1List the applications of De Morgan's theorem.
Realization of basic gates using universal gates, simplification of Boolean expressions for efficient logic, and its use in mathematical duality.
2What is a literal?
A literal is a single variable within a term which may or may not be complemented.
3Mention the types of standard forms of expressions.
The two standard forms of expressions are Sum of Products (SOP) and Product of Sum (POS).
4What is a minterm? Explain with example.
A minterm is a logical product of variables where each input variable appears exactly once in the normal form or its complement form. Example: For a truth table, you can write a sum of minterms expression by picking rows where the function output is 1.
5What are the possible minterms for a function with 'n' variables?
A function with 'n' variables has 2^n minterms. Example: For F(X, Y), there are 4 minterms (XY, XY̅, X̅Y, X̅Y̅).
6What is a maxterm? Explain with example.
A maxterm is a logical sum of variables where each input variable appears exactly once in the normal form or its complement form. Example: For a truth table, you can write a product of maxterm expressions by picking rows where the function output is 0.
7What are the possible maxterms for a function with 'n' variables?
A function with 'n' variables has 2^n maxterms. Example: For F(X, Y), there are 4 maxterms (X + Y, X + Y̅, X̅ + Y, X̅ + Y̅).
8How to convert a given expression into minterms?
Convert the expression into SOP form, multiply missing variables in each term, expand the expression, and remove duplicate terms to obtain the minterm expression.
9How to convert a given expression into maxterms?
Convert the expression into POS form, add missing variables in each term, expand the expression, and remove duplicate terms to obtain the maxterm expression.
10Explain minterm notation.
A minterm is a logical product of variables where each input variable appears exactly once in its normal or complement form. Example: F(X, Y) has 4 minterms: X̅Y̅ (m0), X̅Y (m1), XY̅ (m2), XY (m3).
11Explain maxterm notation.
A maxterm is a logical sum of variables where each input variable appears exactly once in its normal or complement form. Example: F(X, Y) has 4 maxterms: X + Y (M0), X + Y̅ (M1), X̅ + Y (M2), X̅ + Y̅ (M3).
12Name two forms of expressing Boolean expressions.
Sum of Products (SOP) and Product of Sum (POS).
13Explain canonical expression.
An expression expressed either in SOP or POS form is called a canonical expression.
14What do you understand by a logic function?
A logic function is a computer switching circuit, helpful for designing electronic devices.
15Give an example for a logic function.
x.y = y.x
16Explain Sum of Products expression.
SOP expression is the sum of two or more product terms. Example: F(X, Y, Z) = X̅Y̅Z + X̅YZ̅ + XY̅Z̅ + XYZ.
17Explain Product of Sum expression.
POS expression is the multiplication of two or more sum terms. Example: F(X, Y, Z) = (X + Y + Z̅)(X + Y̅ + Z).
18What is K-map? What is the use of K-map?
A K-map is a pictorial method to simplify Boolean expressions without using theorems or equations.
19Who introduced K-map?
Maurice Karnaugh introduced the K-map in 1953.
20Draw the general K-map for SOP with 2 variables.
The 2-variable K-map is represented as: X̅Y̅ (m0), X̅Y (m1), XY̅ (m2), XY (m3).