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.