ROBDD to RMNF

Question

I have read the posts on this type of problem but the answer I am submitting is not accepted. Can someone please tell me what is my mistake?

Please confirm that: The process to solve this problem is take 1 path of robdd and write the dnf form. then convert dnf form to rmnf.

Is it also possible to solve this problem by - take 1's path of robdd diagram--->write in DNF---->then compute positive davio decomposition ----> then get RMNF.

Are both process correct?

Answer 1

Get the DNF:

    c&!b | c&b&a | !c&b&a

Make it a full DNF

    c&!b&!a | c&!b&a | c&b&a | !c&b&a

Replace or by xor:

    c&!b&!a ⊕ c&!b&a ⊕ c&b&a ⊕ !c&b&a

Replace negations and multiply out

    c&(b⊕1)&(a⊕1) ⊕ c&(b⊕1)&a ⊕ c&b&a ⊕ (c⊕1)&b&a
    = c&b&(a⊕1) ⊕ c&(a⊕1) ⊕ c&(b⊕1)&a ⊕ c&b&a ⊕ (c⊕1)&b&a
    = c&b&a ⊕ c&b ⊕ c&a ⊕ c ⊕ c&b&a ⊕ c&a ⊕ c&b&a ⊕ c&b&a ⊕ b&a
    = (c&b&a ⊕ c&b&a) ⊕ c&b ⊕ (c&a ⊕ c&a) ⊕ c ⊕ (c&b&a ⊕ c&b&a) ⊕ b&a
    = c&b ⊕ c ⊕ b&a

Comments

I got my mistake. Thank you.