Convert to FDD

Question

2019 Feb Problem 1 a

Covert the formula to fdd (a ∨ ¬b) ∧ c. I tried to approach fdd coversion like below

1) a&c  ⊕ c  ⊕ b&c

On writing in RMNF I got the following

= a&!b&c  ⊕ !a&!b&c  ⊕ !a&b&c

= a&c  ⊕ c  ⊕ a&b&c  ⊕ a&b

Complete DNF

a&!b&c  ⊕ !a&!b&c  ⊕ a&b&c  ⊕ a&b&c

on performing davio decompostion where a=0 b=1 its leading to node 0 which varies from the solution given.

Please help me to optimally solve the question

Answer 1

Not sure what you are doing. If you have to compute the FDD of a formula like (a ∨ ¬b) ∧ c, it is sufficient to compute the RMNF since that is the textual representation of the FDD.

    (a∨¬b)∧c
    = ((0∨¬b)∧c) ⊕ a∧((0∨¬b)∧c⊕(1∨¬b)∧c)
    = ¬b∧c ⊕ a∧(¬b∧c⊕c)
    = ¬b∧c ⊕ a∧(b∧c)
    = (¬0∧c) ⊕ b∧(¬0∧c⊕¬1∧c) ⊕ a∧((0∧c) ⊕ b∧(0∧c⊕1∧c))
    = c ⊕ b∧c ⊕ a∧b∧c

From here, it should be easy to draw the FDD.