Answer to Question #109915 in Databases | SQL | Oracle | MS Access for chibuzor

Question #109915
GivenF1  M(0,4,5,6) and F2  M(0,4,7),find the maxterm expansion for F1F2. State a general rule for finding the maxterm expansion of F1F2 given the maxterm expansions of F1 and F2. Prove your answer by using the general form of the maxterm expansion.
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Expert's answer
2020-04-19T07:40:22-0400

Given that F1=ΠM(0,4,5,6)F_1 = \Pi\Mu(0,4,5,6) and F2=ΠM(0,4,7)F_2 = \Pi\Mu(0,4,7) .

Let there be three literals A, B and C, truth table for the functions F1 , F2 and F1 F2 , is created below



From truth table we can write the Maxterm expression for F1 F2

F1F2=ΠM(0,4,5,6,7)F_1F_2 = \Pi \Mu(0,4,5,6,7)

A General rule therefore can be formulated for F1 F2 as,

The Maxterm expression of product F1 F2 contains the Maxterms present in either F1 or F2 .

It can be proved using general maxterm expansion.



F1=i=07(ai+Mi)F_1 = \displaystyle\prod_{i=0}^7 (a_i + M_i)




F2=j=07(bj+Mj)F_2 = \displaystyle\prod_{j=0}^7 (b_j + M_j)

F1F2=i,j=07(ai+bj+Mi+Mj)F_1F_2 = \displaystyle\prod_{i,j=0}^7 (a_i+b_j + M_i + M_j)


the index for P.O.S is varying from 0 to 7, which is same for both indices i and j, and Mi = Mj , therefore it can be written as


F1F2=i=07(ai+bi+Mi)F_1F_2 = \displaystyle\prod_{i=0}^7 (a_i+b_i + M_i)

Which shows that the product of F1F2 will have terms of both F1 and F2 , with common terms written once.

The Maxterm expression of product F1F2 contains the Maxterms present in either F1 or F2. It can be proved using general maxterm expansion.







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