Karnaugh Mapping
- Karnaugh mapping is a graphic technique for reducing a Sum-of-Products (SOP) expression to its minimum form.
- Two, three and four variable k-maps will have 4, 8 and 16 cells respectively.
- Each cell of the k-map corresponds to a particular combination of the input variable and between adjacent cells only one variable is allowed to change.
- Use the following steps to reduce an expression using a k-map.
- Use the rules of Boolean Algebra to change the expression to a SOP expression.
- Mark each term of the SOP expression in the correct cell of the k-map. (kind of like the game Battleship)
- Circle adjacent cells in groups of 2, 4 or 8 making the circles as large as possible. (NO DIAGONALS!)
- Write a term for each circle in a final SOP expression. The variables in a term are the ones that remain constant across a circle.
- The cells of a k-map are continuous left-to-right and top-to-bottom. The wraparound feature can be used to draw the circles as large as possible.
- When a variable does not appear in the original equation, the equation must be plotted so that all combinations of the missing variable(s) are covered.
This is a very visual problem so watch the video for examples on how to complete and solve Karnaugh Maps!
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