Boolean Algebra and Digital Logic
Boolean algebra uses the binary values $0$ and $1$ to describe logical functions and digital circuits.
Summary
Boolean algebra uses the binary values and to describe logical functions and digital circuits. Expressions and circuits are equivalent when their outputs agree for every input combination. Boolean identities simplify expressions while preserving their truth tables.
| Operation | Output condition |
|---|---|
| AND | True only when both inputs are true |
| OR | True when at least one input is true |
| NOT | Reverses the input value |
A truth table lists all combinations for binary inputs. A canonical sum-of-products expression joins, using OR, the minterms for rows with output . Each minterm contains every input variable exactly once, complemented or uncomplemented.
🧠 Key Concepts
- Boolean equivalence
- Truth tables
- De Morgan's laws
- Canonical sum of products
- Minterms
- Absorption law
- Functional completeness
- Exclusive OR
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Boolean Algebra and Digital Logic
📘 Overview Boolean algebra represents binary logic using variables that take the values and . Boolean expressions describe digital circuits, and algebraic equivalence allows a circuit to be simplified without changing its truth table.
🧠 Key Idea A Boolean expression and a digital circuit represent the same logical function when they produce identical outputs for every input combination. Boolean identities transform expressions while preserving that function.
⚔️ Core Details: - Basic operations:
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Part of 🌱 BSCS Year 1 — Computing & College Foundations
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