➳✦➼ ➉ ➑✄➞ ➈❃➏ ➍❨➹✄➹❇✁✄✂✆☎❤➹❫➺ ➵ ➠❯➤ ➍ ➉ ➑❁✂ ➉❡➙✰➋ ✁✍✂ ➊ ➑❁✁ ➉ ✂ ➉ ✂ ➈▼➏ ➌ ➉ ✁ ➛☞➉ ➌ ➉❡➊ ➎ ➉ ➍ ➓❁➛ ➍ ➏✕➈❃➭✄➏ ☎③✁✄➍ ➊▼➜☞➏ ➍ ➉✢➟▲➏✟➓ ➒ ➊▼➜✆➏❭➋✕➈▼➉✢➊▼➉♣➋ ✁✄➌❚☎ ➏▲➭✳➉♣➋❀➏ ➍ ➉ ➍ ➉ ✂ ➋✕➈▼➏ ✁✄➍ ➏ ☎❼➠ ➾ ➒ ➊▼➜☞➏ ➍ ➉❲➟✕➏✛➓ ➒⑧☎ ➏▲➭❄➉❲➋✕➏ ➍ ➉ ➍ ➒◗➞ ➈▼➊▼➜☞➏▲➈✛➉ ✂ ➋✕➈▼➏ ✁✄➍ ➏ ☎ ➈▼➏ ➌ ➉ ✁ ➛✆➉ ➌ ➉❡➊ ➎ ➝ ➉ ➌✢➌ ➉✢➐ → ➈❃➓★➭✄➏❨➛ ➞ ➊❝➉❡➊❭➐❜➉ ➑ ➜✳➊ ➏ ❀➉❲➏ ✂ ➊❈➊❃➓✾➉ ✂ ➋✕➈▼➏ ✁✄➍ ➏✗➊▼➜☞➏ ➍ ➉✢➟▲➏s➓ ➒ ➊▼➜☞➏ ☎ ➏▲➭❄➉❲➋✕➏ ➍ ✂ ➓✄➊✭➛❚➏ → ➓ ➝ ➏✕➈❖☎✄①➋ ➛✰➏ ➎ ➓ ✂✆☎❤✁ ➋✕➏✕➈▼➊ ✁ ➉ ✂❦➌ ➉❲➐❪➉❡➊ ➠✿➤➔➍ ➉✢➟▲➉ ✂✆➑④➒✦✁ ➋✏➊❃➓✄➈❨➋ ✁✍✂ ➛✰➏ ☎ ➏✕➊▼➏✕➈▼↔ ➐❪➉ ✂ ➏ ☎ ➛ ✁✄➍ ➏ ☎ ➓ ✂ ➊❃➜☞➏ → ➓ ➝ ➏✕➈❇➛ ➞❚☎✱➑ ➏✕➊ ➒ ➓✄➈❨➊▼➜☞➏ ➍✙➎✱➍ ➊▼➏▲➐ ➳ ➓✄➈ ➊▼➜✆➏❇➋❀➉❲➈❃➋ ➞ ➉❡➊✏➵ ➠

130

0

✗✞✠

➇❵➓ ➞☞✂ ▼➊ ➏✕➈ ✄➓ ➈❃➐ ✄✁ ➌ ➚ ➉❚ ✂ ✁ ➈ ➎ ➺✂✁ ➫✄✁ ✕ ✁ ➓✄➈❃➐ ✄✁ ➌ ➪ ➈ ✁❳➎ ➺✂✁ ➫✄✁ ✕ ✁

✁

➩✶✁ ➛ ➌ ➏ ➻✆➸ Comparison of counters using various resistance values

60

➈ ✁✍✂☞➑ ➉ ✂☞➑✟➒ ➈❃➓✄➐

20

➼ ➉ ➑✄➞ ➈▼➏ ✰☞➸ Effect of resistance on reliability ➊▼➈ ✁✍✂✆➍ ➉❲➏ ✂ ➊ ✁✍✂✆☎ ➊▼➜ ➞✆➍ ➉✢➐ → ➈❃➓★➭✄➏ ➍ ➈▼➏ ➌ ➉ ✁ ➛☞➉ ➌ ➉❡➊ ➎❁➠ ➧ ✂☞➌❲➎r➍ ➏ ➌ ➏▲➋✏➊❃➏ ☎ ➜☞➉ ➑ ➜ ➌❲➎❽➍ ➏ ✂❚➍ ➉✢➊▼➉❲➭✄➏ ✂ ➓ ☎ ➏ ➍③➍ ➜☞➓ ➞✆➌❲☎ ➛✰➏⑥➈❃➏ ➍ ➉✢➟▲➏ ☎ ➊▼➓⑤➉✢➐ → ➈❃➓★➭✄➏ ➊▼➜☞➏ ➒✦✁✍➞✆➌ ➊▼↔✒➊❃➓ ➌ ➏✕➈ ✁✍✂ ➋✕➏ ➝ ➉❡➊❃➜☞➓ ➞ ➊❭➉ ✂ ➋❀➈❃➏ ✁❁➍ ➉ ✂☞➑ ➊❃➜☞➏ ✁ ➈❃➏ ✁①➍ ➉ ➑❁✂ ➉✢➙☞↔ ➋ ✁✄✂ ➊ ➌✢➎❁➠ ➇❵➈▼➉✢➊▼➉♣➋ ✁✄➌❚✂ ➓ ☎ ➏ ➍ ➝ ➏✕➈❃➏ ➍ ➉❲➟✕➏ ☎ ➛ ➎✓✁❇➒✦✁ ➋✏➊❃➓✄➈✗➓ ➒✶➺ ↔ ✁✍✂✆☎ ✕ ➊▼➜☞➏▲➉✢➈❪➏✕➯✰➏❫➋✏➊✓➓ ✂⑥➒✦✁✍➞☞➌ ➊✙↔✺➊▼➓ ➌ ➏▲➈ ✁✄✂ ➋❀➏ ✁✍✂✆☎❧→ ➓ ➝ ➏✕➈ ➝ ✁✄➍❜➍ ➊ ➞✆☎ ➉❲➏ ☎ ➳✦➩✧✁ ➛ ➌ ➏ ➫ ➵ ➠❜➩ ➜☞➉ ➍ ➊❃➏▲➋✤➜ ✂ ➉❲➥ ➞ ➏❪➈❃➏ ➍▼➞☞➌ ➊❃➏ ☎ ➉ ✂❢✁✍✂❦✁ ➈❃➏ ✁①→ ➏ ✂❚✁✍➌ ➊ ➎

5. Conclusions and Future work ➼ ➈▼➓❁➐✇➊❃➜☞➉ ➍ ➝ ➓❁➈▼➣ ➝ ➏✓➋ ✁✄✂ ➋❀➓ ✂ ➋ ➌❲➞✆☎ ➏❪➊▼➜ ✁ ➊✟➋✕➓ ✂ ➭✄➏ ✂ ➊❃➉✢➓ ✂✆✁✍➌ ➓➌ ➝ ↔ → ➓ ➝ ➏▲➈ ✁✄✂✆☎✓➒✦✁✄➞☞➌ ➊✙↔✺➊▼➓ ➌ ➏✕➈ ✁✍✂ ➋❀➏ ☎ ➏ ➍ ➉ ➑❁✂ ➊❃➏▲➋✤➜ ✂ ➉♣➥ ➞ ➏ ➍s✁ ➈▼➏ ✁ ➊ ➓ ☎☞☎☞➍❢➳✦➼ ➉ ➑✄➞ ➈❃➏ ➹❫➻ ➵ ✁✄✂✆☎➂➍ ➓✄➐❪➏ ➑❁➞ ➉ ☎ ➏ ➌ ➉ ✂ ➏ ➍✻✁✄✂✆☎♠✂ ➓★➭❁➏ ➌✛☎ ➏❀↔ ➍ ➉ ➑❁✂ ➊▼➏❫➋✤➜ ✂ ➉♣➥ ➞ ➏ ➍❛✁ ➈▼➏❶➈❃➏▲➥ ➞ ➉❲➈❃➏ ☎ ➊▼➓ ✁✄☎☞☎ ➈▼➏ ➍▼➍ ➛✰➓✍➊❃➜①➓✄➛ ✏ ➏▲➋✏➊❃➉✢➭❁➏ ➍ ➍ ➉✢➐ ➞☞➌ ➊ ✁✍✂ ➏▲➓ ➞✆➍▼➌❲➎✄➠✿➤ ➊❨➊❃➜☞➏ ✁ ➈❃➋✤➜✆➉❡➊❃➏▲➋✏➊ ➞ ➈❃➏ ➌ ➏▲➭✄➏ ➌ ✎✺✥✴✑❪✞❉✌▼✞✤✩★✯✱✔❚■ ✩✄☛✍✔✰✣✕✹ ➍ ➜☞➓ ➞☞➌♣☎ ➛✰➏❤➏✕➐ →☞➌ ➓ ➎ ➏ ☎ ➝ ➜✆➏✕➈❃➏✕➭✄➏▲➈ → ➓ ➍▼➍ ➉❲➛ ➌ ➏❢➊❃➓♠➉✢➐❜↔ → ➈❃➓★➭✄➏❨➊▼➜☞➏ ➒✦✁✍➞☞➌ ➊✙↔✺➊▼➓ ➌ ➏▲➈ ✁✄✂ ➋❀➏✟➓ ➒ ➊❃➜☞➏ ➍✙➎✱➍ ➊▼➏▲➐ ➠ ➾ ➊ ➝ ✁✄➍❭➍ ➜✆➓ ➝ ✂ ➊▼➜ ✁ ➊❭➊▼➉❲➐❜➏❜➈❃➏ ☎✱➞☞✂❚☎☞✁✍✂ ➊❯➊❃➏▲➋✤➜ ✂ ➉♣➥ ➞ ➏ ➍ ➏ ✂❚☎✿➞☞→ ➋✕➓ ✂✆➍▼➞ ➐❪➉ ✂☞➑✻➞☞→

Proceedings of the International Symposium on Quality Electronic Design (ISQED’02) 0-7695-1561-4/02 $17.00 © 2002 IEEE

➍ ✢➉ ➐ ➞☞➌❲✁ ➊▼➉❲➓ ✂ ➝ ➉ ➌❲➌ ➜☞➏ ➌✢→ ➉ ✂ ➐ ✁ ➣❄➉ ✂☞➑ ➊▼➜☞➉ ➍✬✁✍✂❚✁✍➌❲➎❄➍ ➉ ➍✻➒ ➏ ✁✄➍ ➉✢➛ ➌ ➏ ➒ ➓✄➈ ➌♣✁ ➈ ➑ ➏✕➈✟➋❀➉❲➈❃➋ ➞ ➉❡➊ ➍✕➠❦➩ ➓ → ➏✕➈ ➒ ➓✄➈❃➐ ➊❃➜☞➏ ➍ ➊ ➞❚☎✱➎❢➒ ➓✄➈❜➐❜➓ ☎ ➏▲➈ ✂ ✁✍✂❚☎❪➒◗➞ ➊ ➞ ➈▼➏✮➊▼➏▲➋✤➜ ✂ ➓ ➌ ➓ ➑ ➉✢➏ ➍ ➊▼➜☞➏▲➈▼➏✛➉ ➍❵✁✾✂ ➏✕➏ ☎ ➊▼➓ ☎ ➏✕➭❁➏ ➌ ➓ →❪➒✦✁✍➞✆➌ ➊ ➐❪➓ ☎ ➏ ➌♣➍❵➒ ➓✄➈ ➌❲✁ ➊▼➏ ➍ ➊✗➊▼➏❫➋✤➜ ✂ ➓ ➌ ➓ ➑ ➉✢➏ ➍✕➠❖➤❯➌♣➍ ➓✟➐ ✁✍✂❄➎ ➓ ➒ ➊▼➜☞➏ ➞☞➌ ➊▼➈ ✁ ↔ ➌ ➓ ➝ → ➓ ➝ ➏✕➈ ➍▼➎✱➍ ➊❃➏✕➐ ➍ ➋❀➓ ✂ ➊ ✁ ➉ ✂①➒✦✁✍➞✆➌ ➊▼↔ ➍ ➏ ✂✆➍ ➉✢➊▼➉❲➭✄➏❭➐❜➉✢➢✱➏ ☎ ↔ ➍ ➉ ➑❁✂✆✁✍➌ ➋❀➉❲➈✤➋ ➞ ➉✢➊ ➍❪✁✍✂❚☎ ➜☞➏ ✂ ➋❀➏❣➉✢➊❪➉ ➍ ➉✢➐ → ➓✄➈▼➊ ✁✄✂ ➊❜➊▼➓ → ➏✕➈ ➒ ➓✄➈❃➐ ➍ ➉❲➐❪➉ ➌♣✁ ➈ ➍ ➊ ➞✆☎ ➉❲➏ ➍❶➒ ➓✄➈❶➐❪➉❡➢✱➏ ☎ ↔ ➍ ➉ ➑✄✂✆✁✄➌ ➋❀➉❲➈❃➋ ➞ ➉❡➊ ➍✕➠

140 Binary Counter Gray Counter

Fault Vulerability

120

100

80

60

➩ ➜✆➉ ➍ ➝ ➓✄➈❃➣ ➝ ✁✄➍❹➍✙➞✆→☞→ ➓❁➈✙➊❃➏ ☎ ➉ ✂ Acknowledgment: →✆✁ ➈✙➊❯➛ ➎ ➨❄➜ ✁ ➈ → ➇❵➓❁➈ → ➓✄➈ ✁ ➊❃✢➉ ➓ ✂❺➠

40

20

1

2

3 4 Size (time original size)

5

6

6. References

➼ ➉ ➑❁➞ ➈❃➏ ➹❁➹✄➸ Effect of sizing on reliability

[1] Karaolis E., Nikolaidis ➅▼S., ✚✭✚✭Goutis ✚ ➅✏✔❚✎❞C.E., ✞✕✌✏✔✰☛✍✎✒“Fault ✥✦✖✍✔✰☛✍✜✟Secure ✫✭✖★✔❫✘❀✞❀Binary ✌❃✞❀✔✪✣❃✞ Counter ✖★✔✬✚✗✜✢✞✤✣✕Design,” ✎✒✌▼✖✍✔✆✥✦✣❀✸✤❅✛✫❖in✥✴✌▼✣✕✯✱✥✴✎✦✸❨☛★✔✪✩✓➃✰✹❳✸✏✎❞✞✕✑❨✸ , 1999, pp. 16591662.

0.1 Binary Counter Gray Counter

Power Consumed (in mW)

0.09

[2] Su C. L., Tsui C. Y. and Despain A. “Saving ➄✗✌▼✖❫power ✣❃✞✤✞✤✩★✥✴✔❄in ✲★✸✿the ✖✼✘ control path ➅▼✚❛✚✭✚t✝✟ ✞❀✸✏✥❡✲✍of✔✿embedded ☛★✔✪✩✿♥✆✞❀✸✏✎✭processors,” ✖✼✘✟✫❈✖✍✑❯✠✪✯✱✎❞✞✕in✌✤✸ , 1994, pp. 24-31.

0.08 0.07

✄✂☎

0.05

☎✆ ✝✆

0.04 0.03

1

2

3 4 Size (times original size)

5

6

✞

[6] Iyer R. and Rosetti D., load of CPU ➄✗✌❃✖▲“A ✣✤✞✤statistical ✞✤✩★✥✴✔✳✲✍✸❨✖✼✘✛ ✈❝♥❛dependency ✫✧➃ errors at SLAC,” in , 1982.

0.085

6X Size

0.08

Binary Counter Gray Counter

✠✟

6X Size

0.075

[7] Messenger G. C., “Collection charge junction ➅▼✚✭✚❛✚ ♥☞of ✌▼☛✍✔☞ ✸✕☛✄✣✕✎✒✥✦✖✍on ✔☞✾✯✸❤ ✆ ✣✕✖★✜✢✔ ✞✤☛★✌ nodes from ion tracks,” in ➃✪✣✕✥✦✞✕✔✰✣✤✞ , 1982, pp. 2024-2031.

0.07

10K Res

0.065 0.06 0.055

10K Res

[8] Laguna G. and Treece R. “VLSI ➄✗✌▼✖❫✣✤✞❃✞✤modeling ✩✍✥✴✔✳✲✍✸✓✖✙✘❝and ➅❃✚✭✚✭design ✚ ➅❀✔✆✎✡✞❀for ✌✏■ radiation environments,” in ✔✰☛✍✎✒✥✦✖✍✔✰☛✍✜❶✫❈✖✍✔▲✘❀✞✕✌▼✞✕✔✰✣✤✞✻✖✍✔➂✫✭✖★✑✮✠✰✯✱✎✡✞❀✌❇✝❜✞✏✸✏✥❡✲✄✔ , 1986, pp. 380-384.

Normal

0.05 0.045

Normal

0.04 0.035

[4] Hakenes R. and Manoli Y., “A segmented Gray code ✚✟❨➆ ✵ ✗ ✽✻ ✟➆➅★for ✫ lowpower microcontroller address buses,” in ✫✭✖★✔❫✘❀✞❀✌▼✞✕✔✰✣✤✞ , 1999, pp. 240-243. [5] Ball H. and Hardy F., “Effects and ➄✗✌▼✖❫detection ✣✤✞✤✞❃✩✍✥✴✔✳✲✍❶✫ ✸❜of s ✖✼✘❭ ✫✶intermit✈❅ tent failures in digital systems,” in ❆✮✈✧➅❃➄❵➃❦✣✤✖★✔❫✘❀✞❀✌❃✞❀✔✪✣❃✞ , 1969, pp. 329-335.

➼ ➉ ➑✄➞ ➈❃➏ ➹❫➺✱➸ Effect of sizing on power

Power Consumed (in mW)

✁

[3] Mehta H., Owens R. M.➄✗and ✌▼✖❫✣✤✞❃Irwin ✞✤✩✍✥✴✔✳✲✍M. ✸④✖✼J.✘✻“Some ➃❚✥❡⑧☛ q❁✎◗❫❂♠ ❬✄✞issues ❷s✌▼✞✤☛✍✎in Gray code ➃❚✹★✑✮✠✆addressing,” ✖❳✸✏✥✴✯✱✑ ✖✍✔ ✧➃❄in➅ , 1996, pp. 178-181.

0.06

30

40

50

60

70 80 90 Fault Vulnerability

100

110

120

130

➼ ➉ ➑✄➞ ➈❃➏ ➹▲➻✆➸ Power and reliability trade off ➊▼➓ ➻❁✞✠➽ ❋➌ ➏ ➍❃➍❯→ ➓ ➝ ➏▲➈ ✁✄➍ ➋❀➓✄➐ →✆✁ ➈▼➏ ☎ ➊▼➓✻➊▼➜☞➏ ✁ ➈❃➏ ✁ ➈❃➏ ☎✱➞☞✂❚☎☞✁✍✂ ➊ ➊▼➏❫➋✤➜ ✂ ➉♣➥ ➞ ➏ ➠⑥➩ ➝ ➓③➊ ➎❄→ ➏ ➍ ➓ ➒ ➋❀➉❲➈❃➋ ➞ ➉✢➊✟➊❃➏▲➋✤➜ ✂ ➉♣➥ ➞ ➏ ➍ ➝ ➏✕➈❃➏ ☎ ➉ ➍ ↔ ➋ ➞✆➍❃➍ ➏ ☎❦✁✍✂✆☎❦✁❣✂ ➏▲➏ ☎❢➒ ➓✄➈✾➏✕➢ →☞➌ ➓❁➈▼➉ ✂☞➑ ➓✍➊❃➜☞➏✕➈❇➊▼➏▲➋✤➜ ✂ ➉❲➥ ➞ ➏ ➍ ➝ ✁✄➍ ➐❪➓✍➊▼➉❲➭ ✁ ➊❃➏ ☎❼➠ ➇❵➉❲➈❃➋ ➞ ➉✢➊❜➊❃➏▲➋✤➜ ✂ ➉❲➥ ➞ ➏ ➍①✁✍➌❲➌ ➓ ➝ → ➓ ➝ ➏✕➈▼↔✺➈❃➏ ➌ ➉ ✁ ➛☞➉ ➌ ➉✢➊ ➎ ➊▼➈ ✁✄☎ ➏▲➓✍➯ ➍ ➓ ➒❖✁ ➛✰➓ ➞ ➊ ➽ ✝✡✠ ➉ ✂ ➏ ✁ ➋✤➜❉➐❪➏ ✁✄➍▼➞ ➈❃➏ ➠ ➼✆➞ ➊ ➞ ➈❃➏ ➝ ➓❁➈▼➣✬➉ ✂ ➭✄➓ ➌ ➭❁➏ ➍❭☎ ➏✕➭❁➏ ➌ ➓ → ➉ ✂☞➑✻✂ ➓★➭✄➏ ➌ ➋✕➉✢➈✤➋ ➞ ➉✢➊❝➊▼➏❫➋✤➜✱↔ ♣ ➉ ➥ ✂ ➞ ➏ ➍ ➝ ➜☞➉♣➋✤➜ ✁✄☎✆☎ ➈▼➏ ➍▼➍ ➛❚➓✄➊▼➜➁➊▼➜☞➏ ➌ ➓ ➝ ↔ → ➓ ➝ ➏▲➈ ✁✄✂✆☎❹➒✦✁✍➞✆➌ ➊▼↔ ➊▼➓ ➌ ➏▲➈ ✁✄✂ ➋❀➏❵➉ ➍❃➍✙➞ ➏ ➍▲➠✶➤⑥➒✦✁✄➍ ➊▼➏✕➈ ➒✦✁✄➞☞➌ ➊▼↔ ➍ ➉❲➐ ➞☞➌♣✁ ➊❃➓✄➈⑧➛ ✁✄➍ ➏ ☎ ➓ ✂❇➌ ➓ ➑ ➉♣➋

[9] Singh M., Rachala R., and Koren I., “Transient Fault Sensitivity Analysis Converters (ADCs),” in ➅▼✚❛✚✭✚⑤ ❆✛✬✖ ✔❚✔✆★✌▼✯✆❬★☛★✸▼of ✜ ❂☞✖✤Analog-to-Digital ✠⑥ ✧➃❄✖✍➅ ✔ , Apr. 2001, pp. 140145.

☛✡

✄✂☎

[10] Kang S. and Chu D., “CMOS➅▼✚❛ circuit preven✚✭✚ ➅✏design ✔❚✎❞✞✕✌✏✔✰☛✍for ✎✒✥✦✖✍the ✔✰☛★✜❶ ✫✭✖✍✔✆■ tion of single event upset,” in ✘❀✞✕✌▼✞❀✔✪✣✤✞✟✖✍✔⑥✫✭✖★✑✮✠✰✯✱✎✡✞❀✌✮✝❜✞❀✸✤✥❡✲✄✔ , 1986, pp. 385-388. [11] Cha H., and Patel J.H., “A Logic-Level ➄s✌▼✖▲✣✤✞✤✞✤✩★✥✴✔❄✲★Model ✸✓✖✼✘❝➅▼for ✚✭✚✭✚ -Particle ➅❀✔✆✎✡✞❀✌✏■ Hits in CMOS Circuits,” in ✔✰☛✍✎✒✥✦✖✍✔✰☛✍✜❵✫✭✖★✔❫✘❀✞❀✌❃✞❀✔✪✣❃✞✓✖✍✔❹✫❈✖✍✑❯✠✪✯✱✎❞✞✕✌❭✝❜✞❀✸✤✥❡✲✄✔ , Oct 1993, pp. 538–542. [12] Singh M., and Koren I., “Reliability Enhancement ➅❃✚✭✚✭✚ ➅✏✔❚✎❞✞✕✌✏of✔✰Analog☛✍✎✒✥✦✖✍✔✰☛★✜ to-Digital Converters (ADCs),” in ➃❚✹★✑✮✠✆✖❳✸✏✥✴✯✱✑ ✖✍✔✻✝✟✞✒✘❀✞✤✣❀✎s☛★✔✰✩✟✈⑧☛✍✯✱✜❩✎❭♥❚ ❖➃✖★❄✜✢➅ ✞✕✌▼☛★✔✪✣✤✞✾✥✴✔

Proceedings of the International Symposium on Quality Electronic Design (ISQED’02) 0-7695-1561-4/02 $17.00 © 2002 IEEE

➃❚✹❳✸✏✎✡✞❀✑✟✸

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, Oct. 2001.

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