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Chapter 3
Signals and SystemsDigital Logic System
Prof. Wonhee Kim
Karaugh Map
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Karaugh Map
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Karaugh Map
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Karaugh Map
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Karaugh Map
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Karaugh Map
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Karaugh Map
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Karaugh Map
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Karaugh Map
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Karaugh Map
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Karaugh Map
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Karaugh Map
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Karaugh Map
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Karaugh Map
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Karaugh Map
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Karaugh Map
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Karaugh Map
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Prime implicant: A'B'C'D', ABC', CD, ABD
Essential prime implicatn: A'B'C'D', ABC', CD (NOT ABD!)
Minimum Sum of Product Expressions Using the Karnaugh MAP
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Minimum Sum of Product Expressions Using the Karnaugh MAP
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Map Method 1
1. Find all essential prime implicants. Circle them on the map and mark the minterm(s) that make them essential with a star (★). Do this by examining each 1 on the map that has not already been circled. It is usually quickest to start with the most isolated 1’s, that is, those that have the fewest adjacent squares with 1’s in them.
2. Find enough other prime implicants to cover the function. Do this using two criteria:
a. Choose a prime implicant that covers as many new 1’s (that is,those not already covered by a chosen prime implicant).
b. Avoid leaving isolated uncovered 1’s.
Karaugh Map
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Karaugh Map
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Karaugh Map
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Karaugh Map
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Karaugh Map
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Karaugh Map
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Karaugh Map
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Karaugh Map
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Karaugh Map
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Karaugh Map
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Karaugh Map
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Minimum Sum of Product Expressions Using the Karnaugh MAP
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Map Method 2
1. Circle all of the prime implicants.
2. Select all essential prime implicants; they are easily identified by finding 1’s that have only been circled once.
3. Then choose enough of the other prime implicants (as in Method 1). Of course, these prime implicants have already been identified in step 1.
Minimum Sum of Product Expressions Using the Karnaugh MAP
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Minimum Sum of Product Expressions Using the Karnaugh MAP
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Minimum Sum of Product Expressions Using the Karnaugh MAP
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Minimum Sum of Product Expressions Using the Karnaugh MAP
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Minimum Sum of Product Expressions Using the Karnaugh MAP
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Minimum Sum of Product Expressions Using the Karnaugh MAP
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Minimum Sum of Product Expressions Using the Karnaugh MAP
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Minimum Sum of Product Expressions Using the Karnaugh MAP
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Don’t Care
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Don’t Care
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Don’t Care
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Don’t Care
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Don’t Care
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Don’t Care
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Product of Sums
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Product of Sums
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Product of Sums
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Product of Sums
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Product of Sums
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Product of Sums
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Five And Six Variable Map
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Five And Six Variable Map
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Five And Six Variable Map
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Five And Six Variable Map
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Five And Six Variable Map
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Five And Six Variable Map
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Multi Output Problems
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Multi Output Problems
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Multi Output Problems
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Multi Output Problems
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Multi Output Problems
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Multi Output Problems
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Multi Output Problems
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Multi Output Problems
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Multi Output Problems
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Multi Output Problems
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Multi Output Problems
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Multi Output Problems
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Multi Output Problems
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