Explicit implicants
Explicit implicants represent the minimal set of terms needed to cover all the output 1s in the truth table. They are used in logic optimization techniques such as Karnaugh maps and Quine-McCluskey method to simplify the logic function.
Example:
|
A |
B |
C |
X |
|---|---|---|---|
|
0 |
0 |
0 |
1 |
|
0 |
0 |
1 |
0 |
|
0 |
1 |
0 |
0 |
|
0 |
1 |
1 |
1 |
|
1 |
0 |
0 |
0 |
|
1 |
0 |
1 |
1 |
|
1 |
1 |
0 |
0 |
|
1 |
1 |
1 |
1 |
minterms = (0,3,5,7)
Lets make group of this minterms , there are several possible groupings, lets make two groups (0,3) and (5,7)
Therefore, (A’ B’ C’ + A’ B C) and (A B’ C + A B C) are explicit implicants.
Prime Implicants and Explicit Implicants
Implicants play a crucial role in Boolean logic, as they form the building blocks for both SOP and POS expressions. An implicant can be thought of as a product term in SOP or a sum term in POS representing a Boolean function. Essentially, implicants encapsulate the various input combinations (minterm or maxterm) for which the Boolean function evaluates to true.