Finding POS expressions from K-Map

Rules for simplification of POS Expressions:

  1. First of all check whether the given function is of SIGMA or of PI. If it is a PI, goto step 3.
  2. If the given function is of SIGMA, convert it in to function of PI by complementing it.
  3. Prepare the respective map depending upon the number of variables used in the PI function.
  4. Put 0 on appropriate places for every min-term obtained in the function.
  5. Make groups of 0’s in the map.
  6. At last, deduce the expression simply like a normal K-map.
  7. Check that the obtained expression is of SOP type, Convert it in to POS by complementing it.

Ex.   Simplify the following function in SOP form using K-map method.


First of all see that the function is a 3-variable function hence it’d require a 23 = 8 square map. Now see that it’s of SIGMA type; hence first convert it to PI type: