Systematic Procedure for Simplifying Boolean Functions (3.2)

1. Generate all PIs of the function.

2. Include all essential PIs.

3. For remaining minterms not included in the essential PIs, select a set of other PIs (which have already been generated earlier) to cover them, with minimal overlap in the set.

4. The resulting simplified function is the logical OR of the product terms selected above.

Example

·         f(a,b,c,d) = m(0,1,2,3,4,5,7,14,15).

·          Five grouped terms, not all needed.

·         3 shaded cells covered by only one term

·         3 EPIs, since each shaded cell is covered by a different term.

·         F(a,b,c,d) = a’c’ + a’d + a’b’ + abc  (EPIs are indicated in bold)

PI  a’d must be added to EPIs (because it covers remaining 1 and is larger than other PI (bcd), which covers the same 1)