Digital Logic | Implicants in K-Map



Prerequisite – K – Map (Karnaugh Map)
Implicant is a product/minterm term in Sum of Products (SOP) or sum/maxterm term in Product of Sums (POS) of a Boolean function. E.g., consider a boolean function, F = AB + ABC + BC. Implicants are AB, ABC and BC.

  1. Prime Implicants –
    A group of square or rectangle made up of bunch of adjacent minterms which is allowed by definition of K-Map are called prime implicants(PI) i.e. all possible groups formed in K-Map.
    Example:

  2. Essential Prime Implicants –
    These are those subcubes(groups) which cover atleast one minterm that can’t be covered by any other prime implicant. Essential prime implicants(EPI) are those prime implicants which always appear in final solution.
    Example:
  3. Redundant Prime Implicants –
    The prime implicants for which each of its minterm is covered by some essential prime implicant are redundant prime implicants(RPI). This prime implicant never appears in final solution.
    Example:
  4. Selective Prime Implicants
    The prime implicants for which are neither essential nor redundant prime implicants are called selective prime implicants(SPI). These are also known as non-essential prime implicants. They may appear in some solution or may not appear in some solution.
    Example:

Example-1: Given F = ∑(1, 5, 6, 7, 11, 12, 13, 15), find number of implicant, PI, EPI, RPI and SPI.



No. of Implicants = 8
No. of Prime Implicants(PI) = 5
No. of Essential Prime Implicants(EPI) = 4
No. of Redundant Prime Implicants(RPI) = 1
No. of Selective Prime Implicants(SPI) = 0

Example-2: Given F = ∑(0, 1, 5, 8, 12, 13), find number of implicant, PI, EPI, RPI and SPI.

No. of Implicants = 6
No. of Prime Implicants(PI) = 6
No. of Essential Prime Implicants(EPI) = 0
No. of Redundant Prime Implicants(RPI) = 0
No. of Selective Prime Implicants(SPI) = 6

Example-3: Given F = ∑(0, 1, 5, 7, 15, 14, 10), find number of implicant, PI, EPI, RPI and SPI.

No. of Implicants = 7
No. of Prime Implicants(PI) = 6
No. of Essential Prime Implicants(EPI) = 2
No. of Redundant Prime Implicants(RPI) = 0
No. of Selective Prime Implicants(SPI) = 4

Example-4: GATE IT 2006 | Question 35



My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.



Improved By : Ankit87