## Boolean Algebra MCQ

Boolean Algebra MCQ, Objectives on Boolean Algebra, Multiple Choice Questions on Boolean Algebra, De Morgan’s theorem MCQ, Engineering MCQ, Digital Electronics MCQ,

MCQ on Combinational Logic Circuits

### Objective Type Questions

Q.1. A + AB + ABC + ABCD + ABCDE + …… =

- 1
- A
- A+ AB
- AB

**Answer: **A

Q.2. A+\bar{A}B+\bar{A}\bar{B}C+\bar{A}\bar{B}\bar{C}D+....=

- A+B+C+….
- \bar{A}+\bar{B}+\bar{C}+\bar{D}+....=
- 1
- 0

**Answer:** A+B+C+….

Q.3. De Morgan’s theorem states that

- \bar{A+B}=\bar{A}\bar{B} and \bar{AB}=\bar{A}+\bar{B}
- \bar{A+B}=\bar{A}+\bar{B} and \bar{AB}=\bar{A}\bar{B}
- \bar{A+B}=A+B and \bar{AB}=AB
- \bar{A+B}=\bar{A}\bar{B} and \bar{AB}=\bar{A}\bar{B}

**Answer: **\bar{A+B}=\bar{A}\bar{B} and \bar{AB}=\bar{A}+\bar{B}

Q.4. The logic expression (A+B)(\bar{A}+\bar{B}) can be implemented by giving the inputs A and B to a two-input

- NOR gate
- NAND gate
- X-OR gate
- X-NOR gate

**Answer:** X-OR gate

Q.5. The logic expression (\bar{A}+B)(A+\bar{B}) can be implemented by giving the inputs A and B to a two-input

- NOR gate
- NAND gate
- X-OR gate
- X-NOR gate

**Answer:** X-NOR gate

Q.6. Which of the following Boolean algebraic expressions is incorrect?

- A+\bar{A}B=A+B
- A+AB=B
- (A+B)(A+C)=A+BC
- (A+\bar{B})(A+B)=A

**Answer:** A+AB=B

Q.7. The simplified form of the Boolean expression (X + Y + XY)(X + Z) is

- X+Y+Z
- XY + YZ
- X + YZ
- XZ + Y

**Answer:** X + YZ

Q.8. The simplified form of the Boolean expression (X+\bar{Y}+Z)(X+\bar{Y}+\bar{Z})(X+Y+Z) is

- \bar{X}Y+Z
- X+\bar{Y}Z
- \bar{X}Y+\bar{Z}
- XY+\bar{Z}

**Answer:** X+\bar{Y}Z

Q.9. A + B = B + A; AB = BA represent which laws?

- Commutative
- Associative
- Distributive
- Idempotence

**Answer:** Commutative

Q.10. (A + B) + C = A + (B + C); (AB)C = A(BC) represent which laws?

- Commutative
- Associative
- Distributive
- Idempotence

**Answer:** Associative

Q.11. A(B + C) =AB + AC; A + BC = (A + B)(A + C) represent which laws?

- Commutative
- Associative
- Distributive
- Idempotence

**Answer:** Distributive

Q.12. A + AB = A; A(A + B) = A represent which laws?

- Idempotence
- Absorption
- Associative
- Commutative

**Answer:** Absorption

Q.13. AB+\bar{A}C+BC=AB+\bar{A}C represents which theorem?

- Consensus
- Transposition
- De Morgan’s
- None of these

**Answer:** Consensus

Q.14. AB+\bar{A}C=(A+C)+(\bar{A}+B) represents which theorem

- Consensus
- Transposition
- De Morgan
- Included factor

**Answer:** Transposition

Q.15. The dual of a Boolean expression is obtained by

- interchanging all 0s and 1s
- interchanging all 0s and 1s, all + and ‘.’ signs
- interchanging all 0s and 1s, all + and ‘.’ signs and complementing all the variables
- interchanging all + and ‘.’ signs and complementing all the variables

**Answer:** interchanging all 0s and 1s, all + and ‘.’ signs

Q.16. The complement of a Boolean expression is obtained by

- interchanging all 0s and 1s
- interchanging all 0s and 1s, all + and ‘.’ signs
- interchanging all 0s and 1s, all + and ‘.’ signs and complementing all the variables
- interchanging all + and ‘.’ signs and complementing all the variables

**Answer:** interchanging all 0s and 1s, all + and ‘.’ signs and complementing all the variables

Q.17. The logic expression F=AB+\bar{B}C+AC is in

- SOP form
- POS form
- standard SOP form
- standard POS form

**Answer:** SOP form

Q.18. The logic expression F=(A+B+C)(A+\bar{C})(B+\bar{C})(A+C) is in

- SOP form
- POS form
- standard SOP form
- standard POS form

**Answer:** POS form

Q.19. K-map is used

- to minimize the number of flip-flops in a digital circuit
- to minimize the number of gates only in a digital circuits
- to minimize the number of gates and the fan in requirements of the gates in a digital circuit
- to design gates

**Answer:** to minimize the number of gates and the fan in requirements of the gates in a digital circuit

Q.20. The number of cells in a 6- variable K-map is

- 6
- 12
- 36
- 64

**Answer:** 64

Q.21. The code used for labeling cells of the K-map is

- natural BCD
- Hexadecimal
- Gray
- Octal

**Answer: **Gray