10 Questions
Which term is a single literal or multiple literals connected by OR?
Sum term
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
Which expression connects multiple product terms with OR?
Sum-of-Product (SOP)
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?
Maxterm
Which expression connects multiple sum terms with AND?
Product-of-Sum (POS)
For a 2-variable Boolean function, how many minterms and maxterms are possible?
8 minterms and 8 maxterms
In the given truth table, what is the canonical Sum-of-Product (SOP) expression for the Boolean function F?
$F(X,Y) = X̅Y + XY̅$
What is the canonical Product-of-Sum (POS) expression for the Boolean function F?
$F(X,Y) = (X̅+Y)(X̅+Y̅)$
For a 3-variable Boolean function, how many minterms and maxterms are possible?
16 minterms and 16 maxterms
Based on the given truth table, what would be the canonical POS expression for the Boolean expression F = A+B+C?
$F(A,B,C) = (A+B)(A+B+C)(A+B+C̅)$
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').
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.
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