# Prime Implicants discussion with help of `Karnaugh map` (K-map) - Contd.

Gate level minimization example. Refer prime implicants basics from here

Example:- Consider a function F (x, y, z, w) of 11 Minterms shown in Truth Table.

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K– map plot of 11 MintermsThere are Four essential terms for the function in discussion. The essential terms are shown within squares in the Truth Table.

So Following are the Four Essential Prime Implicants.

z’w, xz’, xw, x’zw’

Next step is to map remaining two(7 and 10)  minterms in all possible combinations.

for Minterm 7,

yw or yz

for Minterm 10,

xy or yz

So the final simplified solutions of the function are

Solution 1.   z’w + xz’+ xw + x’zw’ + yw + xy

Solution 2.   z’w + xz’+ xw + x’zw’ + yz

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