How many prime Implicants are there, 2 or 3? F(w,x,y,z)=Σ(5,7,8,10)+d(9,11,13,15) enter image description here

I am confused if red block will be counted as Prime Impicant or not?

  • \$\begingroup\$ Is it just me or have there been so many questions about Prime Implicants recently? \$\endgroup\$
    – Tyler
    Aug 17, 2018 at 18:03
  • \$\begingroup\$ It's not just you. There have even been several that were clearly from the same homework assignment. I wonder if Stack Exchange is especially popular at some particular university. \$\endgroup\$
    – Darius
    Aug 17, 2018 at 18:09
  • \$\begingroup\$ I don't know about others.. I am currently studying this topic for a competitive examination. \$\endgroup\$ Aug 17, 2018 at 18:14

1 Answer 1


By the definition:

A prime implicant of a function is an implicant that cannot be covered by a more general, (more reduced - meaning with fewer literals) implicant.

it is a prime implicant as it cannot be covered by some other (single) implicant.

But it is not an essential prime implicant defined as:

Essential prime implicants (aka core prime implicants) are prime implicants that cover an output of the function that no combination of other prime implicants is able to cover.

because it is fully covered by two other implicants.

  • \$\begingroup\$ Thank you. Yes it's fulfilling the conditions for prime implicants but is there any rule for incompletely specified functions that a block MUST include atleast 1 minterm from the function otherwise it won't be considered as prime implicant ? \$\endgroup\$ Aug 17, 2018 at 18:09
  • \$\begingroup\$ No. These terms have no notion of incomplete function. Once you choose specific "don't cares" to be your 1s , you have completely defined your function. \$\endgroup\$
    – Eugene Sh.
    Aug 17, 2018 at 18:13
  • \$\begingroup\$ I have never seen a formal definition stating that. Don't cares is just a transparent way to let you choose one of the several possible functions fulfilling your requirements. \$\endgroup\$
    – Eugene Sh.
    Aug 17, 2018 at 18:21
  • \$\begingroup\$ Even I think it's a valid prime implicant. Thank you \$\endgroup\$ Aug 17, 2018 at 18:24

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