Rules to simplify logic expressions, including De Morgan's laws.
Laws: identity, null, idempotent, complement, commutative, associative, distributive, absorption, De Morgan (¬(A·B)=¬A+¬B). Boolean simplification reduces gates and delay. Canonical forms are sum-of-products and product-of-sums.
A + A·B = A (absorption).
Boolean algebra lets you simplify logic before building it, which saves gates, power and delay in a real design.
Rules to simplify logic expressions, including De Morgan's laws.
Boolean algebra lets you simplify logic before building it, which saves gates, power and delay in a real design.
The complement of an AND equals the OR of the complements, and the complement of an OR equals the AND of the complements.
Fewer gates reduce cost, power and propagation delay, which is important for speed and battery life.
Typical applications include simplifying the enable logic of a control panel to fewer gates, using De Morgan's laws to convert a design to NAND logic and checking that two logic expressions are equivalent before synthesis.
Study "Logic gates" first (topic 37 of 104 in Electronics & Embedded). It covers the groundwork this topic builds on.
Duality principle. Minterms and maxterms. Consensus theorem.
A + A·B = A (absorption).
The next topic is "Karnaugh maps", which builds directly on this one.
It is classed as Intermediate in Electronics & Embedded (topic 38 of 104). It is an intermediate topic. Work through the beginner topics in Electronics & Embedded first.
Want to practise? Open the interactive course for quick checks, quizzes, simulations and progress tracking.