Lecture #10 - Karnaugh Maps and Determining a Minimal Cover

# Lecture #10 - Karnaugh Maps and Determining a Minimal Cover...

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ECE 301 – Digital Electronics Karnaugh Maps Determining a Minimal Cover (Lecture #10)

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Learning Objectives How to use K-Maps Simplifying an incompletely specified function Determining a Minimal Cover Implicants Prime implicants Essential prime implicants Shannon’s Expansion Theorem Simplifying functions of 5 or more variables Spring 2012 2 ECE 301 - Digital
Reading Sections 5.4, 5.6 – 5.7 Spring 2012 ECE 301 - Digital 3

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Incompletely Specified Functions Completely specified function The output is specified for all input combinations. Incompletely specified function The output is not specified for all combinations of the input variables. Use “don’t care” (“x” or “d”) for those outputs. Karnaugh maps can be used to simplify incompletely specified functions. Spring 2012 ECE 301 - Digital 4
Deriving a Minimum SOP Expression Populate the K-map with the 0’s, 1’s, and “x”s. Treat the “x”s as 1’s. Group the 1’s and “x”s together. Must form a rectangle of a “power of 2” number of cells. All 1’s must be “covered” “Cover” those “x”s that help simplify the expression. That help to increase the size of the rectangle. All “x”s do not need to be “covered” May include a 1 or an “x” in more than one group. Spring 2012 ECE 301 - Digital 5

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Deriving a Minimum POS Expression Populate the K-map with the 0’s, 1’s, and “x”s. Treat the “x”s as 0’s.
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## Lecture #10 - Karnaugh Maps and Determining a Minimal Cover...

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