Boolean Algebra
1. In Boolean algebra, "1" represents:
a) Any true statement
b) A high voltage level
c) Any false statement
d) A low voltage level
Answer: a) Any true statement
Explanation: In Boolean algebra, 1 represents any logical TRUE statement, often associated with a high voltage level in digital circuits.
2. The distributive property of Boolean algebra states:
a) A + (B ∨ C) = (A + B) ∨ (A + C)
b) A ∧ (B ∨ C) = (A ∧ B) ∨ (A ∧ C)
c) A ∨ (B ∧ C) = (A ∨ B) ∧ (A ∨ C)
d) ¬(A ∧ B) = ¬A ∧ ¬B
Answer: b) A ∧ (B ∨ C) = (A ∧ B) ∨ (A ∧ C)
Explanation: This property allows us to simplify expressions involving AND (∧) and OR (∨) operations.
3. The complement of the expression A ∨ ¬B is:
a) A ∧ B
b) ¬(A ∨ ¬B)
c) ¬A ∧ B
d) A ∧ ¬B
Answer: c) ¬A ∧ B
Explanation: The complement of an expression is obtained by inverting all its literals (variables or their negations).
4. The simplified form of A ∧ (A ∨ B) is:
a) A
b) B
c) A ∨ B
d) 1
Answer: a) A
Explanation: Using the absorption property, A ∧ (A ∨ B) = A.
5. Which of the following is NOT a valid Boolean operator?
a) ∧ (AND)
b) ¬ (NOT)
c) ⊕ (XOR)
d) + (OR)
Answer: None of the above (All options are valid Boolean operators).
Explanation: All listed options are fundamental Boolean operators used in logic operations.
6. De Morgan's Law states that the complement of the product of two variables is equivalent to the:
a) Product of their complements
b) Sum of their complements
c) Product of their inverses
d) Sum of their inverses
Answer: b) Sum of their complements
Explanation: De Morgan's Law allows us to simplify complex expressions by replacing one operation with another and their negations.
7. In a K-map, a "1" in a cell signifies:
a) Both inputs are 1
b) At least one input is 1
c) The output is 1
d) The cell is irrelevant
Answer: c) The output is 1
Explanation: A K-map is a visual tool used to simplify Boolean expressions. A "1" in a cell represents the product term where the output is 1 for the corresponding combination of input values.
8. What is the SOP (Sum of Products) form of the Boolean expression Y = ¬A ∨ B ∨ C?
a) Y = ¬A + B + C
b) Y = A ∧ (B ∨ C)
c) Y = (¬A ∧ B) ∨ (¬A ∧ C)
d) Y = (A ∨ B) ∧ (A ∨ C)
Answer: a) Y = ¬A + B + C
Explanation: SOP form represents an expression as the sum of product terms, where each product term includes all literals (variables or their negations) connected by AND operations.