An implicant is a product term that covers only allowed one-cells, optionally including don't-care cells. A prime implicant cannot be enlarged further. An essential prime implicant covers at least one required one-cell that no other prime implicant covers, so it must appear in the selected cover.
Worked example
For F(A,B,C) = Σm(0,1,2,3,6,7), one four-cell group gives NOT A and another gives B. The first uniquely covers rows 0 and 1; the second uniquely covers 6 and 7. Both are essential, giving F = NOT A OR B.
What to watch for
A prime implicant is not automatically essential. After selecting essential groups, some remaining cells may allow a choice between several covers.
Try it yourself
Why is a lone uncovered one-cell useful when checking a solution?
Answer: It proves the selected groups are incomplete. Every required one-cell must belong to at least one selected implicant.
How to study this topic
Keep the original truth table beside your simplified result. Check required ones and zeros separately, and document any don't-care assumptions. A smaller expression is useful only when it still matches the specification.
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