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CS2100 Computer Organisation http://www.comp.nus.edu.sg/~cs2100/

CS2100 Computer Organisation http://www.comp.nus.edu.sg/~cs2100/. K-maps: Finding PIs and EPIs ( AY2013/4) Semester 2. Y. YZ. 00 01 11 10. WX. W' ∙ X ∙ Y'. 00 01 11 10. W ∙ X ∙ Z. 1. 1. X. 1. 1. X ∙ Y' ∙ Z. W. Z. ESSENTIAL PRIME IMPLICANTS (1/5).

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CS2100 Computer Organisation http://www.comp.nus.edu.sg/~cs2100/

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  1. CS2100 Computer Organisationhttp://www.comp.nus.edu.sg/~cs2100/ K-maps: Finding PIs and EPIs (AY2013/4) Semester 2

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

  3. Can we remove this? Y YZ 00 01 11 10 WX EPI 00 01 11 10 1 1 X 1 1 W Z ESSENTIAL PRIME IMPLICANTS (2/5) Essential Prime Implicants (EPIs) – how to determine? NO! Prime Implicants (PIs) W'∙X∙Y' W∙X∙Z X∙Y'∙Z K-maps: Finding PIs and EPIs

  4. Can we remove this? Y YZ 00 01 11 10 WX EPI EPI 00 01 11 10 1 1 X 1 1 W Z ESSENTIAL PRIME IMPLICANTS (3/5) Essential Prime Implicants (EPIs) – how to determine? NO! Prime Implicants (PIs) W'∙X∙Y' W∙X∙Z X∙Y'∙Z K-maps: Finding PIs and EPIs

  5. Can we remove this? Y YZ 00 01 11 10 WX EPI EPI 00 01 11 10 1 1 X 1 1 Not an EPI W Z ESSENTIAL PRIME IMPLICANTS (4/5) Essential Prime Implicants (EPIs) – how to determine? Yes. Prime Implicants (PIs) W'∙X∙Y' W∙X∙Z X∙Y'∙Z K-maps: Finding PIs and EPIs

  6. Y YZ 00 01 11 10 WX EPI EPI 00 01 11 10 1 1 X 1 1 W Z ESSENTIAL PRIME IMPLICANTS (5/5) Essential Prime Implicants (EPIs) – how to determine? CONCLUSION Prime Implicants (PIs) W'∙X∙Y' W∙X∙Z X∙Y'∙Z Simplified SOP: W'∙X∙Y' + W∙X∙Z K-maps: Finding PIs and EPIs

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

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

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

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

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

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

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

  14. END K-maps: Finding PIs and EPIs

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