Boolean Algebra and Truth Tables
Truth tables list outputs for every input combination.
About this topic
Boolean algebra is the mathematics of true and false values, named after George Boole. Its operations AND, OR and NOT combine values, and a truth table lists every possible combination of inputs with the resulting output. For n inputs, the table has 2 to the power n rows.
Rules help simplify expressions: A AND true equals A, A OR false equals A, A AND NOT A equals false, and De Morgan's laws say NOT (A AND B) equals (NOT A) OR (NOT B), and NOT (A OR B) equals (NOT A) AND (NOT B). Simplifying reduces the number of gates a circuit needs, saving cost and power.
In programming the same ideas drive conditions such as if age is at least 13 AND has permission. To check that two expressions are equal, build both truth tables and compare. A common mistake is confusing everyday English with logic: when someone says soup or salad, they usually mean one, but logical OR is also true when both are chosen. Another is forgetting that NOT applies before AND and OR unless brackets say otherwise. Test your expressions with every row of the table.
Key ideas
- True and false
- De Morgan's laws
- Used in conditions
Quick check
Use cases: where Boolean Algebra and Truth Tables helps
- Homework: review the key idea behind Boolean Algebra and Truth Tables before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Boolean Algebra and Truth Tables without notes.
- Visual learning: play with the interactive lab to see how Boolean Algebra and Truth Tables changes when you adjust its inputs.
- Teaching a friend: explain Boolean Algebra and Truth Tables in your own words, then compare your version with the key ideas.
Computing ideas run phones, search engines, games and the wider internet.
Frequently asked questions
What is Boolean Algebra and Truth Tables?
Truth tables list outputs for every input combination.
What will I learn in Boolean Algebra and Truth Tables?
True and false. De Morgan's laws. Used in conditions.
Is Boolean Algebra and Truth Tables part of Computer Science?
Yes. It is one of 80 Computer Science topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Boolean Algebra and Truth Tables lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Boolean Algebra and Truth Tables?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.