Karnaugh Map POS (Production Of Sum) Minimization

exercise 07 

Map the following standard SOP expression on a Karnaugh map:

Solution

Evaluate the expression as shown below and place a 0 on the 4-variable Karnaugh map for each standard sum term in the expression.


exercise 08 

Use a Karnaugh map to minimize the following standard POS expression:
Also, derive the equivalent SOP expression.

Solution

The combinations of binary values of the expression are:

Map the standard POS expression and group the cells as shown in Karnaugh map:


Notice how the 0 in the 110 cell is included into a 2-cell group by utilizing the 0 in the 4-cell group. The sum term for each blue group is shown in the figure and the resulting minimum POS expression is:

Keep in mind that this minimum POS expression is equivalent to the original standard POS expression.

Grouping the 1s as shown by the gray areas yields an SOP expression that is equivalent to grouping the 0s.

exercise 09 

Use a Karnaugh map to minimize the following POS expression:
Also, derive the equivalent SOP expression.

Solution

The first term must be expanded into A + B + C + D and A + B + C + D to get a standard POS expression, which is then mapped; and the cells are grouped as shown in Karnaugh map

The sum term for each group is shown and the resulting minimum POS expression is:

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