$f(a,b,c) = a'c+ac'+b'c$
We can write these product of sum terms into canonical product of sum form.
$f(a,b,c) = \underbrace{a'b'c}_{001}+\underbrace{a'bc}_{011}+\underbrace{ab'c'}_{100}+\underbrace{abc'}_{110}+\underbrace{ab'c}_{101}+\underbrace{a'b'c}_{001}$
$f(a,b,c) = \sum(1,3,4,5,6)$
Now, we can draw the k-map for these minterms.
- Prime implicant of $f$ is an implicant that is minimal - that is, the removal of any literal from product term results in a non-implicant for $ f$.
- Essential prime implicant is an prime implicant that cover an output of the function that no combination of other prime implicants is able to cover.
Prime implicants are$:a'c,b'c,ab',ac'$
Essential prime implicants are$:a'c,ac'\:\text{(green color)}$.
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