Boolean Algebra using Logic Gates

Boolean Algebra is used to simplify long/complex Boolean expressions. It is needed to optimise the use of logics gates (and hence transistors) when making an electronic circuit. Considering that the CPU is made of billions of logic gates, it is essential to find the optimal logic gates circuits to solve a given problem.

There are a few Boolean Algebra rules that are used to simplify Boolean expressions. In this challenge, you will recreate some logic gates circuits to verify some of these rules.

You can also investigate these rules further by simplifying Boolean expressions on this challenge.

The first few circuits have already been completed and your task is to create more logic gates circuits to verify the following rules.

Double NegationComplement LawsAssociative LawsDistributive LawsAbsorptive LawsDe Morgan's Rules

Double Negation

¬ ¬A = A

Logic Gates Circuit

Click on the above circuit to test it online

Complement Laws

A ∧ ¬A = 0

A ∨ ¬A = 1

Logic Gates Circuit

Click on the above circuit to test it online

Click on the above circuit to test it online

Associative Laws

(A ∧ B) ∧ C = A ∧ (B ∧ C)

(A ∨ B) ∨ C = A ∨ (B ∨ C)

Logic Gates Circuit

Click on the above circuit to test it online

Click on the above circuit to test it online

Distributive Laws

A ∧ (B ∨ C) = (A ∧ B) ∨ (A ∧ C)

A ∨ (B ∧ C) = (A ∨ B) ∧ (A ∨ C)

Logic Gates Circuit

Click on this picture to create a logic gates circuit to verify these rules

Absorptive Laws

A ∧ (A ∨ B) = A

A ∨ (A ∧ B) = A

Logic Gates Circuit

Click on this picture to create a logic gates circuit to verify these rules

De Morgan’s Rules

¬(A ∨ B) = ¬A ∧ ¬B

¬(A ∧ B) = ¬A ∨ ¬B

Logic Gates Circuit

Click on this picture to create a logic gates circuit to verify these rules