Boolean Algebra MCQs (301-400)

The total number of cells in a 5-variable K-map is:
a) 16
b) 32
c) 64
d) 8
Answer: b) 32
Adjacent 1s in K-map differ by:
a) One variable
b) Two variables
c) Three variables
d) None
Answer: a) One variable
The largest possible group in a 5-variable K-map has:
a) 16 cells
b) 8 cells
c) 32 cells
d) 4 cells
Answer: a) 16 cells
A group of two adjacent cells in K-map eliminates:
a) 1 variable
b) 2 variables
c) 3 variables
d) 0 variable
Answer: a) 1 variable
A group of four adjacent cells in K-map eliminates:
a) 2 variables
b) 3 variables
c) 1 variable
d) None
Answer: a) 2 variables
A group of eight cells in K-map eliminates:
a) 3 variables
b) 4 variables
c) 2 variables
d) None
Answer: a) 3 variables
The term formed by grouping all 1s in a K-map is:
a) 1
b) 0
c) A + B
d) Undefined
Answer: a) 1
The term formed by grouping no 1s in a K-map is:
a) 0
b) 1
c) Undefined
d) A
Answer: a) 0
In K-map, grouping must be of size:
a) 1, 2, 4, 8, … (power of 2)
b) 2, 3, 5
c) 4, 5, 7
d) 1, 3, 6
Answer: a) 1, 2, 4, 8, … (power of 2)
In K-map, a single 1-cell represents:
a) A minterm
b) A maxterm
c) A redundant term
d) A don’t-care
Answer: a) A minterm
A NOR gate followed by a NOT gate acts as:
a) OR gate
b) NAND gate
c) AND gate
d) XOR gate
Answer: a) OR gate

A NAND gate followed by a NOT gate acts as:
a) AND gate
b) OR gate
c) NOR gate
d) XOR gate
Answer: a) AND gate
Which logic family uses diode-resistor logic?
a) DTL
b) RTL
c) TTL
d) ECL
Answer: b) RTL
Which logic family uses transistor-transistor logic?
a) TTL
b) RTL
c) CMOS
d) DTL
Answer: a) TTL
The main advantage of CMOS logic family is:
a) Low power consumption
b) High speed
c) Large current drive
d) Expensive
Answer: a) Low power consumption
Fan-in of a logic gate means:
a) Number of inputs
b) Number of outputs
c) Power consumption
d) Propagation delay
Answer: a) Number of inputs
Fan-out of a logic gate means:
a) Number of gates driven by output
b) Number of inputs
c) Delay time
d) Power used
Answer: a) Number of gates driven by output
The logic level “1” in TTL corresponds approximately to:
a) 5V
b) 0V
c) 2.4V to 5V
d) 0.8V
Answer: c) 2.4V to 5V
The logic level “0” in TTL corresponds approximately to:
a) 0V to 0.8V
b) 2.4V to 5V
c) 5V
d) 1.5V
Answer: a) 0V to 0.8V
The propagation delay of logic gates is measured in:
a) Nanoseconds
b) Microseconds
c) Seconds
d) Picofarads
Answer: a) Nanoseconds

NAND and NOR gates are called universal because:
a) They can implement any Boolean function
b) They have more inputs
c) They are cheapest
d) They are fastest
Answer: a) They can implement any Boolean function
Using NAND gates, NOT function can be made by:
a) Connecting both inputs together
b) Using two NANDs
c) Inverting one input
d) Adding an OR gate
Answer: a) Connecting both inputs together
Using NOR gates, NOT function can be made by:
a) Connecting both inputs together
b) Using two NORs
c) Adding an AND
d) Using OR
Answer: a) Connecting both inputs together
AND gate using NAND only:
a) (A·B)”
b) (A + B)”
c) (A·B)’
d) (A + B)’
Answer: a) (A·B)”
OR gate using NOR only:
a) (A + B)”
b) (A·B)”
c) (A·B)’
d) (A + B)’
Answer: a) (A + B)”
XOR gate can be implemented using:
a) 4 NAND gates
b) 2 NOR gates
c) 1 AND + 1 OR
d) 1 NAND
Answer: a) 4 NAND gates
A NOR gate can be used to realize:
a) NOT, OR, NOR
b) XOR only
c) AND only
d) None
Answer: a) NOT, OR, NOR
A NAND gate can be used to realize:
a) NOT, AND, NAND
b) OR only
c) XOR
d) NOR
Answer: a) NOT, AND, NAND
A logic circuit producing output = 1 only when all inputs are 0 is:
a) NOR gate
b) NAND gate
c) XOR gate
d) XNOR gate
Answer: a) NOR gate
A logic circuit producing output = 0 only when all inputs are 1 is:
a) NAND gate
b) NOR gate
c) AND gate
d) OR gate
Answer: a) NAND gate

🔹 Practical and Theoretical Laws

The Distributive Law of Boolean algebra:
a) A(B + C) = AB + AC
b) (A + B)C = AC + BC
c) Both a and b
d) None
Answer: c) Both a and b
The Involution Law says:
a) (A’)’ = A
b) (A’)’ = A’
c) (A”)’ = 0
d) (A + A’)’ = A
Answer: a) (A’)’ = A
Which of the following is not a valid Boolean law?
a) A + A = A
b) A + 1 = A
c) A + 0 = A
d) A·1 = A
Answer: b) A + 1 = A
The Absorption Law simplifies A + AB to:
a) A
b) B
c) AB
d) A + B
Answer: a) A
The Consensus Theorem eliminates redundant terms in:
a) AB + A’C + BC
b) AB + A’C’ + BC’
c) A + B + C
d) AB + AC + BC
Answer: a) AB + A’C + BC
The Duality Principle means:
a) Replace + with · and 1 with 0
b) Replace 1 with 0 only
c) Replace A with A’
d) Complement all literals
Answer: a) Replace + with · and 1 with 0
Shannon’s Expansion Theorem states that:
a) F = A·F(1) + A’·F(0)
b) F = A + A’
c) F = A·B + A’·B’
d) F = A·B’ + A’·B
Answer: a) F = A·F(1) + A’·F(0)
Simplify using Shannon’s theorem: F(A,B) = A + B.
a) F = A + B
b) F = AB
c) F = A’ + B’
d) F = A’B
Answer: a) F = A + B
The Distributive Law helps in:
a) Factoring or expanding expressions
b) Complementing variables
c) Implementing NOT
d) Creating XORs
Answer: a) Factoring or expanding expressions
The Commutative Law helps in:
a) Changing the order of operands
b) Complementing variables
c) Simplifying NOR
d) Eliminating redundancy
Answer: a) Changing the order of operands

🔹 Logic Circuit Applications

The basic digital building blocks are:
a) Logic gates
b) Microprocessors
c) Transistors
d) Registers
Answer: a) Logic gates
A decoder is used for:
a) Converting binary input to one-hot output
b) Storing data
c) Adding binary numbers
d) Multiplying numbers
Answer: a) Converting binary input to one-hot output
An encoder performs the reverse of:
a) Decoder
b) Multiplexer
c) Demultiplexer
d) Adder
Answer: a) Decoder
A multiplexer is also called:
a) Data selector
b) Decoder
c) Encoder
d) Flip-flop
Answer: a) Data selector
A demultiplexer is also called:
a) Data distributor
b) Encoder
c) Comparator
d) Flip-flop
Answer: a) Data distributor
In a 4-to-1 multiplexer, number of select lines is:
a) 2
b) 3
c) 4
d) 1
Answer: a) 2
The number of outputs in a 2-to-4 decoder is:
a) 4
b) 2
c) 8
d) 1
Answer: a) 4
The output of a NAND gate is logic 0 when:
a) All inputs are 1
b) Any input is 0
c) Any input is 1
d) Both inputs are 0
Answer: a) All inputs are 1
The output of a NOR gate is logic 1 when:
a) All inputs are 0
b) Any input is 1
c) Any input is 0
d) Both inputs are 1
Answer: a) All inputs are 0
The Boolean expression for a 2-input NAND is:
a) (A·B)’
b) (A + B)’
c) A’ + B’
d) A·B
Answer: a) (A·B)’

🔹 Boolean & Logic Design (Application & Conceptual)

In Boolean algebra, A(A + B) = ?
a) A
b) AB
c) A + B
d) 0
Answer: a) A
Simplify A + AB’:
a) A + B’
b) A
c) A’ + B
d) B’
Answer: b) A
Simplify A(A’ + B):
a) AB
b) A’ + B
c) A + B
d) AB + A’
Answer: a) AB
Simplify A + A’B:
a) A + B
b) A’ + B’
c) A·B
d) A’·B
Answer: a) A + B
Simplify A(B + C) + A’C:
a) AB + C
b) A + C
c) B + C
d) AB’ + C
Answer: a) AB + C
Simplify A’B + AB + AB’:
a) A + B
b) A + B’
c) A’ + B
d) B + A’
Answer: a) A + B
Simplify (A + B)(A + B’):
a) A
b) B
c) A + B
d) A·B
Answer: a) A
Simplify A + AB + AB’:
a) A
b) B
c) A + B
d) A’ + B
Answer: a) A
Simplify A·(A + B’):
a) A
b) AB’
c) A + B’
d) B’
Answer: a) A
Simplify (A + B’)(A’ + B’):
a) B’
b) A’
c) A + B’
d) B
Answer: a) B’

Boolean algebra is used in:
a) Digital circuits
b) Probability theory
c) Relativity
d) Analog amplifiers
Answer: a) Digital circuits
Boolean algebra was developed by:
a) George Boole
b) Isaac Newton
c) Charles Babbage
d) Alan Turing
Answer: a) George Boole
The output of XOR gate when both inputs are 1 is:
a) 0
b) 1
c) Undefined
d) Same as input
Answer: a) 0
A 3-input NAND gate gives output 0 only when:
a) All inputs = 1
b) All inputs = 0
c) One input = 0
d) Two inputs = 0
Answer: a) All inputs = 1
A 3-input NOR gate gives output 1 only when:
a) All inputs = 0
b) All inputs = 1
c) Any input = 1
d) One input = 0
Answer: a) All inputs = 0
The output of XNOR gate when inputs differ is:
a) 0
b) 1
c) Undefined
d) Same as A
Answer: a) 0
Logic 1 corresponds to:
a) High voltage
b) Low voltage
c) Negative
d) Floating state
Answer: a) High voltage
Logic 0 corresponds to:
a) Low voltage
b) High voltage
c) Undefined
d) Constant
Answer: a) Low voltage
In Boolean algebra, A + 0 = ?
a) A
b) 0
c) 1
d) A’
Answer: a) A
In Boolean algebra, A·0 = ?
a) 0
b) 1
c) A
d) Undefined
Answer: a) 0

🔹 Conceptual True/False Type (MCQ Format)

XOR is associative.
a) True
b) False
Answer: a) True
AND gate is commutative.
a) True
b) False
Answer: a) True
OR gate is distributive over AND.
a) True
b) False
Answer: a) True
AND gate distributes over OR.
a) True
b) False
Answer: a) True
NOR gate is associative.
a) False
b) True
Answer: a) False
NAND gate is commutative.
a) True
b) False
Answer: a) True
XNOR is associative.
a) True
b) False
Answer: b) False
(A + B)’ = A’ + B’
a) False
b) True
Answer: a) False
(A·B)’ = A’ + B’
a) True
b) False
Answer: a) True
(A + B)(A’ + B) = B
a) True
b) False
Answer: a) True

🔹 Mixed Application & Numerical Logic

Number of Boolean functions of 4 variables = ?
a) 16
b) 65,536
c) 256
d) 1024
Answer: b) 65,536
Number of literals in a 3-variable Boolean equation:
a) 3
b) 8
c) 2³
d) 2⁸
Answer: b) 8
Boolean algebra is similar to:
a) Set algebra
b) Arithmetic algebra
c) Matrix algebra
d) Vector algebra
Answer: a) Set algebra
Which operation corresponds to union in set theory?
a) OR
b) AND
c) NOT
d) XOR
Answer: a) OR

Which operation in Boolean algebra corresponds to intersection in set theory?
a) AND
b) OR
c) NOT
d) XOR
Answer: a) AND
Which operation in Boolean algebra corresponds to complementation in set theory?
a) NOT
b) OR
c) AND
d) XOR
Answer: a) NOT
The Boolean expression for a 3-input majority gate is:
a) AB + BC + AC
b) A + B + C
c) A’B’ + BC
d) AB’C’ + A’BC
Answer: a) AB + BC + AC
The dual of the Boolean equation $A + 0 = A$ is:
a) A·1 = A
b) A·0 = 0
c) A + 1 = 1
d) A’ + 1 = A’
Answer: a) A·1 = A
A half adder can be implemented using:
a) XOR and AND gates
b) NAND and NOR gates
c) OR and AND gates
d) NOT and OR gates
Answer: a) XOR and AND gates
The carry output of a half adder is:
a) A·B
b) A + B
c) A ⊕ B
d) (A + B)’
Answer: a) A·B
The sum output of a half adder is:
a) A ⊕ B
b) A + B
c) A·B
d) A’ + B’
Answer: a) A ⊕ B
A full adder can be implemented using:
a) Two half adders and one OR gate
b) Two XOR gates
c) One NAND and one NOR gate
d) Three AND gates only
Answer: a) Two half adders and one OR gate
The Boolean equation for a 2-to-1 multiplexer is:
a) Y = S’A + SB
b) Y = SA + S’B
c) Y = A + B
d) Y = A·B
Answer: a) Y = S’A + SB
The number of minterms in a 3-variable Boolean function is:
a) 8
b) 4
c) 16
d) 32
Answer: a) 8
A don’t-care condition in K-map is used to:
a) Simplify expressions more easily
b) Create new terms
c) Increase variables
d) Add redundancy
Answer: a) Simplify expressions more easily
The Boolean expression for exclusive OR (XOR) is:
a) A’B + AB’
b) AB + A’B’
c) (A + B)’
d) (A·B)’
Answer: a) A’B + AB’
The XNOR gate is also known as:
a) Equality gate
b) Inequality gate
c) Parity checker
d) Inverter
Answer: a) Equality gate
The output of XNOR gate is 1 when:
a) Both inputs are equal
b) Both inputs are different
c) One input is 1
d) Both are 0 only
Answer: a) Both inputs are equal
Simplify the Boolean expression: A·B + A·B’
a) A
b) B
c) A + B
d) A’
Answer: a) A
Simplify the Boolean expression: (A + B)(A + B’)
a) A
b) B
c) A + B
d) AB
Answer: a) A

Boolean Algebra MCQs (301-400)

🔹 Practical and Theoretical Laws

🔹 Logic Circuit Applications

🔹 Boolean & Logic Design (Application & Conceptual)

🔹 Conceptual True/False Type (MCQ Format)

🔹 Mixed Application & Numerical Logic

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