Every row of a truth table is either a 1 or a 0 of F, never both and never neither. So the row numbers split into two lists that don't overlap and together cover all of them:
F = Σm(the 1-rows) = ΠM(the 0-rows)
To convert, change the symbol and use the other rows.
The recipe:
- Read n, the number of inputs, from the function's name, F(A, B, C, D), not from the biggest number in the list.
- Write all rows 0 to 2ⁿ − 1 and cross off the listed ones.
- Whatever is left goes in the other list.
- Check: the two lists together have 2ⁿ entries.
With don't-cares, the rows split three ways: 1s, 0s and don't-cares. The don't-cares stay in d(…) and never move into either list.
Related move: complementing F. Change the symbol or the list, not both; see complement of a function.