# Karnaugh map

This graphic method simplify a logic equation of combanational circuit. To understand combinational circuits click on this button.

This method is useful when the circuit has 4, 5 or 6 variables.

Procedure

Here is an example with 4 variables, first build the truth table:

After build the Karnaugh map and put “1” where the input combination is have high value in output, in the rest you put “0”.

Looking to the map, you can simplify the combinational circuit in the following way:

The logic equation become:

$X=AB+\bar{C}D$

If the map was in this form:

You could simplify in the following way:

And would stay like this:

$X=B$

Others possible combination forms, depending on the map:

$X=\bar{B}\bar{D}$

$X=A\bar{D}$

$X=\bar{B}$

$X=\bar{C}D+BC\bar{D}+\bar{A}\bar{B}CD$

The secret is to get the greatest number of “1” possible with least contours possible.

5 or 6 variables

To use the map with 5 variables, you must make 2 maps, one with A=0 and another with A=1 and solve both.

The contours in A=0 map only will have $\bar{A}$ in your expression, while the contours in A=1 map will have A in expression. Therefore, the equation will stay like this:

To 6 variables is the same thing, but with 4 maps.

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