How to Simplify Boolean Functions
Boolean algebra is a way of expressing logic using mathematical notation. Boolean equations can be very complicated, but there are a number of ways to simplify the Boolean functions so that you can more easily solve a Boolean equation. One of the most common ways to simplify Boolean functions is by using a Karnaugh map. Construct and use a Karnaugh map to simplify a Boolean function using the simple function
AB + AB' as an example.
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Instructions
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1
Understand the terminology. In order to follow the example, it's important to understand the mathematical notation and the terminology. The example we're using to illustrate a Karnaugh map is AB + AB'. That translates to the statement AB OR A NOT-B, where the ' signifies NOT. In simple language, the Boolean expression means "if A is true AND B is true OR if A is true and B is not true."
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Draw a grid where each square in the grid represents one possible outcome of each of the product pairs. In the example statement, there are two variables. Each variable can be true or not true.
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Place a check mark in the square that represents each pair in the Boolean equation. For our example equation, you'd place a check in the square where A and B intersect and a check in the square where A and B' intersect.
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Circle adjacent check marks.
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Write down the variables in each pair. In the case of our example, you have the variables A B A B'.
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Eliminate duplicates in your list of variables. When you eliminate the duplicated A in our example list, you are left with A B B'.
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Eliminate variables that cancel each other out. In the case of our example, B and B' cancel each other out just as 1 and -1 would cancel each other out in an algebraic equation. That leaves us with just A, which can not be reduced any further. Thus, AB + AB' = A.
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Tips & Warnings
An algorithm or computer program can be helpful in constructing Karnaugh maps for more complex Boolean functions.
