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Karnaugh Maps
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Sistemas de Control, MR2013, ITESM – Chihuahua, August 15
Karnaugh Maps
Karnaugh maps are a simple and straight-forward graphical method to simplify binary (Boolean)
functions (expressions). This method always produces the simplest possible result and it is also
applicable to complex functions.
A Karnaugh map provides a pictorial method of grouping together expressions with common factors
and therefore eliminating unwanted variables. The Karnaugh map is a truth table graph, which aids in
visually simplifying logic.
a. Karnaugh map for two variables
b
a’b’ a’b
a ab’ ab
b. Karnaugh map for three variables
b
a’b’c a’b’c a’bc a’bc’
a ab’c’ ab’c abc abc’
c
Sistemas de Control, MR2013, ITESM – Chihuahua,August 15 2
c. Karnaugh map for four variables
c
a’b’c’d’ a’b’c’d a’b’cd a’b’cd’
a’b c’d’ a’b c’d a’b cd a’b cd’ b
a ab c’d’ ab c’d ab cd ab cd’
ab’ c’d’ ab’ c’d ab’ cd ab’ cd’
d
d. Karnaugh map for five variables
c
a’b’c’d’ a’b’c’d a’b’cd a’b’cd’
a’b c’d’ a’b c’d a’b cd a’b cd’ b
a ab c’d’ ab c’d ab cd ab cd’
ab’ c’d’ ab’ c’d ab’ cd ab’ cd’
d
c
a’b’c’d’ a’b’c’d a’b’cd a’b’cd’
a’b c’d’ a’b c’d a’b cd a’b cd’ b
a ab c’d’ ab c’d ab cd ab cd’
ab’ c’d’ ab’ c’d ab’ cd ab’ cd’
d
e