4.6.5 Boolean Algebra

Question 1

Define Boolean Algebra.

Answer 1

A way of working with logical values, where variables are either true or false.
It is used to represent and simplify logic circuits using a mathematical approach.

Question 2

What are the identity laws?

Answer 2

A + 0 = A
A . 1 = A

Question 3

What are the null laws?

Answer 3

A + 1 = 1
A . 0 = 0

Question 4

What are the idempotent laws?

Answer 4

A + A = A
A . A = A

Question 5

What are the inverse laws?

Answer 5

A + -A = 1
A . -A = 0

Question 6

What is the commutative law?

Answer 6

The order of variables do not matter in the same operation.

Question 7

What is the associative law?

Answer 7

Brackets can be removed as long as the operators are the same.

Question 8

What is the absorption law?

Answer 8

Variables that do not affect the final output can be removed.
X + (X . Y) = X
X . (X + Y) = X
the symbols inside and outside the brackets have to be opposite.

Question 9

What is the distributive law?

Answer 9

Considers the . operator as a multiply and the + operator as addition, equivalent of expanding brackets or factorising in normal algebra.
X + (Y . Z) = (X + Y) . (X + Z)

Question 10

What are De Morgan’s Laws?

Answer 10

X . Y = -(-X + -Y)-
X + Y = -(-X . -Y)-

split the line and change the sign.

Question 11

What is the order of precedence?

Answer 11

1. Brackets
2. NOT
3. AND
4. OR
   (Boole never ate olives)