4.6.5 Boolean Algebra

Who was Augustus de Morgan?

- A mathematician and logician

- Formulated laws to simplify boolean expressions

What are De Morgan’s laws?

1) A NAND B = NOT A OR NOT B

2) NOT A AND NOT B = A NOR B

What are the simplification rules?

1) X ⋅ 0 = 0

2) X ⋅ 1 = X

3) X ⋅ X = X

4) X ⋅ !X = 0

5) X + 0 = X

6) X + 1 = 1

What is the commutative rule?

1) X ⋅ Y = Y ⋅ X

2) X + Y = Y + X

What is the associative rule?

1) X ⋅ (Y ⋅ Z) = (X ⋅ Y) ⋅ Z

2) X + (Y + Z) = (X + Y) + Z

What is the distributive rule?

1) X ⋅ (Y + Z) = X ⋅Y + X ⋅ Z

2) (X + Y)(W + Z) = X ⋅ W + X ⋅ Z + Y ⋅ W + Y ⋅ Z

X + (Y ⋅ Z) = (X + Y)(X + Z)

What is the absorption rule?

1) X + (X ⋅ Y) = X

2) X ⋅ (X + Y) = X