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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##### Document information

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ashwini

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University:
Chitkara University

Subject:
Discrete Mathematics

Upload date:
27/04/2013