Lecture 1
Lecture 2
Lecture 3
Lecture 4
Lecture 5
Lecture 6
Lecture 7
Lecture 8
Lecture 9
Lecture 11
100
A logic circuit has a HIGH on one input and a LOW on the other, and the output is LOW. Name the circuit.
Answer: An AND gate.
Explanation: An AND gate produces a LOW output unless both inputs are HIGH. When one input is HIGH and the other is LOW, the result is LOW.
100
Convert the binary number 1101 to decimal.
Answer: 13
Explanation: To convert a binary number to decimal, multiply each bit by 2^n, where n is the position of the bit from right (starting at 0).
1101 = (1 x 2^3) + (1 x 2^2) + (0 x 2^1) + (1 x 2^0) = 8 + 4 +0 + 1 = 13
100
What is the output of a 2-input AND gate when one input is HIGH and the other is LOW?
Answer: LOW. An AND gate only produces a HIGH output when all of its inputs are HIGH.
Explanation: The AND gate outputs HIGH only when both inputs are HIGH. If one input is LOW, the result is always LOW due to the logic operation (A·B). This makes it a fundamental and straightforward concept.
100
This law of Boolean algebra states that A + 1 = 1
Answer: The Dominance Law or the Identity Law.
Explanation: According to Boolean algebra, A + 1 = 1 demonstrates the Dominance Law because adding 1 to any Boolean variable results in 1, as 1 dominates in the OR operation. This is one of the simplest and most fundamental laws.
100
This type of logic circuit combines AND gates, OR gates, and an inverter.
Answer: An AND-OR-Invert (AOI) circuit.
Explanation: AOI circuits are a combination of basic logic gates (AND, OR, and NOT) arranged to perform specific operations in digital logic. They are frequently used in combinational logic design.
100
What are the two outputs of a full adder?
Answer: Sum (Σ) and carry-out (Cout). A full adder takes three inputs: two bits to be added (A and B) and a carry-in (Cin) from a previous stage. It outputs the sum of the bits and a carry-out if the sum exceeds the maximum value representable by a single bit.
Explanation: Full adders are a fundamental concept in digital logic, often one of the first combinational logic circuits introduced in class. The ability to compute the sum and carry-out are central to performing binary addition in hardware.
100
What are the two stable states of a flip-flop?
Answer: SET (1) and RESET (0).
Explanation: Flip-flops are the fundamental building blocks of memory in digital systems. They store one bit of information and remain in one of two stable states (SET or RESET) until an input signal directs a change. This is an introductory concept and hence the easiest question.
100
This type of shift register loads all data bits simultaneously.
Answer: A parallel-in shift register.
Explanation: A parallel-in shift register allows all bits of data to be loaded at the same time, which is advantageous for fast data transfer. This concept is fundamental and straightforward, making it an ideal 100-point question.
100
What is the maximum count of a 4-bit binary counter?
Answer: 15 (decimal) or 1111 (binary).
- Explanation: A 4-bit binary counter can represent 2^4=16 distinct states, ranging from 0 to 15. The maximum count is therefore 15 in decimal or 1111 in binary.
- Difficulty: 100 points (Easy) – This is a basic fact about binary counters.
100
This type of memory is volatile, meaning it loses its contents when power is removed.
Answer: RAM (Random Access Memory). RAM is commonly used as the main memory in computer systems due to its fast read and write speeds. However, it requires a constant power supply to maintain its stored data.
Explanation: RAM's volatility means it loses data without power, making this the easiest question based on fundamental memory knowledge.
200
Name two advantages of digital data compared to analog data.
Answer: Immunity to noise and data can be easily stored.
Explanation: Digital data is less affected by noise because it operates with discrete levels (e.g., 0 and 1). Additionally, digital data can be efficiently stored and retrieved using digital storage devices.
200
Determine the 2's complement of the binary number 1010.
Answer: 0110
Explanation:
To find the 2's complement:
- Invert all the bits of 1010 → 0101.
- Add 1 to the result:
- 0101 + 1 = 0110
200
This gate produces a HIGH output only when all of its inputs are LOW.
Answer: A NOR gate.
Explanation: The NOR gate is the inverse of an OR gate. It produces a HIGH output only when all inputs are LOW because it is equivalent to the NOT operation on the OR function (¬(A + B)).
200
Simplify the Boolean expression A + AB
Answer: A. Applying the distributive law, the expression becomes A(1+B). Since 1 + B equals 1, the expression simplifies to A * 1, which equals A.
Explanation: This question requires applying the distributive law to recognize that 1 + B will always be true, leading to the simplification.
200
This Boolean algebra theorem allows us to express an AND function using only OR gates and inverters.
Answer: What is DeMorgan's Theorem?
Explanation: This question emphasizes a key concept in combinational logic design: the ability to express one type of logic gate function in terms of other gate types. While the sources don't explicitly mention DeMorgan's Theorem, it is a fundamental principle that underpins many of the techniques covered in Lecture 5. It is directly relevant to the problems that ask to implement logic expressions using different combinations of gates (AND, OR, NAND, NOR). DeMorgan's Theorem provides a way to convert between AND and OR functions by using inverters, which is essential for understanding how different logic gates can be used interchangeably to create equivalent circuits.
200
This type of adder uses the concept of carry look-ahead to speed up the addition process.
Answer:A look-ahead carry adder. This type of adder reduces the delay associated with ripple-carry adders by calculating carry bits in parallel, speeding up the addition process, especially for larger numbers of bits.
Explanation: The carry look-ahead adder is an optimized adder design that tackles the limitations of ripple-carry adders by eliminating the dependency on sequential carry propagation. This makes it faster for adding numbers with many bits, a critical improvement in computer processors.
200
What is the key difference between a latch and a flip-flop?
Answer: A latch is level-triggered, meaning its output changes in response to the level (HIGH or LOW) of the input signal. A flip-flop is edge-triggered, meaning its output changes only on the rising or falling edge of a clock signal.
Explanation: Understanding the distinction between a latch and a flip-flop is a foundational concept in digital logic. Latches are used for asynchronous systems, while flip-flops are used in synchronous systems, making this question slightly more complex.
200
This type of shift register can shift data in both directions.
Answer: A bidirectional shift register.
Explanation: Bidirectional shift registers can move data left or right depending on control inputs, offering flexibility for data manipulation. This is slightly more complex than the previous question but still relatively easy.
200
This type of counter experiences a cumulative delay as each flip-flop triggers the next one in sequence.
Answer: An asynchronous counter (also known as a ripple counter).
- Explanation: In asynchronous counters, the clock signal triggers the first flip-flop. Each subsequent flip-flop is triggered by the output of the preceding one. This chaining effect introduces a delay that accumulates through the stages, which can cause timing problems in high-speed applications.
200
What is the purpose of the address bus in a memory system?
Answer: The address bus carries the memory address to be accessed. This allows the CPU or other devices to specify the location in memory where data is to be read from or written to.
Explanation: The address bus is a key concept in understanding memory system communication, making this slightly more complex but still straightforward.
300
This is the frequency of a waveform with a period of 10 milliseconds.
Answer: 100 Hz. The frequency is the inverse of the period (1/period).
Frequency is calculated as f = 1/T, where T is the period in seconds. For T = 10 ms=0.01 s, the frequency is f = 1/0.01 = 100 Hz.
300
What is the hexadecimal equivalent of the binary number 11111010
Answer: FA
Explanation: Group the binary number into 4-bit segments from right to left: 1111 and 1010.
Convert each group to hexadecimal:
- 1111 = F
- 1010 = A
- Thus, 11111010 in hexadecimal is FA.
300
What is the only input combination that produces a HIGH output from an Exclusive-NOR gate?
Answer: When all inputs are the same logic level.
Explanation: The XNOR gate outputs HIGH when its inputs are either all HIGH or all LOW. This is due to its behavior as the complement of the XOR gate, which outputs HIGH only when inputs differ.
300
Apply DeMorgan's theorem to the following expression: (AB)′
Answer: A′+B′.
Explanation: DeMorgan's theorem states that the complement of a product is equal to the sum of the complements. Thus, (AB)' = A′+B′. This is a straightforward application of one of DeMorgan's laws.
300
What is the purpose of a decoder?
Answer: A decoder is a circuit that converts a coded input into a decoded output. It activates one specific output line corresponding to the input code.
Explanation: Decoders are essential components in digital systems for interpreting binary inputs and selecting one of many output lines. Common applications include address decoding in memory systems.
300
What is the purpose of a comparator?
Answer: A comparator compares two binary numbers and indicates their relationship, such as whether they are equal (A=B), A is greater than B (A>B), or A is less than B (A<B).
Explanation: Comparators are important for decision-making in digital systems, as they enable circuits to branch or trigger specific actions based on relative magnitudes or equality of binary numbers. They are widely used in control systems and digital arithmetic.
300
This type of flip-flop changes its output state only on the rising or falling edge of a clock pulse.
Answer: An edge-triggered flip-flop.
Explanation: Edge-triggering allows flip-flops to be more predictable and stable, as state changes occur only on clock edges. This is a critical property for synchronous digital systems, making this a medium-difficulty question.
300
What is the most common application for a Johnson counter?
Answer: Generation of a specific sequence of states or timing signals.
Explanation: Johnson counters are used for generating timing signals or specific sequences, making them a key component in sequential logic design. The added complexity of understanding its unique operation elevates this to a medium-difficulty question.
300
This type of counter is capable of counting both up and down.
Answer: An up/down counter.
- Explanation: Up/down counters have a control input to determine the counting direction. They are used in applications such as motor control or frequency synthesis, where bidirectional counting is necessary.
300
What is the capacity of a DRAM that has 14 address lines?
Answer: 16,384 bits. The capacity of a DRAM is determined by 2^(number of address lines). Therefore, a DRAM with 14 address lines has a capacity of 2^14=16,3842 bits.
Explanation: Calculating DRAM capacity requires a basic understanding of powers of two, making this moderately challenging.
400
A pulse waveform with a frequency of 2 kHz is applied to the input of a counter. During 50 ms, how many pulses are counted?
Answer: 100 pulses. The number of pulses is the product of the frequency and the duration (2 kHz * 50 ms = 100 pulses).
Explanation: The total number of pulses is given by Frequency x Time. For a 2 kHz frequency and a time of 50 ms (0.05 s), the total pulses are 2,000 x 0.05 = 100.
400
Add the binary numbers 1011 and 1101.
Answer: 11000
Explanation:
Perform binary addition: 1011 + 1101 = 11000
- Start from the rightmost bit: 1+1=10 (write 0, carry 1).
- Continue for the remaining bits, propagating the carry: 1+0+1=10, 0 + 1 = 1, and 1 + 1 = 10.
- The result is 11000
400
This type of logic gate is functionally equivalent to a Negative-OR gate.
Answer: A NAND gate.
Explanation: A NAND gate performs the AND operation followed by a negation. However, when reconfigured using De Morgan’s Theorems, a NAND gate can be shown to be equivalent to a Negative-OR gate.
400
Convert the expression A(B+C) to its sum-of-products (SOP) form.
Answer: AB+AC.
Explanation: The sum-of-products (SOP) form requires distributing A over B+C, resulting in AB+AC. This ensures the expression is written as a sum (OR operation) of products (AND operations).
400
What is the difference between a multiplexer and a demultiplexer?
Answer: A multiplexer (MUX) selects one of several input signals and routes it to a single output line, acting like a digital switch. A demultiplexer (DEMUX) performs the reverse operation, routing a single input signal to one of several output lines based on select inputs, acting as a data distributor.
Explanation: This question focuses on distinguishing two closely related digital devices based on their operation and purpose in circuits.
400
This digital circuit converts a binary code into a corresponding decimal output, often used to activate a specific output line or device.
Answer: A decoder. A decoder activates one specific output line for each unique combination of input bits, making it useful for selecting memory locations, activating devices based on input codes, and converting between different code formats.
Explanation: Decoders are critical for translating encoded data into actionable outputs. For example, in memory access, they select which memory location to read or write based on an address.
400
This type of flip-flop acts as a basic memory element, holding the data present on its input at the moment a clock pulse occurs.
Answer: A D flip-flop (data flip-flop).
Explanation: The D flip-flop synchronously captures and holds data based on the clock pulse. It's commonly used in registers, counters, and other sequential circuits. Identifying the D flip-flop's functionality requires a solid understanding of flip-flop types, making this moderately challenging.
400
A serial-in/serial-out shift register has the data input sequence 1011 applied to it. What is the state of the register after four clock pulses, assuming it was initially cleared?
Answer: 1011.
Explanation: In a serial-in/serial-out shift register, each clock pulse shifts the data one position to the right. After four clock pulses, the input sequence (1011) is fully loaded. This requires understanding timing and sequential operation, making it slightly harder.
400
What is the primary advantage of a synchronous counter compared to an asynchronous counter?
Answer: Synchronous counters have improved speed and reliability.
- Explanation: In synchronous counters, all flip-flops are triggered by the same clock signal simultaneously, eliminating the cumulative delay present in asynchronous counters. This results in faster and more predictable performance, especially for high-speed systems or with multiple flip-flops.
400
Explain the difference between SRAM and DRAM.
Answer: SRAM (Static RAM) uses latches to store data and retains its contents as long as power is applied. DRAM (Dynamic RAM) uses capacitors to store data and requires periodic refreshing to prevent data loss due to charge leakage. SRAM is typically faster and more expensive than DRAM.
Explanation: Differentiating between SRAM and DRAM involves technical knowledge of how memory works, making it more advanced.
500
This acronym describes a type of programmable logic device.
Answer: PAL, GAL, SPLD, CPLD, AHDL, and FPGA.
Explanation: Programmable Logic Devices (PLDs) are hardware components that can be configured to perform specific logic functions. Examples include Programmable Array Logic (PAL), Generic Array Logic (GAL), Simple PLDs (SPLD), Complex PLDs (CPLD), and Field Programmable Gate Arrays (FPGA). AHDL refers to the hardware description language used to program some of these devices.
500
Express the decimal number -25 in 8-bit 2's complement form.
Answer: 11100111
Explanation:
To represent a negative number in 2's complement:
- Convert the absolute value of the number (25) to binary: 25 = 00011001 in 8 bits.
- Invert all the bits: 00011001 --> 11100110.
- Add 1 to the result: 11100110 + 1 = 11100111
- Thus, the 8-bit 2's complement representation of -25 is 11100111
500
This is the Boolean expression for a 3-input OR gate.
Answer: X = A + B + C.
Explanation: The Boolean expression represents the OR operation for three inputs. It is harder because it introduces multiple inputs and requires understanding the addition operation in Boolean algebra to combine them logically.
500
What should the logic circuit look like for the Boolean expression AB + C?
Answer: The circuit will have one AND gate and one OR gate. The inputs to the AND gate will be A and B. The output of the AND gate will connect to one input of the OR gate, and the other input of the OR gate will connect directly to C. The output of the OR gate represents the final output of the circuit.
Explanation: This circuit implements the logical operation AB+C. The AND gate performs the operation AB, and the OR gate combines the output of AB with C, ensuring the final output is HIGH if either AAA and BBB are both HIGH, or if C is HIGH.
500
Given the truth table below, construct a simplified boolean expression implement the output X.
X = A̅B + AB
500
A circuit has an 8-to-1 multiplexer. How many select lines are required to control which input is selected?
Answer: Three select lines. In general, a multiplexer with 2^n inputs requires n select lines. Since 8 is 2^3, three select lines are needed.
Explanation: Multiplexers are crucial for data routing, and understanding the relationship between the number of inputs and select lines is essential for designing and using them effectively in larger systems. This concept requires deeper understanding of powers of two, making it slightly more challenging.
500
A 74121 one-shot has an external resistor of 10 kΩ and an external capacitor of 1000 pF. What is the approximate pulse width it generates?
Answer: Approximately 7 μs.
The pulse width tW of a 74121 one-shot is estimated using the formula tw = 0.7 x R(ext) x C(ext). Substituting R(ext) = 10,000Ω and C(ext) = 1000 pF, tW = 0.7 x 10,000 x 1000 x 10^-12 = 7 x 10 ^-6 seconds or 7 μs.
500
What is the difference between a ring counter and a Johnson counter?
Answer: A ring counter circulates a single 1 through its stages, creating a sequence where only one output is HIGH at a time. A Johnson counter generates a more complex sequence by connecting the complement of the last flip-flop's output to the first flip-flop's input. This results in a modulus that is double the number of flip-flops and a sequence that includes both 1s and 0s.
Explanation: This question requires understanding the detailed operation of both ring and Johnson counters, as well as their practical differences. The advanced knowledge required makes it the hardest question in the set.
500
A counter is designed to have a modulus of 12. How many flip-flops are required to implement this counter?
Answer: Four flip-flops.
- Explanation: To achieve a modulus of 12, the counter must cycle through 12 unique states. Since 2^4=16, four flip-flops can represent up to 16 states, which is sufficient for the modulus of 12. Any fewer flip-flops (e.g., three) would only allow for 2^3=8 states, which is inadequate.
500
Give two reasons why ROM is used instead of RAM for certain applications.
Answer: What is non-volatility and data security?
Explanation:
● Non-volatility: ROM retains its data even when power is turned off. This makes it ideal for storing information that needs to persist even when the device is not powered, such as firmware or boot instructions.
● Data Security: The read-only nature of ROM makes it inherently secure against accidental or malicious writes. This is beneficial for applications where data integrity is paramount, as the data cannot be easily overwritten or corrupted.