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Quiz: Boolean Algebra Fundamentals

Test your understanding of Boolean algebra, logic operations, and simplification laws with these questions.

1. What is the result of the Boolean expression A + 1?

  1. A
  2. 1
  3. 0
  4. A'
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The correct answer is B. According to the Null Law (also called the Dominance Law), any variable ORed with 1 equals 1. This makes sense because if either input to an OR is true, the output is true—and 1 is always true.

Concept Tested: Null Law

2. Which Boolean law states that A + AB = A?

  1. Identity Law
  2. Distributive Law
  3. Absorption Law
  4. Complement Law
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The correct answer is C. The Absorption Law states that A + AB = A and A(A + B) = A. It allows us to "absorb" redundant terms. The intuition: if A is true, the whole expression is true regardless of B.

Concept Tested: Absorption Law

3. What does De Morgan's Theorem state about (A + B)'?

  1. (A + B)' = A' + B'
  2. (A + B)' = A'B'
  3. (A + B)' = AB'
  4. (A + B)' = A'B
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The correct answer is B. De Morgan's Theorem states that the complement of a sum equals the product of the complements: (A + B)' = A'B'. Similarly, (AB)' = A' + B'. This theorem is fundamental for converting between AND/OR forms and implementing circuits with NAND/NOR gates.

Concept Tested: De Morgan's Theorem

4. In a truth table for a 3-input Boolean function, how many rows are required?

  1. 3
  2. 6
  3. 8
  4. 16
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The correct answer is C. A truth table must include all possible input combinations. For n inputs, there are 2ⁿ combinations. With 3 inputs, there are 2³ = 8 rows, covering all combinations from 000 to 111.

Concept Tested: Truth Table

5. Which expression is equivalent to A ⊕ B (XOR)?

  1. AB + A'B'
  2. A'B + AB'
  3. (A + B)'
  4. A'B'
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The correct answer is B. XOR (exclusive OR) outputs 1 when exactly one input is 1. The expression A'B + AB' captures this: either A is 0 and B is 1, or A is 1 and B is 0. Option A describes XNOR (equivalence), not XOR.

Concept Tested: Boolean Expression

6. What is the Commutative Law of Boolean algebra?

  1. A + (B + C) = (A + B) + C
  2. A + B = B + A
  3. A + A = A
  4. A + 0 = A
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The correct answer is B. The Commutative Law states that the order of operands doesn't matter: A + B = B + A and AB = BA. Option A is the Associative Law, option C is the Idempotent Law, and option D is the Identity Law.

Concept Tested: Commutative Law

7. Simplify the expression ABC + ABC' using Boolean algebra.

  1. ABC
  2. AB
  3. AC
  4. A
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The correct answer is B. Factor out AB: ABC + ABC' = AB(C + C'). By the Complement Law, C + C' = 1. Therefore, AB(1) = AB. This is a common simplification pattern where a variable and its complement appear in adjacent terms.

Concept Tested: Algebraic Simplification

8. What is a Boolean function?

  1. A circuit made of logic gates
  2. A mapping from Boolean input combinations to Boolean outputs
  3. A variable that can only be 0 or 1
  4. A type of arithmetic operation
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The correct answer is B. A Boolean function is a mathematical mapping that takes Boolean input combinations (each variable being 0 or 1) and produces a Boolean output (0 or 1). It defines the relationship between inputs and outputs, which can then be implemented as a circuit.

Concept Tested: Boolean Function

9. According to the Distributive Law, what is A(B + C)?

  1. AB + C
  2. AB + AC
  3. A + BC
  4. ABC
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The correct answer is B. The Distributive Law states A(B + C) = AB + AC. This is similar to distribution in regular algebra. Boolean algebra also has a unique dual form: A + BC = (A + B)(A + C), which differs from standard algebra.

Concept Tested: Distributive Law

10. What does the Complement Law state about A · A'?

  1. A · A' = 1
  2. A · A' = 0
  3. A · A' = A
  4. A · A' = A'
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The correct answer is B. The Complement Law states that A · A' = 0 (a variable ANDed with its complement is always 0) and A + A' = 1 (a variable ORed with its complement is always 1). This makes sense: A and A' can never both be true simultaneously.

Concept Tested: Complement Law