Boolean Algebra
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Study Boolean algebra, logic gates, simplification techniques, and digital circuit design.
Concepts in this topic
- Boolean Basics - Understand Boolean algebra and its laws
- Logic Gates - Learn the fundamental logic gates used in digital circuits
- Simplification - Simplify Boolean expressions using algebraic methods and Karnaugh maps
- Circuits - Design and analyze combinational digital circuits
Key formulas & identities
| Name | Formula | Meaning |
|---|---|---|
| Identity Law (OR) | x + 0 = x | ORing with 0 leaves the value unchanged |
| Identity Law (AND) | x · 1 = x | ANDing with 1 leaves the value unchanged |
| Null/Domination (OR) | x + 1 = 1 | ORing with 1 always gives 1 |
| Complement Law | x + x̄ = 1, x · x̄ = 0 | A variable ORed with its complement is 1; ANDed is 0 |
| De Morgan's (Boolean OR) | (x + y)̄ = x̄ · ȳ | The complement of a sum is the product of the complements |
| De Morgan's (Boolean AND) | (x · y)̄ = x̄ + ȳ | The complement of a product is the sum of the complements |
| XOR Expression | x ⊕ y = x · ȳ + x̄ · y | XOR outputs 1 when exactly one input is 1 |
| Absorption Law | x + x · y = x, x · (x + y) = x | A variable absorbs terms containing it |
Sample practice problem
From the free practice sample - 75 guided problems cover this topic in interactive practice.
What is the value of 1 · 0 in Boolean algebra?
- 0
- 1
- Undefined
- 10
Show answer
Answer: 0
In Boolean algebra, 1 · 0 = 0. The AND operation outputs 1 only when both inputs are 1.