I am a bit confused about deciding which implicants to turn into prime. If I group implicants 1 and 2 into a bigger implicant, can I group implicants 2 and 3 as well?

For example, if I have the K-map below, I can find implicants as follows: K-map

There are three options:

  1. Group the red and orange into a bigger implicant.

  2. Group the red and green into a bigger implicant.

  3. Do both (1) and (2), resulting in two overlapping implicants.

Do I choose only one option or do all of them?

  • 3
    \$\begingroup\$ Try all three and see which produces the smallest simplest result. \$\endgroup\$
    – user16324
    Commented Oct 2, 2019 at 14:20

1 Answer 1


In terms of number of operators needed (inverter, or, and) it does not matter.

However, in a real life situation, it can depend on (just summing up things coming in my mind):

  • Some operator (ICs/logic/transistors (on an IC) can be more costlier or more space consuming than others, prefering one type of operator above another
  • Some operator can be faster than another, prefering the faster type above the other
  • Some operator ICs come in multipliers of 2, 4 or 8 and having an exact (or almost) number of one type of operator can favor into another. Example: if you can chose between 5 not operators and 10 or operators, and an each IC has 8 operators, you need three. But if you can have a different formula that has e.g. 7 not operators and 8 or operators, you need only 2 ICs.

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