Is there a systematic way to write an expression in disjunctive normal form? Here is disjunctive normal form. < I understand what it is. However, I lack a systematic way of converting any complicated expression into it. For instance, should I expand all negations with DeMorgan's rules first? Should I distribute ANDs over ORs first? Is there a systematic way to do this conversion?

In addition to the truth table method described by André, there is also a syntactical approach:

First push the negations down to the leaves of the syntax tree using De Morgan's laws and double-negation elminiation.

Then float the disjunctions to the top using the distributive law $a\land(b\lor c)=(a\land b)\lor(a\land c)$.

This will often create shorter DNF's -- but there is still a risk of exponential blowup, of course.,