Karnaugh Maps - Discrete Mathematical Structures - Lecture Slides, Slides for Discrete Mathematics. Chitkara University

Discrete Mathematics

Description: During the study of discrete mathematics, I found this course very informative and applicable.The main points in these lecture slides are:Karnaugh Maps, Boolean Expressions, Input-Output Table, Sum of Product, Product of Sum, Min Terms, Canonical Representation, Truth Table, K-Map Tables, Number of Variables, Function Form, K-Map Edges
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Karnaugh Maps
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Karnaugh Maps
K-maps provide a simple approach to reducing
Boolean expressions from a input-output
table.
The output from the table is used to fill-in the
K-map.
1’s are used to create a Sum of Product (SOP)
solution. (min terms)
0’s are used to create a Product of Sum (POS)
solution. (max terms)
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Min Terms
Canonical representation of a Boolean
expression is in the form of ^ v ~ (AND, OR,
NOT).
Example: A^B v ~A^~B v A^~B (AB + AB + AB)
Candidates for canonical representation are
taken from the truth table (input-output).
Candidates are identified where the output is
“1”. (Max Term canonical representation
candidates are identified by “0”)
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Min Terms
Min terms are taken directly from the truth tables. Where ever there is a “1”
for an output, F(), we note the min term value and place a “1” in the K-map
corresponding to the min term value of the table.
Min term short hand is often used to replace a full input-output table. The
short hand indicate the variables and the min terms that are “1”.
Example: f(A,B,C) = Σ (1, 5, 7)
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