Boolean Algebra MCQs (01-100)

  1. Which of the following is a universal gate?
    a) AND
    b) OR
    c) NAND
    d) XOR
    Answer: c) NAND

  2. The output of an AND gate is HIGH when:
    a) All inputs are HIGH
    b) Any input is HIGH
    c) All inputs are LOW
    d) Only one input is HIGH
    Answer: a) All inputs are HIGH

  3. The output of an OR gate is LOW when:
    a) All inputs are LOW
    b) Any input is HIGH
    c) All inputs are HIGH
    d) Only one input is HIGH
    Answer: a) All inputs are LOW

  4. Which gate performs the operation Y = A·B + A·B’?
    a) XOR
    b) XNOR
    c) NAND
    d) NOR
    Answer: a) XOR

  5. The complement of an OR gate output can be implemented by:
    a) NOR gate
    b) NAND gate
    c) XOR gate
    d) AND gate
    Answer: a) NOR gate

  6. Which gate produces a HIGH output only if all inputs are LOW?
    a) NOR
    b) NAND
    c) AND
    d) OR
    Answer: a) NOR

  7. Which logic gate is known as an “inverter”?
    a) NOT
    b) AND
    c) OR
    d) NAND
    Answer: a) NOT

  8. A NAND gate is equivalent to:
    a) NOT(AND)
    b) NOT(OR)
    c) AND(OR)
    d) OR(AND)
    Answer: a) NOT(AND)

  9. A NOR gate is equivalent to:
    a) NOT(OR)
    b) NOT(AND)
    c) AND(OR)
    d) OR(AND)
    Answer: a) NOT(OR)

  10. Which of the following gates can be used to implement any Boolean function?
    a) NAND and NOR
    b) AND and OR
    c) XOR and XNOR
    d) NOT only
    Answer: a) NAND and NOR

  11. The Boolean expression for a two-input AND gate is:
    a) Y = A·B
    b) Y = A + B
    c) Y = A ⊕ B
    d) Y = A’ + B’
    Answer: a) Y = A·B

  12. The Boolean expression for a two-input OR gate is:
    a) Y = A + B
    b) Y = A·B
    c) Y = A ⊕ B
    d) Y = A’·B’
    Answer: a) Y = A + B

  13. What is the output of a NOT gate if input is 1?
    a) 0
    b) 1
    c) Undefined
    d) 2
    Answer: a) 0

  14. Which gate has the property of idempotence: A·A = A?
    a) AND
    b) OR
    c) NAND
    d) XOR
    Answer: a) AND

  15. Which gate has the property: A + A = A?
    a) OR
    b) AND
    c) NAND
    d) NOR
    Answer: a) OR

  16. The truth table of XNOR gate gives output 1 when:
    a) Both inputs are same
    b) Both inputs are different
    c) Any input is HIGH
    d) Both inputs are LOW
    Answer: a) Both inputs are same

  17. XOR gate is used for which of the following operations?
    a) Addition (without carry)
    b) Multiplication
    c) Division
    d) Subtraction
    Answer: a) Addition (without carry)

  18. The output of a 3-input AND gate is 1 when:
    a) All inputs are 1
    b) Only two inputs are 1
    c) At least one input is 1
    d) All inputs are 0
    Answer: a) All inputs are 1

  19. Which logic gate output is 1 when at least one input is 1?
    a) OR
    b) AND
    c) NAND
    d) NOR
    Answer: a) OR

  20. NAND gate is also called a:
    a) Universal gate
    b) Controlled gate
    c) Identity gate
    d) Buffer gate
    Answer: a) Universal gate

  1. The Boolean expression A + 0 = A is an example of:
    a) Identity Law
    b) Null Law
    c) Complement Law
    d) Idempotent Law
    Answer: a) Identity Law

  2. The Boolean expression A·1 = A is an example of:
    a) Identity Law
    b) Null Law
    c) Complement Law
    d) Idempotent Law
    Answer: a) Identity Law

  3. The Boolean law: A + A’ = 1 is called:
    a) Complement Law
    b) Distributive Law
    c) Associative Law
    d) Identity Law
    Answer: a) Complement Law

  4. The Boolean law: A·A = A is called:
    a) Idempotent Law
    b) Demorgan’s Law
    c) Complement Law
    d) Associative Law
    Answer: a) Idempotent Law

  5. The Boolean law: A + A = A is called:
    a) Idempotent Law
    b) Demorgan’s Law
    c) Complement Law
    d) Commutative Law
    Answer: a) Idempotent Law

  6. The Boolean law: A·B = B·A is called:
    a) Commutative Law
    b) Associative Law
    c) Distributive Law
    d) Identity Law
    Answer: a) Commutative Law

  7. The Boolean law: A + B = B + A is called:
    a) Commutative Law
    b) Associative Law
    c) Distributive Law
    d) Identity Law
    Answer: a) Commutative Law

  8. The law: A·(B·C) = (A·B)·C is called:
    a) Associative Law
    b) Distributive Law
    c) Commutative Law
    d) Identity Law
    Answer: a) Associative Law

  9. The law: A + (B + C) = (A + B) + C is called:
    a) Associative Law
    b) Commutative Law
    c) Distributive Law
    d) Identity Law
    Answer: a) Associative Law

  10. The law: A·(B + C) = A·B + A·C is called:
    a) Distributive Law
    b) Commutative Law
    c) Associative Law
    d) Identity Law
    Answer: a) Distributive Law

  11. Demorgan’s Law states: (A·B)’ = ?
    a) A’ + B’
    b) A’·B’
    c) A + B
    d) AB
    Answer: a) A’ + B’

  12. Demorgan’s Law states: (A + B)’ = ?
    a) A’·B’
    b) A’ + B’
    c) A·B
    d) A + B
    Answer: a) A’·B’

  13. Complement of 1 is:
    a) 0
    b) 1
    c) Undefined
    d) 2
    Answer: a) 0

  14. Complement of 0 is:
    a) 1
    b) 0
    c) Undefined
    d) 2
    Answer: a) 1

  15. Which law states A + AB = A?
    a) Absorption Law
    b) Distributive Law
    c) Idempotent Law
    d) Complement Law
    Answer: a) Absorption Law

  16. Which law states A·(A + B) = A?
    a) Absorption Law
    b) Demorgan’s Law
    c) Identity Law
    d) Complement Law
    Answer: a) Absorption Law

  17. The law A + 1 = 1 is called:
    a) Dominance Law
    b) Identity Law
    c) Null Law
    d) Complement Law
    Answer: a) Dominance Law

  18. The law A·0 = 0 is called:
    a) Dominance Law
    b) Identity Law
    c) Null Law
    d) Complement Law
    Answer: a) Dominance Law

  19. The law A + A’B = A + B is called:
    a) Consensus Theorem
    b) Distributive Law
    c) Commutative Law
    d) Identity Law
    Answer: a) Consensus Theorem

  20. The law A·(A’ + B) = A·B is called:
    a) Consensus Theorem
    b) Distributive Law
    c) Commutative Law
    d) Identity Law
    Answer: a) Consensus Theorem

  1. Which form represents a Boolean expression as a sum of product terms?
    a) SOP
    b) POS
    c) K-map
    d) XOR
    Answer: a) SOP

  2. Which form represents a Boolean expression as a product of sum terms?
    a) POS
    b) SOP
    c) K-map
    d) XOR
    Answer: a) POS

  3. SOP expression is minimized using which method?
    a) Karnaugh Map
    b) Truth Table
    c) Logic Gates
    d) XOR
    Answer: a) Karnaugh Map

  4. POS expression is minimized using which method?
    a) Karnaugh Map
    b) Truth Table
    c) Logic Gates
    d) XOR
    Answer: a) Karnaugh Map

  5. SOP form of Y = A’B + AB’ is:
    a) Sum of two products
    b) Product of sums
    c) Single product
    d) Single sum
    Answer: a) Sum of two products

  6. POS form of Y = (A + B)(A’ + C) is:
    a) Product of sums
    b) Sum of products
    c) Single sum
    d) Single product
    Answer: a) Product of sums

  7. SOP expression is preferred for:
    a) Implementing with AND-OR logic
    b) Implementing with OR-AND logic
    c) Implementing with NAND only
    d) Implementing with XOR only
    Answer: a) Implementing with AND-OR logic

  8. POS expression is preferred for:
    a) Implementing with OR-AND logic
    b) Implementing with AND-OR logic
    c) Implementing with NAND only
    d) Implementing with XOR only
    Answer: a) Implementing with OR-AND logic

  1. A minterm is a product term in SOP that represents:
    a) A single combination of inputs giving output 1
    b) All combinations of inputs
    c) A sum term giving 0
    d) Only complemented variables
    Answer: a) A single combination of inputs giving output 1

  2. A maxterm is a sum term in POS that represents:
    a) A single combination of inputs giving output 0
    b) All combinations of inputs
    c) A product term giving 1
    d) Only uncomplemented variables
    Answer: a) A single combination of inputs giving output 0

  3. The SOP form of Y = A + AB is simplified to:
    a) Y = A
    b) Y = AB
    c) Y = B
    d) Y = A + B
    Answer: a) Y = A

  4. The POS form of Y = (A + B)(A + B’) simplifies to:
    a) Y = A + B
    b) Y = B
    c) Y = A
    d) Y = 0
    Answer: a) Y = A + B

  5. How many minterms are possible for 3 variables?
    a) 8
    b) 4
    c) 6
    d) 3
    Answer: a) 8

  6. How many maxterms are possible for 4 variables?
    a) 16
    b) 8
    c) 4
    d) 32
    Answer: a) 16

  7. Which expression represents a minterm for variables A=1, B=0, C=1?
    a) A·B’·C
    b) A’·B·C
    c) A·B·C
    d) A’·B’·C
    Answer: a) A·B’·C

  8. Which expression represents a maxterm for variables A=0, B=1, C=0?
    a) (A + B’ + C)
    b) (A’ + B + C’)
    c) (A + B + C)
    d) (A’ + B’ + C’)
    Answer: a) (A + B’ + C)

  9. SOP form is more suitable for implementation with:
    a) AND-OR logic
    b) OR-AND logic
    c) XOR logic
    d) NAND-only logic
    Answer: a) AND-OR logic

  10. POS form is more suitable for implementation with:
    a) OR-AND logic
    b) AND-OR logic
    c) XOR logic
    d) NAND-only logic
    Answer: a) OR-AND logic

  11. SOP expression for 2-variable XOR gate is:
    a) A’B + AB’
    b) AB + A’B’
    c) A + B
    d) A·B
    Answer: a) A’B + AB’

  12. POS expression for 2-variable XNOR gate is:
    a) (A + B)(A’ + B’)
    b) (A + B’)(A’ + B)
    c) (A’ + B)(A + B’)
    d) (A + B)(A + B’)
    Answer: a) (A + B)(A’ + B’)

  13. K-map is used for:
    a) Minimizing Boolean expressions
    b) Drawing logic circuits
    c) Counting minterms
    d) Writing SOP only
    Answer: a) Minimizing Boolean expressions

  14. How many cells are there in a K-map for 2 variables?
    a) 4
    b) 2
    c) 6
    d) 8
    Answer: a) 4

  15. How many cells are there in a K-map for 3 variables?
    a) 8
    b) 4
    c) 6
    d) 16
    Answer: a) 8

  16. How many cells are there in a K-map for 4 variables?
    a) 16
    b) 8
    c) 4
    d) 32
    Answer: a) 16

  17. Adjacent 1s in a K-map are combined to form:
    a) Groups for simplification
    b) Maxterms
    c) Variables
    d) Input lines
    Answer: a) Groups for simplification

  18. Each cell in a K-map corresponds to:
    a) One minterm
    b) One maxterm
    c) Multiple minterms
    d) None of these
    Answer: a) One minterm

  19. In a 3-variable K-map, the cell order is based on:
    a) Gray code
    b) Binary code
    c) Decimal code
    d) Random arrangement
    Answer: a) Gray code

  20. K-map simplification reduces:
    a) Number of literals
    b) Number of variables
    c) Number of inputs
    d) Number of outputs
    Answer: a) Number of literals

  21. Maximum group size in K-map should be:
    a) Powers of 2
    b) Odd numbers
    c) Prime numbers
    d) Any number
    Answer: a) Powers of 2

  22. For 2-variable K-map, group of 2 ones represents:
    a) Single variable term
    b) Two-variable term
    c) Constant 1
    d) Zero
    Answer: a) Single variable term

  23. In a 4-variable K-map, grouping 4 ones together reduces the expression by:
    a) 2 variables
    b) 1 variable
    c) 3 variables
    d) 4 variables
    Answer: a) 2 variables

  24. A K-map with all 1s represents:
    a) Constant 1
    b) Constant 0
    c) Variable expression
    d) Minterm 0 only
    Answer: a) Constant 1

  25. A K-map with all 0s represents:
    a) Constant 0
    b) Constant 1
    c) Variable expression
    d) Minterm 1 only
    Answer: a) Constant 0

  26. K-map simplification of Y = A·B + A·B’ yields:
    a) Y = A
    b) Y = B
    c) Y = AB
    d) Y = A + B
    Answer: a) Y = A

  27. K-map grouping must be:
    a) Rectangular and in powers of 2
    b) Random
    c) Circular
    d) Triangular
    Answer: a) Rectangular and in powers of 2

  28. A K-map for 3 variables has rows labeled by:
    a) Two variables
    b) One variable
    c) Three variables
    d) None
    Answer: a) Two variables

  29. Columns of a 3-variable K-map represent:
    a) One variable
    b) Two variables
    c) Three variables
    d) None
    Answer: a) One variable

  30. Minimum number of groups in K-map is determined by:
    a) Number of 1s
    b) Number of 0s
    c) Number of variables
    d) Number of gates
    Answer: a) Number of 1s

  31. Grouping 8 ones in a 4-variable K-map reduces the term by:
    a) 3 variables
    b) 2 variables
    c) 1 variable
    d) 0 variables
    Answer: a) 3 variables

  32. K-map is not suitable for more than:
    a) 6 variables
    b) 4 variables
    c) 3 variables
    d) 5 variables
    Answer: a) 6 variables

Logic Gates & Boolean Algebra (Advanced)

  1. XOR gate is equivalent to:
    a) A·B’ + A’·B
    b) A·B + A’·B’
    c) A + B
    d) A·B
    Answer: a) A·B’ + A’·B

  2. XNOR gate output is:
    a) 1 when inputs are equal
    b) 1 when inputs are different
    c) Always 0
    d) Always 1
    Answer: a) 1 when inputs are equal

  3. The complement of A·B + A·C is:
    a) A’ + B’C’
    b) A’ + B’·C’
    c) A + B + C
    d) A + B·C
    Answer: b) A’ + B’·C’

  4. Boolean expression A·(A + B) simplifies to:
    a) A
    b) B
    c) AB
    d) A + B
    Answer: a) A

  5. Boolean expression A + A·B simplifies to:
    a) A
    b) B
    c) AB
    d) A + B
    Answer: a) A

  6. (A + B)·(A + B’) simplifies to:
    a) A + B
    b) A·B
    c) B
    d) A
    Answer: a) A + B

  7. (A + B) + (A + B’) simplifies to:
    a) A + 1 = 1
    b) A
    c) B
    d) AB
    Answer: a) 1

  8. Which gate is called “universal gate”?
    a) NAND
    b) AND
    c) OR
    d) XOR
    Answer: a) NAND

  9. Boolean expression for 3-input AND gate is:
    a) Y = A·B·C
    b) Y = A + B + C
    c) Y = A⊕B⊕C
    d) Y = (A·B)’
    Answer: a) Y = A·B·C

  10. Boolean expression for 3-input OR gate is:
    a) Y = A + B + C
    b) Y = A·B·C
    c) Y = (A + B)’
    d) Y = A⊕B⊕C
    Answer: a) Y = A + B + C

  11. A 2-input NOR gate output is:
    a) (A + B)’
    b) (A·B)’
    c) A·B
    d) A + B
    Answer: a) (A + B)’

  12. A 2-input NAND gate output is:
    a) (A·B)’
    b) (A + B)’
    c) A·B
    d) A + B
    Answer: a) (A·B)’

  13. Demorgan’s theorem states: (A + B)’ = ?
    a) A’·B’
    b) A’ + B’
    c) AB
    d) A + B
    Answer: a) A’·B’

  14. Demorgan’s theorem states: (A·B)’ = ?
    a) A’ + B’
    b) A’·B’
    c) AB
    d) A + B
    Answer: a) A’ + B’

  15. SOP expression is obtained from:
    a) Truth table output 1
    b) Truth table output 0
    c) Both 1 and 0
    d) Only complemented variables
    Answer: a) Truth table output 1

  16. POS expression is obtained from:
    a) Truth table output 0
    b) Truth table output 1
    c) Both 0 and 1
    d) Only uncomplemented variables
    Answer: a) Truth table output 0

  17. A K-map for 2 variables has how many prime implicants maximum?
    a) 3
    b) 2
    c) 1
    d) 4
    Answer: a) 3

  18. Boolean expression A + AB + AC simplifies to:
    a) A + C·B
    b) A
    c) B + C
    d) AB + AC
    Answer: b) A

  19. Boolean expression (A + B)·(A + C) simplifies to:
    a) A + B·C
    b) A·B + C
    c) A + B + C
    d) AB + AC
    Answer: a) A + B·C

  20. Boolean expression (A·B) + (A·B’) + (A’·B) simplifies to:
    a) A + B
    b) AB
    c) A·B
    d) 1
    Answer: a) A + B

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