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