طراحی مدارهای منطقی
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دانشگاه آزاد اسالمی واحد پرند
دانشگاه آزاد اسالمی واحد پرندطراحی مدارهای منطقی
بهینه سازی مدارهای منطقی: جدول کارنو
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
Optimization
Cost directly related to
The number of gates
&
Gate inputs used
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)
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
Karnaugh Map (2-variable)
Karnaugh Map (3-variable)
Karnaugh Map (3-variable)
Karnaugh Map (3-variable)
Karnaugh Map (3-variable)
Proving boolean algebra equations Consensus theorem
Karnaugh Map (3-variable)
Minimized SOP Not unique
Karnaugh Map (4-variable)
Karnaugh Map (4-variable)
Karnaugh Map (4-variable)
With Don’t cares
Group X’s if they simplify the function
Karnaugh Map (4-variable)
POS extraction
Karnaugh Map (EPI)
Using PIs and EPIs
Implicant
Prime Implicant (PI)
Essential Prime Implicant (EPI)
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
Karnaugh Map (EPI)
Karnaugh Map (EPI)
Karnaugh Map (5-variable)
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