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CS2100 Computer Organisation http://www.comp.nus.edu.sg/~cs2100/ http://www.comp.nus.edu.sg/~cs2100/ K-maps: Finding PIs and EPIs (AY2014/5) Semester 2

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CS2100 K-maps: Finding PIs and EPIs 2 ESSENTIAL PRIME IMPLICANTS (1/5) Essential Prime Implicants (EPIs) – how to determine? 11 W 00 01 11 10 00 01 11 10 Z WX YZ 11 X Y W'∙X ∙ Y' W∙X∙ZW∙X∙Z Prime Implicants (PIs) X∙Y' ∙ Z

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CS2100 K-maps: Finding PIs and EPIs 3 ESSENTIAL PRIME IMPLICANTS (2/5) Essential Prime Implicants (EPIs) – how to determine? W'∙X∙Y' W∙X∙Z 11 W 00 01 11 10 00 01 11 10 Z WX YZ 11 X Y Prime Implicants (PIs) X∙Y'∙Z Can we remove this? NO! EPI

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CS2100 K-maps: Finding PIs and EPIs 4 ESSENTIAL PRIME IMPLICANTS (3/5) Essential Prime Implicants (EPIs) – how to determine? W'∙X∙Y' W∙X∙Z 11 W 00 01 11 10 00 01 11 10 Z WX YZ 11 X Y Prime Implicants (PIs) X∙Y'∙Z EPI Can we remove this? NO! EPI

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CS2100 K-maps: Finding PIs and EPIs 5 ESSENTIAL PRIME IMPLICANTS (4/5) Essential Prime Implicants (EPIs) – how to determine? W'∙X∙Y' W∙X∙Z 11 W 00 01 11 10 00 01 11 10 Z WX YZ 11 X Y Prime Implicants (PIs) X∙Y'∙Z EPI Can we remove this? Yes. Not an EPI

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CS2100 K-maps: Finding PIs and EPIs 6 ESSENTIAL PRIME IMPLICANTS (5/5) Essential Prime Implicants (EPIs) – how to determine? W'∙X∙Y' W∙X∙Z 11 W 00 01 11 10 00 01 11 10 Z WX YZ 11 X Y Prime Implicants (PIs) X∙Y'∙Z EPI CONCLUSION Simplified SOP: W'∙X ∙ Y' + W∙X ∙ Z

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CS2100 K-maps: Finding PIs and EPIs 7 EPI – ONE MORE TIME (1/3) 1.If it is an EPI, it must appear in answer. 2.If it is not an EPI, it may or may not appear in answer. 11 A D 1 B C 1 1 Prime Implicants (PIs) A'∙C'∙D' A'∙B∙C' A'∙B∙D B∙C∙D

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CS2100 K-maps: Finding PIs and EPIs 8 EPI – ONE MORE TIME (2/3) 1.If it is an EPI, it must appear in answer. 2.If it is not an EPI, it may or may not appear in answer. 11 A D 1 B C 1 1 Prime Implicants (PIs) A'∙C'∙D' A'∙B∙C' A'∙B∙D B∙C∙D Which are the EPIs? EPI Answer: A'∙C'∙D + B∙C∙D ? Is the answer complete?

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CS2100 K-maps: Finding PIs and EPIs 9 EPI – ONE MORE TIME (3/3) 1.If it is an EPI, it must appear in answer. 2.If it is not an EPI, it may or may not appear in answer. 11 A D 1 B C 1 1 Prime Implicants (PIs) A'∙C'∙D' A'∙B∙C' A'∙B∙D B∙C∙D EPI Answer: A'∙C'∙D + B∙C∙D ? Is the answer complete? No, there is still a minterm not covered. Correct answer: A'∙C'∙D + B∙C∙D + A'∙B∙C' or A'∙C'∙D + B∙C∙D + A'∙B∙D

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CS2100 K-maps: Finding PIs and EPIs 10 IVLE ASSESSMENT Q31 (1/4) What are the Prime Implicants (PIs)? 1 1 A D 1 1 B C 11

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CS2100 K-maps: Finding PIs and EPIs 11 IVLE ASSESSMENT Q31 (2/4) A'∙B' ∙ C A'∙B ∙ D Prime Implicants (PIs): A'∙C ∙ D 1 1 A D 1 1 B C 11 A∙B ∙ C' B∙C' ∙ D What are the Essential Prime Implicants (EPIs)?

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CS2100 K-maps: Finding PIs and EPIs 12 IVLE ASSESSMENT Q31 (3/4) A' ∙ B' ∙ C A' ∙ B ∙ D Prime Implicants (PIs): A' ∙ C ∙ D 1 1 A D 1 1 B C 11 A ∙ B ∙ C' B ∙ C' ∙ D EPI So what is the simplified SOP expression?

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CS2100 K-maps: Finding PIs and EPIs 13 IVLE ASSESSMENT Q31 (4/4) A'∙B ∙ D A' ∙ B' ∙ C A' ∙ B ∙ D Prime Implicants (PIs): A' ∙ C ∙ D 1 1 A D 1 1 B C 11 A ∙ B ∙ C' B ∙ C' ∙ D EPI So what is the simplified SOP expression? A'∙B' ∙ C + A∙B ∙ C' +

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CS2100 K-maps: Finding PIs and EPIs 14 END

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