Simplify given expressions to a product of sum form. Eliminate any redundant terms. There have 2 questions below
Simplify given expressions to a product of sum form. Eliminate any redundant terms.
There have 2 questions below.
1.
Given
AC'+(B+A'D')'+(C+D')'
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(A+B)'=A'.B'
(AB)'=A'+B'
(a')'=a
a.a=a
1+a=a
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AC'+B'.(A'D')'+(C'.D)
AC'+B'(A+D)+(C'D)
AC'+AB'+B'D+C'D
Let F = AC'+AB'+B'D+C'D
Complement F twice to get product of sums form of F
F' = (AC'+AB'+B'D+C'D)'
F' = (A'+C)(A'+B)(B+D')(C+D')
F' = (A'.A'+A'B+A'C+CB)(BC+BD'+CD'+D'.D')
F' = (A'+A'B+A'C+CB)(BC+BD'+CD'+D')
F' = (A'(1+B)+A'C+CB)(BC+BD'+D'(1+C))
F' = (A'+A'C+CB)(BC+BD'+D')
F' = (A'(1+C)+CB)(BC+D'(1+B))
F' = (A'+CB)(BC+D')
F' = A'BC+A'D'+BC+BCD'
F' = BC(1+A')+A'D'+BCD'
F' = BC+A'D'+BCD'
F' = BC(1+D')+A'D'
F' = BC+A'D'
Complement F again
F = (BC+A'D')'
F = (B'+C')(A+D)
which is the required simplified Product of sums equation
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