trying to simplify equation to fullest

Question

I've got an equation down to $F=BA+BC +\bar{A}\bar{C}$ and according to Wolfram Alpha it can simplified to $(\bar{A} + \bar{C}) + B$. What's the next steps? I tried using de Morgan's law and not sure it helped.

Answer 1

This is a derivation for the actual result:

$BA + BC + \bar{A}\bar{C} = (B(A+C))+\overline{A+C} = (B+\overline{A+C})((A+C)+\overline{A+C}) = \overline{A+C}+B$

I used:

• Distributivity of "$\cdot$ over $+$" and DeMorgan (for "NOR")
• Distributivity of "$+$ over $\cdot$"
• $P + \bar{P} = 1$ and $P\cdot 1 = P$

and some Commutativity and Associativity.