CODEWITHSUNDEEP
dictionarykarnaugh-map
Arnav Das
Arnav Das

Reputation: 185

When do Karnaugh Map terms make no groups?

I understand how K-Maps work and what their utility is, but I can't seem to figure out under what conditions there could be no groups made. (When an expression is not simplifiable further? Won't it always be while speaking of canonical terms?) Do help me out.

Upvotes: 2

Views: 3145

Answers (2)

Kevin
Kevin

Reputation: 100

These are the conditions to make groups obtained from here:

  1. Groups must be formed by combining 1, 2, 4 or usually 2n cells.
  2. Cells can be grouped either in horizontal or vertical direction but not diagonally.
  3. The cell having the zero value should not included in the groups.
  4. Group must be as big as possible.
  5. Overlapping of the groups are allowed.
  6. Groups can be formed by wrapping around the grid.
  7. No ones should be left alone.

So you cannot make groups for any situation not falling into any one of the above.

Upvotes: 2

Axel Kemper
Axel Kemper

Reputation: 11322

An example of a Karnaugh map without simplified or merged blocks:

enter image description here

This example depicts the exclusive OR of four inputs a, b, c and d. No pair of terms can be merged as none of them forms an adjacent couple.

Terms in a Karnaugh map correspond to a conjunctions (logical AND) of positive or inverted inputs. Two terms can be merged to one, if they exactly differ in the polarity of one input.

Example:

Term abc can be merged with term abc'. The resulting term is ab. Input c can be omitted as it occurs with opposite polarity in the two original terms.

ab = ab(c+c') = abc + abc'

Recommendation:

My favorite online site to experiment with Karnaugh maps is here.

Upvotes: 1

Related Questions