# 4-variable K-Map

In K-Map, you might find some cells, where each cell represents a minterm, filled with the
letter X. This X is called “Don’t care”.
When forming groups of cells, don’t care conditions (X) are considered as 1, if this allows us
to form a larger group than would otherwise be possible without the don’t cares.
There is no requirement to group all or any of the don’t cares.
Rule: Only use the Don’t cares in a group if this simplifies the logic.
Based on the above note, and applying the same K-Map rules, you are asked to answer the
below questions for the below 4-variable K-Map:
a- Encircle the groups that should be considered, using a minimum number of X’s where
necessary to obtain the optimal solution. (6 marks)
N.B: Your solution is considered optimal, if you have involved the minimum number of
minterms to simplify the function using K-map with the don’t cares.
b- Write the simplified equation of the function F. (4 marks)
c- Find the complement (F’) of the simplified F. Apply De Morgan’s law and show the
steps. You can keep it in the POS form. (4 marks)
d- Draw the logic diagram of the simplified F using only NAND gates. (6 marks)

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