These functions are incompletely specified and contain don t care conditions or conditions for which the output may be a 1 or a zero. We will use don t care conditions to our advantage to minimize the logic of our digital circuits. The uniting theorem is extremely useful for simplifying our Boolean expressions. Read the section titled The Essence of Boolean Simplification on page 66 very carefully to understand the concept behind Boolean simplification. Several simplification techniques are outlined in the reading.
Boolean cubes provide a visual way of identifying adjacencies within a Boolean expression.
Although Boolean cubes are helpful in visualizing opportunities for simplification, they are difficult to use with functions with more than three variables. Instead, Karnaugh maps or K maps are frequently used to simplify Boolean expressions. The K-map method described in the previous section is a handy tool for identifying adjacencies and simplifying Boolean expressions. Section 2.3.5 describes a series of steps for finding the minimum sum of products expression from a K-map. Section 2.3.6 describes how the K-map concept applies to Boolean functions with 5 and 6 variables.