Boolean Algebra Flashcards

Questions and Answers

What is a variable in Boolean algebra?

A number representing a logical quantity

A symbol used to represent a logical quantity (correct)

A type of operation

None of the above

What is the complement of a variable?

The inverse of a variable, indicated by a bar (overbar) over the variable.

What does Boolean addition represent?

NOT operation

AND operation

OR operation (correct)

XOR operation

What is Boolean multiplication equivalent to?

AND operation Signup and view all the answers

The commutative law states that A + B = ___ + A.

B Signup and view all the answers

Match the following laws with their descriptions:

Commutative Law = Order of operations doesn't matter Associative Law = Grouping of operations doesn't matter Distributive Law = Multiplying a variable by a group of variables Signup and view all the answers

What does the associative law of addition state?

A + (B + C) = (A + B) + C. Signup and view all the answers

State the distributive law in Boolean algebra.

A(B + C) = AB + AC. Signup and view all the answers

Study Notes

Key Concepts of Boolean Algebra

Variable: A symbol that represents a logical quantity, essential in Boolean expressions.
Complement: The inverse of a variable, denoted by an overbar, representing the opposite truth value.
Boolean Addition: Functions as the OR operation, combining values to achieve a true outcome if any variable is true.
Boolean Multiplication: Represents the AND operation, where the result is true only if all involved variables are true.

Commutative and Associative Laws

Commutative Laws:
- For addition (OR operation): A + B = B + A, demonstrating order independence in ORing variables.
- For multiplication (AND operation): A . B = B . A, highlighting that the order of ANDing does not affect the outcome.
Associative Laws:
- For addition: A + (B + C) = (A + B) + C, indicating grouping does not affect the result when ORing.
- For multiplication: A(BC) = (AB)C, showing that grouping in ANDing does not influence the final result.

Distributive Law

Distributive Law: Expressed as A(B + C) = AB + AC. This states that combining OR and AND operations follows a distributive pattern, allowing for simplification of expressions involving multiple variables.

Fundamental Laws of Boolean Algebra

Core Laws:
- Commutative Laws (for addition and multiplication)
- Associative Laws (for addition and multiplication)
- Distributive Law, forming the foundation for simplifying and manipulating Boolean expressions.

Description

Test your knowledge of the fundamental concepts of Boolean algebra with these flashcards. Each card features a key term and its definition, covering essential topics like variables, complements, and operations. Perfect for students and professionals looking to brush up on their understanding of logic in computing.