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طراحی مدارهای منطقی

طراحی مدارهای منطقی. دانشگاه آزاد اسلامی واحد پرند. نیمسال دوم 92-93. طراحی مدارهای منطقی. دانشگاه آزاد اسلامی واحد پرند. بهینه سازی مدارهای منطقی: جدول کارنو. Optimization. Algebraic procedures problems The procedures are difficult to apply in a systematic way

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طراحی مدارهای منطقی

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  1. طراحی مدارهای منطقی دانشگاه آزاد اسلامی واحد پرند نیمسال دوم 92-93

  2. طراحی مدارهای منطقی دانشگاه آزاد اسلامی واحد پرند بهینه سازی مدارهای منطقی: جدول کارنو

  3. Optimization • Algebraic procedures problems • The procedures are difficult to apply in a systematic way • It is difficult to tell when you have arrived at a minimum solution • Karnaugh map (For 3 and 4 variables) • Quine-McCluskey

  4. Optimization • Costdirectly related to  The number of gates & Gate inputs used

  5. Optimization • Karnaugh • Minimum cost two-level circuits composed of AND and OR gates • SOP: a group of AND gates feeding a single OR gate • POS:a group of OR gates feeding a single AND gate • Minimum SOP/POS  • has minimum number of terms (Minimum number of gates) • has minimum number of literals (minimum number of gate inputs)

  6. Karnaugh Map • Karnaugh map of a function • Specifies the value of the function for every combination of values of the independent variables • Like Truth table • Terms near each other with one bit difference • Maximum terms in one group (2,4,8,… terms) • Minimum groups

  7. Karnaugh Map (2-variable)

  8. Karnaugh Map (3-variable)

  9. Karnaugh Map (3-variable)

  10. Karnaugh Map (3-variable)

  11. Karnaugh Map (3-variable) • Provingboolean algebra equations  Consensus theorem

  12. Karnaugh Map (3-variable) • Minimized SOP  Not unique

  13. Karnaugh Map (4-variable)

  14. Karnaugh Map (4-variable)

  15. Karnaugh Map (4-variable) • With Don’t cares • Group X’s if they simplify the function

  16. Karnaugh Map (4-variable) • POS extraction

  17. Karnaugh Map (EPI) • Using PIs and EPIs • Implicant • Prime Implicant (PI) • Essential Prime Implicant (EPI)

  18. Karnaugh Map (EPI) • In the process of finding PIs: • don’t-cares are treated just like 1’s • Note  PI composed entirely of X’s can never be part of the minimum solution

  19. Karnaugh Map (EPI)

  20. Karnaugh Map (EPI)

  21. Karnaugh Map (5-variable)

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