K-map: how to decide which implicant to be prime

Question

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:

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?

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.