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CMPUT329 - Fall 2003

CMPUT329 - Fall 2003. Topic C: State Minimization José Nelson Amaral. Reading Assignment. Chapter 7, section 7.10.3. N 1. Z 1. p. X. N 2. Z 2. q. Equivalent States. Given two sequential circuits N 1 and N 2. Let Z 1 be the output sequence produced from state p in N 1

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CMPUT329 - Fall 2003

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  1. CMPUT329 - Fall 2003 Topic C: State Minimization José Nelson Amaral CMPUT 329 - Computer Organization and Architecture II

  2. Reading Assignment Chapter 7, section 7.10.3 CMPUT 329 - Computer Organization and Architecture II

  3. N1 Z1 p X N2 Z2 q Equivalent States Given two sequential circuits N1 and N2. Let Z1be the output sequence produced from state p in N1 with input sequence X. Let Z2be the output sequence produced from state q in N2 with input sequence X. State p in N1 is equivalentto a state q in N2 if Z1= Z2 for all input sequences X. CMPUT 329 - Computer Organization and Architecture II

  4. How to Find Equivalent States? States that have the same next states and that produce the same output are equivalent. CMPUT 329 - Computer Organization and Architecture II

  5. H H H H H Eliminating Redundant States by Row Matching CMPUT 329 - Computer Organization and Architecture II

  6. H H H H J Eliminating Redundant States by Row Matching H CMPUT 329 - Computer Organization and Architecture II

  7. D E Eliminating Redundant States by Row Matching CMPUT 329 - Computer Organization and Architecture II

  8. Eliminating Redundant States by Row Matching CMPUT 329 - Computer Organization and Architecture II

  9. Equivalent States States that have equivalent next states and that produce the same output are also equivalent. But these equivalences cannot be identified by inspection of the state table. How can we identify these states? CMPUT 329 - Computer Organization and Architecture II

  10. Implication Table Method b c d e f g h a b c d e f g CMPUT 329 - Computer Organization and Architecture II

  11. Implication Table Method b c d e f g h a b c d e f g CMPUT 329 - Computer Organization and Architecture II

  12. Implication Table Method b c d e f g h a b c d e f g CMPUT 329 - Computer Organization and Architecture II

  13. Implication Table Method d-f c-h b c d e f g h a b c d e f g CMPUT 329 - Computer Organization and Architecture II

  14. Implication Table Method d-f c-h b c a-d c-e d e f g h a b c d e f g CMPUT 329 - Computer Organization and Architecture II

  15. Implication Table Method d-f c-h b c d c-e e f g h a b c d e f g CMPUT 329 - Computer Organization and Architecture II

  16. Implication Table Method d-f c-h b c d c-e e f b-d c-h g h a b c d e f g CMPUT 329 - Computer Organization and Architecture II

  17. Implication Table Method d-f c-h b c a-f e-h d c-e a-d e e-f b-d c-f a-b f b-f a-b e-h b-d c-h g c-e d-g a-g c-f b-g h a b c d e f g CMPUT 329 - Computer Organization and Architecture II

  18. Implication Table Method d-f c-h b c a-f e-h d c-e a-d e e-f b-d c-f a-b f b-f a-b e-h b-d c-h g c-e d-g a-g c-f b-g h a b c d e f g CMPUT 329 - Computer Organization and Architecture II

  19. Implication Table Method b c a-f e-h d c-e a-d e e-f b-d c-f a-b f b-f a-b e-h b-d c-h g c-e d-g a-g c-f b-g h a b c d e f g CMPUT 329 - Computer Organization and Architecture II

  20. Implication Table Method b c a-f e-h d c-e a-d e e-f b-d c-f a-b f b-f a-b e-h b-d c-h g c-e d-g a-g c-f b-g h a b c d e f g CMPUT 329 - Computer Organization and Architecture II

  21. Implication Table Method b c d c-e a-d e e-f b-d c-f a-b f b-f a-b e-h b-d c-h g c-e d-g a-g c-f b-g h a b c d e f g CMPUT 329 - Computer Organization and Architecture II

  22. Implication Table Method b c d c-e a-d e e-f b-d c-f a-b f b-f a-b e-h b-d c-h g c-e d-g a-g c-f b-g h a b c d e f g CMPUT 329 - Computer Organization and Architecture II

  23. Implication Table Method b c d c-e a-d e e-f b-d c-f a-b f a-b e-h b-d c-h g c-e d-g a-g c-f b-g h a b c d e f g CMPUT 329 - Computer Organization and Architecture II

  24. Implication Table Method b c d c-e a-d e e-f b-d c-f a-b f a-b e-h b-d c-h g c-e d-g a-g c-f b-g h a b c d e f g CMPUT 329 - Computer Organization and Architecture II

  25. Implication Table Method b c d c-e a-d e c-f a-b f a-b e-h b-d c-h g c-e d-g a-g c-f b-g h a b c d e f g CMPUT 329 - Computer Organization and Architecture II

  26. Implication Table Method b c d c-e a-d e c-f a-b f a-b e-h b-d c-h g c-e d-g a-g c-f b-g h a b c d e f g CMPUT 329 - Computer Organization and Architecture II

  27. Implication Table Method b c d c-e a-d e c-f a-b f b-d c-h g c-e d-g a-g c-f b-g h a b c d e f g CMPUT 329 - Computer Organization and Architecture II

  28. Implication Table Method b c d c-e a-d e c-f a-b f b-d c-h g c-e d-g a-g c-f b-g h a b c d e f g CMPUT 329 - Computer Organization and Architecture II

  29. Implication Table Method b c d c-e a-d e f b-d c-h g c-e d-g a-g c-f b-g h a b c d e f g CMPUT 329 - Computer Organization and Architecture II

  30. Implication Table Method b c d c-e a-d e f b-d c-h g c-e d-g a-g c-f b-g h a b c d e f g CMPUT 329 - Computer Organization and Architecture II

  31. Implication Table Method b c d c-e a-d e f b-d c-h g c-e d-g a-g h a b c d e f g CMPUT 329 - Computer Organization and Architecture II

  32. Implication Table Method b c d c-e a-d e f g c-e d-g a-g h a b c d e f g CMPUT 329 - Computer Organization and Architecture II

  33. Implication Table Method b c d c-e a-d e f g a-g h a b c d e f g CMPUT 329 - Computer Organization and Architecture II

  34. 1 a c 1 0 0 0 0 1 d e 1 Implication Table Method b c d c-e a-d e f g h a b c d e f g CMPUT 329 - Computer Organization and Architecture II

  35. Implication Table Method b c d c-e a-d e f g 1 h a 0 1 a b c d e f g c-e 0 0 1 d 1 CMPUT 329 - Computer Organization and Architecture II

  36. Implication Table Method b c d c-e a-d e f g h 1 0 a b c d e f g a-d c-e 0 1 CMPUT 329 - Computer Organization and Architecture II

  37. Implication Table Method b a c a d c-e a-d e f g h a b c d e f g CMPUT 329 - Computer Organization and Architecture II

  38. Implication Table Method b a c c a d c-e a-d e f g h a b c d e f g CMPUT 329 - Computer Organization and Architecture II

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