Why are products called minterms and sums called maxterms?

Question

Do they have a reason for doing so? I mean, in the sum of minterms, you look for the terms with the output 1; I don\'t get why they call it \"minterms.\" Why not maxterms becaus

Answer 1

In Sum Of Products (SOP), each term of the SOP expression is called a "minterm" because,

say, an SOP expression is given as: F(X,Y,Z) = X'.Y'.Z + X.Y'.Z' + X.Y'.Z + X.Y.Z

for this SOP expression to be "1" or true (being a positive logic), ANY of the term of the expression should be 1. thus the word "minterm".

i.e, any of the term (X'Y'Z) , (XY'Z') , (XY'Z) or (XYZ) being 1, results in F(X,Y,Z) to be 1!! Thus they are called "minterms".

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On the other hand, In Product Of Sum (POS), each term of the POS expression is called a "maxterm" because,

say an POS expression is given as: F(X,Y,Z) = (X+Y+Z).(X+Y'+Z).(X+Y'+Z').(X'+Y'+Z)

for this POS expression to be "0" (because POS is considered as a negative logic and we consider 0 terms), ALL of the terms of the expression should be 0. thus the word "max term"!!

i.e for F(X,Y,Z) to be 0, each of the terms (X+Y+Z), (X+Y'+Z), (X+Y'+Z') and (X'+Y'+Z) should be equal to "0", otherwise F won't be zero!!

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Thus each of the terms in POS expression is called a MAXTERM (maximum all the terms!) because all terms should be zero for F to be zero, whereas any of the terms in POS being one results in F to be one. Thus it is known as MINTERM (minimum one term!)