Rewrite the function using only NOR

Question

$F=AC'+BC'+BD'$

I know that $AC' -> (A \lnot\lor A) [ (C \lnot\lor C) \lnot\lor ( C \lnot\lor C)]$ ,and $BC' -> (B \lnot\lor B) [ (C \lnot\lor C) \lnot\lor ( C \lnot\lor C)]$ ,

$BD' -> (B \lnot\lor B) [ (D \lnot\lor D) \lnot\lor ( D \lnot\lor D)]$ , but how do I join them together

Answer 1

First, there is a NOR missing in all of your expressions. For example, you have that:

$AC'= (A \ NOR \ A) \color{red}{NOR} ((C \ NOR \ C) NOR (C \ NOR \ C))$

Second, to put all three together, follow this template:

$ P + Q + R= P + (Q + R) = (P + (Q+R))''= (P \ NOR (Q +R))'= (P \ NOR \ (Q +R)'')'= (P \ NOR \ (Q \ NOR \ R)')' = (P \ NOR \ ((Q \ NOR \ R) NOR ( Q \ NOR \ R)))' = (P \ NOR ((Q \ NOR \ R) NOR ( Q \ NOR \ R))) NOR (P \ NOR ((Q \ NOR \ R) NOR (Q \ NOR \ R)))$