2.4 Boolean Logic
Learn the core principles of Boolean logic and its role in computing.
Overview
Boolean logic underpins how computers process True/False values. Mastering AND, OR, NOT, and other operations empowers you to design efficient circuits and conditionals.
Detailed Content
Basic Concepts
- Boolean Values: True (1) and False (0)
- Variables: Store True or False
- Truth Tables: Show output for every possible input combo
Basic Operations
- AND: True if both inputs are True
- OR: True if at least one input is True
- NOT: Inverts the input
Additional Operations
- XOR: True if inputs differ
- NAND: Inverse of AND
- NOR: Inverse of OR
Boolean Algebra Laws
- Commutative: A AND B = B AND A
- Associative: (A AND B) AND C = A AND (B AND C)
- Distributive: A AND (B OR C) = (A AND B) OR (A AND C)
Applications
- Digital circuit design
- Programming conditionals
- Search queries & filtering logic
Logic Gates
- Basic gates: AND, OR, NOT
- Advanced gates: XOR, NAND, NOR
- Combine gates to form complex circuits
Diagram
Figure: Visual representation of Boolean operations & truth tables.
Interactive Card Sort
Match each Boolean operation to its correct description below.
Exam Questions
Test your understanding with these questions. Click “Show Solution” to reveal sample answers.
Q1: Outline how the NAND operation differs from basic AND logic.
- NAND is True except when both inputs are True. It’s the inverse of AND.
- Commonly used as a universal gate in circuit design.
- Helps reduce the number of different gate types needed.
Q2: Why might XOR be more appropriate than a simple OR in some circuits?
- XOR outputs True only if inputs differ; OR would also be True if both are True.
- Use XOR when you need exclusivity, like in parity checks or toggling bits.
- Important in certain error detection and coding schemes.
Q3: Give one example of how Boolean algebra laws simplify circuit designs.
- By applying distributive/commutative laws, engineers can reduce multiple gates into fewer ones.
- Fewer gates mean lower power usage, less cost, and more reliable hardware.
- Example: A AND (B OR C) might be rearranged to (A AND B) OR (A AND C), optimizing the final circuit.