[Math] Simplifying boolean algebra expression that contains XOR

propositional-calculus

How can I simplify followed boolean algebra expression; Normally I express as simplify without XOR also this expression contains both XOR and multiple variables.

(((A + B)' * C') xor ((A' + B') * C')' ) * A

Best Answer

Lets say X = (A + B)' * C') and Y = ((A' + B') * C')'

We know that XOR can be represented as

$X ⊕ Y = X\overline Y + \overline X Y$

So, first simplify the inners and once you have the simplified version, you can deal with the outer A.