What is the output of an AND gate when all inputs are 1?
A 0
B 1
C Undefined
D Depends on the inputs
An AND gate produces a high (1) output only when all its inputs are high (1). For any low (0) input, the output will be low (0).
What is the binary equivalent of decimal 7?
A 101
B 111
C 110
D 100
The binary equivalent of decimal 7 is 111, calculated as 2^2 + 2^1 + 2^0.
Which logic gate produces a high output only when one of its inputs is high, but not both?
A AND
B OR
C XOR
D XNOR
The XOR gate outputs 1 only when the inputs are different (one is 1, and the other is 0).
What is the main use of a flip-flop in digital circuits?
A Perform arithmetic operations
B Store a single bit of data
C Convert analog signals to digital
D Decode binary data
Flip-flops are used in digital circuits to store a single bit of data and are the fundamental building blocks of sequential circuits.
How many outputs does a 2-to-4 decoder have?
A 2
B 3
C 4
D 8
A 2-to-4 decoder has 2^2 = 4 outputs and converts 2-bit binary inputs into one of the four possible outputs.
Which circuit is used to count clock pulses?
A Register
B Counter
C Flip-Flop
D Multiplexer
A counter is a sequential circuit designed to count clock pulses and store the count in binary form.
What is the characteristic equation of a JK flip-flop?
A Qnext = J⋅Q + K⋅Q’
B Qnext = J⋅Q’ + K⋅Q
C Qnext = J⋅Q’
D Qnext = Q
The JK flip-flop’s characteristic equation determines its next state based on the current state and input values.
What is the purpose of a finite state machine (FSM)?
A Store data temporarily
B Perform arithmetic operations
C Model and control sequential logic behavior
D Decode binary signals
FSMs are used to design systems where outputs and next states depend on the current state and inputs.
Which logic gate is the opposite of an AND gate?
A OR
B NOR
C NAND
D XOR
A NAND gate produces the opposite output of an AND gate. If all inputs to an AND gate are high, the output is low for a NAND gate.
What is the binary equivalent of decimal 12?
A 1100
B 1001
C 1010
D 1111
Decimal 12 equals 2^3 + 2^2, which is represented as 1100 in binary.
How many flip-flops are required to design a 4-bit counter?
A 2
B 4
C 6
D 8
A 4-bit counter requires 4 flip-flops because each flip-flop can store 1 bit.
What is the primary function of a multiplexer?
A Amplify signals
B Perform arithmetic operations
C Select one input from many inputs
D Convert binary to decimal
A multiplexer selects one of several input signals and forwards it to the output based on control signals.
What does the term “propagation delay” refer to in a digital circuit?
A The time required to reset a flip-flop
B The time taken for a signal to travel through a logic gate
C The time to amplify a signal
D The time for a counter to overflow
Propagation delay is the time interval between applying an input and the corresponding output change in a logic gate.
What is the result of A + A’B in Boolean algebra?
A A
B B
C A + B
D 1
By applying the Consensus Theorem, A + A’B simplifies to A + B.
Which circuit stores multiple bits of data in parallel?
A Counter
B Multiplexer
C Register
D Decoder
A register is a group of flip-flops used to store multiple bits of data simultaneously.
How many states does a 3-bit counter have?
A 4
B 6
C 8
D 16
A 3-bit counter has 2^3 = 8 states, ranging from 000 to 111 in binary.
Which logic gate produces a low output only when all inputs are low?
A AND
B OR
C NOR
D NAND
A NOR gate outputs a low (0) result unless all inputs are low (0), in which case it outputs a high (1).
What is the simplified expression of AB + A’B?
A B
B A
C AB
D A + B
By applying the Distributive Law, AB + A’B = B(A + A’), and since A + A’ = 1, the expression simplifies to B.
What does a combinational circuit depend on?
A Past inputs
B Current inputs
C Both past and current inputs
D Clock signals
A combinational circuit’s outputs depend solely on its current inputs, without any memory or storage element.
What is the binary subtraction result of 1010 − 0110?
A 0100
B 0011
C 1001
D 1110
Perform binary subtraction:
1010 − 0110 = 0100.
Which logic gate produces a low output when any of its inputs is high?
A NOR
B OR
C AND
D XOR
A NOR gate produces a high (1) output only when all its inputs are low (0). If any input is high (1), the output will be low (0).
What is the hexadecimal equivalent of binary 101010101010?
A A
B B
C C
D D
In hexadecimal, the binary 101010101010 is equal to AAA, as the decimal value of 101010101010 is 10.
Which Boolean expression simplifies to A⋅(A′+B)?
A AB+A′B
B AB
C A+B
D AB+A′
Using Boolean algebra rules, A⋅(A′+B)=AB, as A⋅A′ is 0.
What is the binary equivalent of decimal 20?
A 10100
B 10010
C 11000
D 11100
Decimal 20 in binary is 10100, calculated as 24+2.
What is the primary function of an encoder?
A To decode binary information
B To amplify input signals
C To convert multiple inputs into a coded binary output
D To generate clock signals
An encoder takes multiple active inputs and generates a coded binary output representing the active input.
How many bits are required to represent the decimal number 31 in binary?
A 4
B 5
C 6
D 7
Decimal 31 in binary is 11111, which requires 5 bits.
What is the output of a 4-to-16 decoder?
A 4 outputs
B 8 outputs
C 16 outputs
D 32 outputs
A 4-to-16 decoder takes 4 inputs and provides 2⁴ = 16 outputs.
What is the purpose of a demultiplexer?
A To combine multiple inputs into one output
B To divide one input into multiple outputs
C To amplify signals
D To perform binary addition
A demultiplexer takes a single input signal and directs it to one of several outputs based on control signals.
Which flip-flop is known as a “data latch”?
A SR Flip-Flop
B JK Flip-Flop
C D Flip-Flop
D T Flip-Flop
The D flip-flop stores and transfers data from the input to the output on a clock edge, hence it is also called a “data latch.”
Which sequential circuit generates a binary sequence based on clock pulses?
A Counter
B Register
C Multiplexer
D Demultiplexer
A counter generates a binary sequence by counting clock pulses, either incrementally or decrementally.
What is the propagation delay in a logic gate?
A Time taken for the signal to reach its destination
B Time taken for the output to change after an input change
C Time required to reset a flip-flop
D Time required for a counter to overflow
Propagation delay is the time a logic gate takes to produce a change in output after the input changes.
How many inputs does a half-adder have?
A 1
B 2
C 3
D 4
A half-adder adds two single-bit binary numbers and produces a sum and carry output.
Which Boolean expression represents a NOR gate?
A (A+B)′
B A⋅B
C A+B
D (A⋅B)′
The NOR gate outputs the complement of an OR gate, represented as (A+B)′.
How many flip-flops are required to create a 3-bit shift register?
A 1
B 2
C 3
D 4
A shift register requires one flip-flop for each bit. For a 3-bit register, 3 flip-flops are required.
What is the primary function of an arithmetic logic unit (ALU)?
A Store data
B Perform arithmetic and logical operations
C Generate clock signals
D Decode binary inputs
An ALU performs basic arithmetic operations (addition, subtraction) and logical operations (AND, OR, NOT) in digital systems.
What is the binary addition result of 1101+1011?
A 11000
B 10110
C 10000
D 11111
Perform binary addition step by step: 1101+1011=11000.
Which circuit generates multiple clock signals with different frequencies?
A Counter
B Shift Register
C Clock Divider
D Flip-Flop
A clock divider takes an input clock signal and generates multiple signals with reduced frequencies.
What is the simplified form of AB+AB′?
A A
B B
C AB
D 1
By applying the Distributive Law, AB+AB′=A(B+B′). Since B+B′=1, the expression simplifies to A.
What is the role of a register in digital circuits?
A Perform logical operations
B Store multiple bits of data temporarily
C Decode binary inputs
D Divide clock signals
Registers are collections of flip-flops used to store multiple bits of data temporarily.
What is the output of an XNOR gate when both inputs are 0?
A 0
B 1
C Undefined
D Depends on inputs
An XNOR gate outputs 1 when both inputs are the same. Since both inputs are 0, the output is 1.
Which Boolean algebra law states A⋅1=A?
A Identity Law
B Null Law
C Distributive Law
D Commutative Law
The Identity Law states that multiplying a variable by 1 does not change its value: A⋅1=A.
What is the purpose of Karnaugh maps in digital design?
A To design sequential circuits
B To simplify Boolean expressions
C To perform arithmetic operations
D To generate clock signals
Karnaugh maps provide a visual method for minimizing Boolean expressions, reducing the number of gates required in a circuit.
What does the term “setup time” mean in sequential circuits?
A Time required to stabilize clock signals
B Time during which the input must remain stable before the clock edge
C Time required for propagation delay
D Time taken to reset the circuit
Setup time is the minimum time the input signal must be stable before a clock edge to ensure proper operation.
What is the binary equivalent of the decimal number 50?
A 101010
B 110010
C 110100
D 101100
The binary representation of 50 is calculated as 32+16+2=110010.
Which type of memory is non-volatile?
A RAM
B SRAM
C ROM
D DRAM
ROM (Read-Only Memory) retains its data even when the power supply is turned off, making it non-volatile.
What is the main purpose of clock signals in digital circuits?
A Amplify signals
B Control timing and synchronization of operations
C Perform arithmetic operations
D Store data
Clock signals provide a timing reference, ensuring that operations in sequential circuits occur at the correct time intervals.
Which Boolean expression is equivalent to A+AB?
A A
B AB
C A+B
D A′+B
Using the Absorption Law, A+AB=A.
What is propagation delay in digital circuits?
A Time required for a circuit to initialize
B Time for a signal to travel through a gate
C Time taken to reset a flip-flop
D Time to complete a clock cycle
Propagation delay is the time it takes for a change in input to cause a change in output in a logic gate.
What is the primary function of Random Access Memory (RAM)?
A Store data permanently
B Store data temporarily for fast access
C Perform logical operations
D Generate clock signals
RAM is a volatile memory used to temporarily store data and instructions that the CPU can access quickly.
Which Boolean algebra law states A+0=A?
A Identity Law
B Complement Law
C Associative Law
D Distributive Law
The Identity Law states that adding 0 to a variable does not change its value: A+0=A.