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Within Boolean Algebra OR relates to Addition and AND relates to Multiplication. I'll be using ! to represent NOT before a given variable. Now consider the following expressions:
(AB) + (B!C) + (CD) read as (A AND B) OR (B AND NOT C) OR (C AND D)
This is a Sum of Products - AND your Inputs take their results and OR them as your output.
(A+C)(!B+C)(!A+D) read as (A OR C) AND (NOT B OR C) AND (NOT A OR D)
This is a Product of Sums. OR your inputs take their results and AND them as your output.
Now using core principles within Boolean Algebra such as DeMorgan's Law you can simplify your derived expression(s) to their simplest of forms thus giving you the smallest and most efficient logical diagram / circuit. Hope this helps.
I agree with Quadrivial. This would be a very useful manual page in the game. Maybe it is... I've only just started.