KS3, GCSE, A-Level Computing Resources
Boolean algebra is a mathematical system for working with logical values (true and false) and the operations that combine them. It's a formal method used to manipulate and simplify logical statements, which is very important in computer science and digital circuit design. Rules for simplifying Boolean expressions, like absorption (X ⋀ (X ⋁ Y) = X) and general (X ⋁ ¬X = 1), help us reduce complex expressions to simpler forms that are easier to understand and use.
De Morgan's laws are a key tool for handling negations of combined terms. Specifically, they state that the opposite of "A or B" is the same as "not A and not B," and the opposite of "A and B" is the same as "not A or not B." These laws are crucial for simplifying and changing Boolean expressions, which often results in more efficient ways of implementing them.
General Rules
Commutative Rules
Associative Rules
Distributive Rules
Absorption Rules
