Question

The number of min - terms after minimizing the following Boolean expression is _________.

[D′ + AB′ + A′C + AC ′D + A′C ′D]’

Answer 1

Let F(A, B, C, D) = [D' + AB' + A'C + AC'D + A'C'D]'

F(A, B, C, D) = [D' + AB' + A'C + C'D (A + A’)]'

F(A, B, C, D) = [D' + AB' + A'C + C'D]'                      [because A + A’ = 1]

F(A, B, C, D) = [D' + DC' + AB’ + A'C]'

F(A, B, C, D) = [D' + C’ + AB’ + A’C]'                         [By rule of duality , A + A’B = A + B]

F(A, B, C, D) = [D' + C' + A' + A.B']'                           [By rule of duality]

F(A, B, C, D) = [D' + C' + A' + B']'                               [By rule of duality]

F(A, B, C, D) = [(A.B.C.D)']'                                        [By DeMorgan's Law]

F(A, B, C, D) = (A.B.C.D)           

Total 1 min-terms after minimization.