Simplify the expression below by using the Algebra laws:

Question

Simplify the expression below by using the Algebra laws: $$ AB + \overline{(\bar AC + B)\cdot \overline{(\bar B \oplus C)}} $$

Answer 1

$$ AB + \overline{(\bar AC + B)\cdot \overline{(\bar B \oplus C)}} $$ $$ \text{Demorgan} $$ $$ AB + (\overline{\overline AC + B}) + (\overline B \oplus C)$$ $$ \text{Demorgan} $$ $$ AB + \overline{\overline A C}\overline B + (\overline B \oplus C)$$ $$ \text{Demorgan sure is busy today} $$ $$ AB + (A + \overline C)\overline B + (\overline B \oplus C)$$ $$ \text {Distribute} $$ $$ AB + A \overline B + \overline C \overline B + (\overline B \oplus C)$$ $$ \text {expand xor} $$ $$ AB + A \overline B + \overline C \overline B + BC + \overline B \overline C$$ $$ \text {simplify A + A} $$ $$ AB + A \overline B + BC + \overline B \overline C$$ $$ \text {undistribute, xnor} $$ $$ A(B + \overline B) + B \overline \oplus C$$ $$ \text {simplify vacuous or} $$ $$ A + B \overline \oplus C$$ $$ \text {copy paste post into homework and hope teacher doesn't catch you}$$