For the following circuits, put them into Product of Maxterms and Sum of Minterm
ID: 3786440 • Letter: F
Question
For the following circuits, put them into Product of Maxterms and Sum of Minterms forms. I do not care which of the two ways I mentioned you use to do it (make a truth table, or manipulate into product of sums/sum of products form). Remember that for complex equations, you may want to evaluate subfunctions first. G = A^OverBar * B * C^OverBar * D + D *C^OverBar (A^OverBar + B^OverBar) + A^OverBar * C(B^OverBar + D^OverBar) + A * B^OverBar * C^OverBar * D F =((A CirclePlus D) * C^OverBar + B) * (A^OverBar *B + C * D^OverBar^OverBar)Explanation / Answer
a) Given function is
G = A'BC'D + DC'(A'+B') + A'C(B'+D') + AB'C'D
Application of Distributive property
A'BC'D + DC'A' + DC'B' + A'CB' + A'CD' + AB'C'D
Creating Min terms
A'BC'D + DC'A'(B + B') + DC'B'(A + A') + A'CB'(D + D') + A'CD'(B + B') + AB'C'D
Removing redundant terms
A'BC'D + A'BC'D + A'B'C'D + AB'C'D + A'B'C'D + A'B'CD + A'B'CD' + A'BCD' + A'B'CD' + AB'C'D
Sum of Min Terms
G(A,B,C,D) = A'BC'D + A'B'C'D + AB'C'D + A'B'CD + A'B'CD' + A'BCD'
Above equation is the sum of min terms equation.
Product of max terms could be easily found by taking missing min terms in G and apply complement on that function using demorgan's theorem.
Let the missing min terms are written as the function
X(A,B,C,D) = A'B'C'D' + A'BC'D' + A'BCD + AB'C'D' + AB'CD' + AB'CD + ABC'D' + ABC'D + ABCD' + ABCD
Product of max terms is obtained by complementing the function X.
X'(A,B,C,D) = A'B'C'D' * A'BC'D' * A'BCD * AB'C'D' * AB'CD' + AB'CD + ABC'D' + ABC'D + ABCD' + ABCD
Product of Max Terms
X'(A,B,C,D) = (A+B+C+D) * (A+B'+C+D) * (A+B'+C'+D') * (A'+B+C+D) * (A'+B+C'+D) * (A'+B+C'+D') * (A'+B'+C+D) * (A'+B'+C+D') * (A'+B'+C'+D) * (A'+B'+C'+D')