Digital Logic Design I: Deriving Boolean Expression from Truth Table
10 Questions
5 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

Which term is a single literal or multiple literals connected by OR?

  • Sum-of-Product (SOP)
  • Product-of-Sum (POS)
  • Product term
  • Sum term (correct)
  • What is the term for a product term in which each of the n variables appears exactly once either complemented or un-complemented, but not in both?

  • Minterm (correct)
  • Product term
  • Maxterm
  • Sum term
  • Which expression connects multiple product terms with OR?

  • Sum term
  • Product term
  • Product-of-Sum (POS)
  • Sum-of-Product (SOP) (correct)
  • What is the term for a sum term in which each of the n variables appears exactly once either complemented or un-complemented, but not in both?

    <p>Maxterm</p> Signup and view all the answers

    Which expression connects multiple sum terms with AND?

    <p>Product-of-Sum (POS)</p> Signup and view all the answers

    For a 2-variable Boolean function, how many minterms and maxterms are possible?

    <p>8 minterms and 8 maxterms</p> Signup and view all the answers

    In the given truth table, what is the canonical Sum-of-Product (SOP) expression for the Boolean function F?

    <p>$F(X,Y) = X̅Y + XY̅$</p> Signup and view all the answers

    What is the canonical Product-of-Sum (POS) expression for the Boolean function F?

    <p>$F(X,Y) = (X̅+Y)(X̅+Y̅)$</p> Signup and view all the answers

    For a 3-variable Boolean function, how many minterms and maxterms are possible?

    <p>16 minterms and 16 maxterms</p> Signup and view all the answers

    Based on the given truth table, what would be the canonical POS expression for the Boolean expression F = A+B+C?

    <p>$F(A,B,C) = (A+B)(A+B+C)(A+B+C̅)$</p> Signup and view all the answers

    Study Notes

    Boolean Algebra Terminology

    • A term is a single literal or multiple literals connected by OR.

    Product Terms

    • A product term is a term in which each of the n variables appears exactly once either complemented or un-complemented, but not in both.
    • Multiple product terms are connected with OR.

    Sum Terms

    • A sum term is a term in which each of the n variables appears exactly once either complemented or un-complemented, but not in both.
    • Multiple sum terms are connected with AND.

    Minterms and Maxterms

    • For a 2-variable Boolean function, there are 2^2 = 4 minterms and 2^2 = 4 maxterms possible.
    • For a 3-variable Boolean function, there are 2^3 = 8 minterms and 2^3 = 8 maxterms possible.

    Canonical Expressions

    • The canonical Sum-of-Product (SOP) expression is derived from the truth table.
    • The canonical Product-of-Sum (POS) expression is also derived from the truth table.
    • For a 3-variable Boolean function F = A+B+C, the canonical POS expression is (A'+B'+C')'(A+B'+C')'(A'+B+C')'(A'+B'+C').

    Studying That Suits You

    Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

    Quiz Team

    Description

    This quiz covers the process of deriving Boolean expressions from a truth table in the context of Digital Logic Design I. It includes definitions such as literals, product terms, and sum terms.

    More Like This

    Use Quizgecko on...
    Browser
    Browser