Boolean Logic And Circuits Flashcards
Properties of Boolean operators
What is commutativity?
Both the AND and OR operators are commutative
= meaning the order of inputs does not affect the result.
A AND B is the same as B AND A ; A OR B is the same as B OR A
AB = BA ; A+B = B+A
Properties of Boolean operators
What is associativity?
Both the AND and OR operators are associative
= meaning the grouping of inputs does not affect the result
(A AND B) AND C is the same as A AND (B AND C)
(AB)C = A(BC)
Properties of Boolean operators
What is distributivity?
The AND and OR operators follow the distributive property
= allowing simplification of complex expressions
A AND (B OR C) is the same as (A AND B) OR (A AND C))
A(B+C) = (AB) + (A*C)
The precedence of logical operators determines the “______” in which they are evaluated in an expression
What is the general precedence of logical operators?
- NOT (highest precedence) evaluated first
- AND evaluated second
- OR (lowest precedence) evaluated last
It’s recommended to use parentheses to explicitly specify the desired order of evaluation to avoid any ambiguity
What is De Morgan’s Law?
State that negation of a logical expression involving AND or OR can be obtained by negating the individual terms and changing the operator
NOT (A AND B) is equivalent to (NOT A) OR (NOT B)
NOT(A OR B) is equivalent to (NOT A) AND (NOTB)
How can we prove that De Morgan’s laws are true?
How can we see if two circuits or Boolean expressions are equivalent?
Using truth tables
(REFER TO SLIDES FOR EXAMPLE)
Given a truth table, what is the Boolean function?
To create a sum of product expression, what are the 5 steps to follow?
- Start with a truth table that describes the desired behavior of the Boolean function, listing all possible input combinations and their corresponding outputs
- Identify the rows of the truth table where the output is “True” (1)
- For each of these rows, create a logical AND term by combining the input variables with their corresponding values. Invert False (0) values with the NOT operator
- Find the product for each row using the AND operator
- Combine all the logical AND terms using the logical OR operator, representing the function as the sum of these terms
Logic operators in python
What are compound conditions?
In python they are used to evaluate multiple conditions together using logical operators
The logical operators used for combining conditions are and, or, and not
Using the “and” operator:
• x > 5 and y < 10
Using the “or” operator:
• age >= 18 or has_permission
Using the not operator:
• not has_permission
