Q: A simple, physical demonstration of multiplexing (selecting 1 of N inputs to a single output) can be modeled most clearly using which manual hardware control?

Introduction / Context: A multiplexer (MUX) routes one of several inputs to a single output line based on select signals. Demonstrating this concept with tangible hardware helps beginners grasp the selection mechanism before moving to ICs and HDL descriptions. Given Data / Assumptions: Goal: manually emulate choosing 1 of N inputs to one output. No need for simultaneous multi-path routing (just one path at a time). Emphasis on intuitive, physical analogy. Concept / Approach: A single-pole, multi-throw rotary switch has one common wiper (the output) and multiple selectable throws (inputs). Rotating the knob selects exactly one input to connect to the output—precisely the behavior of a 1-of-N MUX. DPDT switches route two poles simultaneously and are not a clean 1-of-N model; relays and steppers do not directly illustrate MUX selection. Step-by-Step Solution: 1) Identify MUX behavior: one output, many candidate inputs.2) Map to hardware: the rotary switch wiper corresponds to the MUX output; each throw is an input.3) Selection action: rotating selects one throw at a time, like asserting select lines.4) Therefore, a rotary switch best demonstrates basic multiplexing. Verification / Alternative check: Electronics labs often use rotary selectors to choose among channels, identical in concept to a 1-of-N selector implemented in silicon. Why Other Options Are Wrong: Single-pole relay: on/off control, not 1-of-N selection. DPDT: switches two lines simultaneously, not arbitrary N-way selection. Linear stepper/potentiometer: not discrete 1-of-N routing devices. Common Pitfalls: Confusing multi-throw selection with multi-pole switching. A MUX is about choosing exactly one input path to the output. Final Answer: rotary switch (single-pole, multi-throw)

Q: Which statement best describes the parity method of error detection used in digital communication links?

Introduction / Context: Parity is a classic, low-overhead error-detection technique. Systems append one parity bit to a data word to enforce an overall even or odd count of 1s. Understanding what parity can and cannot detect is essential for selecting appropriate integrity checks. Given Data / Assumptions: We consider single parity (even or odd), not more advanced codes. Transmission errors are modeled as bit flips. Goal is detection, not correction. Concept / Approach: With even parity, the transmitter sets the parity bit so the total number of 1s is even. The receiver recomputes parity; a mismatch indicates an error. Single-bit errors flip parity from even to odd (or vice versa) and are always detected. However, two-bit errors restore the original parity and therefore evade detection. Parity does not provide error correction; it only flags potential corruption. Step-by-Step Solution: 1) Define parity rule (even or odd) across data + parity bit.2) Transmit data; compute parity at receiver.3) If exactly one bit flips, parity mismatches → error detected.4) If two bits flip, parity may match → error not detected. Verification / Alternative check: Truth tables show that parity detects all odd-numbered bit errors and misses even-numbered bit errors. Therefore, it is best for single-bit error detection but not double-bit detection. Why Other Options Are Wrong: (b) Double-bit errors are not reliably detected. (c) False; parity excels at single-bit detection. (d) Parity does not correct errors; codes like Hamming are needed for correction. (e) It does not correct automatically; it only detects odd-error counts. Common Pitfalls: Overestimating parity's power. For stronger guarantees, use CRCs or ECC like Hamming, BCH, or Reed–Solomon. Final Answer: Parity checking is best suited for detecting single-bit errors in transmitted codes.

Q: Which digital subsystem converts coded input characters (for example, BCD or 7-bit ASCII) into a human-readable or device-usable form such as segment drives or control lines?

Introduction / Context: Code translation is pervasive in digital electronics. Systems often produce compact coded representations (e.g., BCD, Gray, ASCII) that must be translated into a format understood by displays or actuators. Knowing which block performs this conversion is foundational. Given Data / Assumptions: Input is a coded representation of information. Output should be a more intelligible form (e.g., seven-segment lines, control signals, or readable symbols). Focus on functional role, not a specific IC part number. Concept / Approach: A decoder maps coded inputs to a set of outputs representing the decoded meaning. Examples include BCD-to-7-segment decoders that translate a 4-bit BCD value into seven segment drive lines, or address decoders that convert binary addresses into one-hot select lines for memory chips. Encoders perform the opposite transformation, compressing many inputs into a code. Step-by-Step Solution: 1) Identify data form: coded inputs.2) Determine desired output: human-readable or device-specific drive signals.3) Functional mapping: decoder expands or translates code to meaningful outputs.4) Conclude that the correct subsystem is a decoder. Verification / Alternative check: Common ICs like BCD-to-7-seg decoders (e.g., classic parts) exemplify this function, turning numeric codes into display segments that humans can read. Why Other Options Are Wrong: Encoder: opposite function (many inputs to fewer coded outputs). Display: a sink device; it does not perform the translation. Counter: produces sequences; no code translation implied. Latch: stores state; does not translate codes. Common Pitfalls: Assuming displays inherently decode; they only render signals they receive. The decoder must drive them correctly. Final Answer: decoder

Q: In instrumentation and embedded systems, what does it mean when a numeric or alphanumeric display is “multiplexed,” and which description best matches that behavior?

Introduction / Context: Multiplexed displays reduce pin count and wiring by sharing segment or digit lines among multiple characters. Microcontrollers rapidly scan or time-share the drive signals so that, due to persistence of vision, users perceive a steady readout. Given Data / Assumptions: Multiple digits or symbols share common segment lines. A controller activates one digit at a time at a high refresh rate. Human vision integrates the rapid updates. Concept / Approach: In multiplexing, the controller presents the appropriate segment pattern for one digit, enables that digit momentarily, then moves to the next, repeating quickly. The effect is a continuous multi-digit display with fewer physical connections than a fully parallel (non-multiplexed) solution, lowering cost and easing routing. Step-by-Step Solution: 1) Partition the display into digits sharing segment lines.2) For each refresh slice, output the segment pattern for one digit and enable its common line.3) Cycle through all digits at, for example, hundreds of hertz.4) Net effect: a single display assembly presents multiple values or digits via time-sharing. Verification / Alternative check: Measure segment currents with an oscilloscope: each digit sees pulsed drive while the average brightness remains steady if refresh is fast enough. Why Other Options Are Wrong: (a) Describes a demultiplexer, not a multiplexed display. (c) Generic switching statement; not about time-shared display driving. (d) Arbitrary BCD limitation; multiplexing is not confined to four BCD lines. (e) Opposite of multiplexing; dedicated continuous drive is non-multiplexed. Common Pitfalls: Driving digits too slowly causes flicker; driving too fast may reduce brightness due to duty cycle. Proper current and timing are essential. Final Answer: uses one display to present two or more pieces of information (time-shared driving of digits/segments)

Q: Regarding demultiplexers (DeMUX) in digital electronics, which statement best describes their typical data-routing function?

Introduction / Context: A demultiplexer (DeMUX) is the conceptual inverse of a multiplexer. Whereas a MUX funnels multiple inputs to a single output, a DeMUX takes a single input and routes it to one of many outputs based on select lines. Mastering this relationship is foundational for data distribution, memory addressing, and bus steering. Given Data / Assumptions: One data input line. Multiple output lines. Log2(N) select lines determine which output is active. Concept / Approach: A DeMUX implements controlled data distribution: data_in appears at exactly one of the N outputs at a time. This makes it ideal for tasks like writing to one of many registers or enabling one device on a shared line. In practice, address decoders used for memory chip selection behave as demultiplexers that assert a single chip-enable line among many. Step-by-Step Solution: Let input be D and outputs Y0..Y7 with selects S2..S0.When S=101, the DeMUX drives Y5 with D; all other Yk are inactive.Changing S redirects the same single input to a different output line as needed.Thus, the function is single input routed to one of many outputs. Verification / Alternative check: Truth tables of 1-to-4 or 1-to-8 DeMUX ICs confirm that exactly one output follows the input for any select code, validating the description. Why Other Options Are Wrong: Decimal to hexadecimal / parity conversions: These are code conversions performed by encoders/decoders, not DeMUX routing. AC to DC: Power conversion, not a logic routing function. Parallel-to-parallel conversion: May be achieved by decoders/ROMs, not the core DeMUX behavior. Common Pitfalls: Assuming multiple outputs are driven simultaneously; a DeMUX selects exactly one (unless specifically designed for multiple enables). Confusing enable polarity and output active levels (active-high vs active-low). Final Answer: single input, multiple outputs

Q: Which decoder type selects exactly one of sixteen output lines as active, based solely on the binary value of a 4-bit input word?

Introduction / Context: Decoders translate binary codes into one-hot outputs. A classic example is using a 4-bit input to activate one of sixteen lines, a building block for address decoding and device selection in digital systems. This is often referred to as a 4-to-16 or binary-to-hexadecimal decoder because sixteen distinct outputs correspond to the sixteen hexadecimal symbols (0–F). Given Data / Assumptions: Input width = 4 bits. Output count = 16 lines. Exactly one output should be asserted for each input pattern. Concept / Approach: A 4-to-16 decoder maps the 4-bit input to a one-hot 16-bit output. For input N (0..15), only YN is active. This functionality is commonly used for memory address line decoding, selecting registers, or enabling peripherals where only one device should respond to a given code. Step-by-Step Solution: Let input be A3..A0 and outputs Y0..Y15.For input 0101 (decimal 5), assert Y5; all others deasserted.Repeat for all 16 combinations to cover 0x0 through 0xF.Thus, a binary-to-hexadecimal (4-to-16) decoder is required. Verification / Alternative check: Commercial parts like the 74HC154 provide 4-to-16 decoding with active-low outputs and enable pins, matching the described behavior and confirming the mapping from 4-bit binary to sixteen one-hot outputs. Why Other Options Are Wrong: Hexadecimal (alone): Not a functional description. Dual octal outputs: Suggests two 3-to-8 decoders, not one 4-to-16. Hexadecimal-to-binary: The opposite direction of decoding. 4-to-8 with enable: Only eight outputs, not sixteen. Common Pitfalls: Overlooking active-low output conventions that invert logic levels. Forgetting enable pins must be set correctly for decoding to operate. Final Answer: binary-to-hexadecimal

Q: A digital circuit that observes an applied coded input pattern and asserts exactly one related output line (often one-hot) is best described as which device?

Introduction / Context: In digital logic, encoders and decoders perform opposite roles. A decoder observes a compact binary input and activates a corresponding output line, commonly as a one-hot signal. Recognizing this behavior is essential in address decoding, chip select schemes, and display selection. Given Data / Assumptions: The input is a coded binary value. Only one output line should be active for any valid input. Outputs may be active-high or active-low depending on implementation. Concept / Approach: A decoder translates an n-bit input into 2^n mutually exclusive outputs. For example, a 3-to-8 decoder maps 3 input bits to one of 8 outputs. Display drivers often include decoding logic internally, but the generic device that directly performs code-to-line activation is a decoder. Step-by-Step Solution: Let the input be A..D representing a binary number N.The decoder asserts output YN corresponding to N; all other Yk remain inactive.Thus the circuit responds to a specific input code and produces a related digital output line.Hence, the correct identification is a decoder. Verification / Alternative check: Datasheets for 74HC138 (3-to-8) and 74HC154 (4-to-16) demonstrate one-hot activation controlled by enables and inputs, validating the functional definition. Why Other Options Are Wrong: BCD matrix: Not a standard logic device category. Display driver: A broader class; may include decoding but is not the generic name. Encoder: Performs the inverse mapping (many inputs to compact binary output). Priority multiplexer: Not a standard term; multiplexers select one of many inputs to one output. Common Pitfalls: Confusing decoders with demultiplexers; a DeMUX routes signals, while a decoder generates one-hot control signals from codes. Ignoring enable pins that gate the decoder outputs. Final Answer: decoder

Q: For a 1-of-10 BCD (binary-coded decimal) decoder that selects one decimal output line (0–9), how many binary input lines are required?

Introduction / Context: BCD represents decimal digits 0–9 using 4-bit binary words. A 1-of-10 BCD decoder asserts exactly one of ten outputs according to the BCD input. Determining the number of input lines helps with pin budgeting and logic design for display and selection circuits. Given Data / Assumptions: Digits 0 through 9 are encoded in BCD. Each BCD digit requires four bits (0000 to 1001). Six combinations (1010 to 1111) are invalid and typically blanked or treated as don’t-care. Concept / Approach: Since BCD uses 4 bits per digit, the decoder must accept four input lines in order to uniquely represent the ten valid decimal values. The decoder then activates one corresponding output line among ten, often with additional blanking or error handling for invalid codes. Step-by-Step Solution: Recognize BCD width: 4 bits.Map valid codes: 0000..1001 → outputs 0..9.Provide four input pins to convey these bit values.Hence, the required inputs = 4. Verification / Alternative check: Standard ICs such as the 7442/74LS42 (BCD-to-decimal decoder) accept four inputs and produce ten active-low outputs, confirming the four-input requirement. Why Other Options Are Wrong: 8 or 10 inputs: Unnecessary for encoding a single decimal digit. 1 input: Insufficient to represent ten possibilities. 5 inputs: Would represent up to 32 values, exceeding BCD needs. Common Pitfalls: Treating invalid BCD inputs as valid; proper designs blank displays or signal error on 1010..1111. Confusing BCD with straight binary for 0–15 which would be a 4-to-16 decoder. Final Answer: 4

Q: In encoder design, when two or more inputs become active at the same time, what is the process used to determine which input takes precedence?

Introduction / Context: Encoders convert many input lines into a compact binary representation. In real systems, more than one input may assert simultaneously (e.g., multiple keys pressed). Priority handling is crucial to ensure deterministic output without ambiguity, which is why priority encoders are a standard logic block. Given Data / Assumptions: Multiple input lines may be active concurrently. The encoder must output one binary code. A defined precedence rule is required. Concept / Approach: A priority encoder assigns an ordering to inputs (e.g., highest-numbered input wins). When several inputs are asserted, the encoder outputs the code corresponding to the highest-priority input and may provide a valid/enable flag. This avoids metastability or ambiguous codes that a simple encoder might produce. Step-by-Step Solution: Define priority: I7 > I6 > ... > I0.If I3 and I6 are high, encoder outputs the code for I6.Output may include a group signal (GS) or enable output (EO) to cascade devices.Thus, the correct process is priority encoding. Verification / Alternative check: ICs such as 74HC148 (8-to-3 priority encoder) implement specified priority rules and demonstrate predictable outputs in multi-assert conditions. Why Other Options Are Wrong: FIFO: A buffering/queuing concept, not instantaneous priority resolution. Ripple blanking: Used in display chains to suppress leading zeros, unrelated to encoders. Priority decoding: Not the conventional term; decoding is the inverse function. TDM: A multiplexing method over time, not a logic priority scheme. Common Pitfalls: Using a simple encoder where a priority encoder is required can lead to undefined outputs. Forgetting to handle the no-input-active case with a valid flag or default code. Final Answer: priority encoding

Question 1

A digital magnitude comparator examines two binary numbers A and B. Which set of outcomes does it determine for any given comparison?

Accepted Answer

Introduction / Context: Magnitude comparators are fundamental building blocks in ALUs, sorting networks, and decision logic. They compare two binary numbers and report relational results that drive control paths or select signals in digital systems. Given Data / Assumptions: Binary operands A and B, of equal width. Comparator outputs indicate equality and ordering. No arithmetic overflow or signed interpretation issues (assume unsigned unless specified). Concept / Approach: A standard magnitude comparator outputs three mutually exclusive signals: AB. These cover all possible orderings. Equality enables exact match detection, while greater-than or less-than flags inform selection and branching. Step-by-Step Solution: 1) Evaluate bitwise from MSB to LSB; the first differing bit determines ordering.2) If all bits match, assert equality (A = B).3) If a higher-order bit in A is 1 while B is 0 at the first difference, A > B; the opposite implies A < B.4) Report exactly one of the three outcomes at a time. Verification / Alternative check: Truth tables for 1-bit comparators expand to n-bit comparators by cascading. Commercial devices (e.g., 74xx85 family) provide AB outputs. Why Other Options Are Wrong: Options with symbols like ≈ or » are not standard comparator outcomes. Options omitting equality or one ordering are incomplete. Using ≥ alone is insufficient; comparators typically give the full ternary result set. Common Pitfalls: Confusing signed and unsigned comparisons; sign handling requires different logic. Also, ensure width matching or include cascading inputs for multi-word comparisons. Final Answer: A = B and whether A > B or A < B

Question 2

A simple, physical demonstration of multiplexing (selecting 1 of N inputs to a single output) can be modeled most clearly using which manual hardware control?

Accepted Answer

Introduction / Context: A multiplexer (MUX) routes one of several inputs to a single output line based on select signals. Demonstrating this concept with tangible hardware helps beginners grasp the selection mechanism before moving to ICs and HDL descriptions. Given Data / Assumptions: Goal: manually emulate choosing 1 of N inputs to one output. No need for simultaneous multi-path routing (just one path at a time). Emphasis on intuitive, physical analogy. Concept / Approach: A single-pole, multi-throw rotary switch has one common wiper (the output) and multiple selectable throws (inputs). Rotating the knob selects exactly one input to connect to the output—precisely the behavior of a 1-of-N MUX. DPDT switches route two poles simultaneously and are not a clean 1-of-N model; relays and steppers do not directly illustrate MUX selection. Step-by-Step Solution: 1) Identify MUX behavior: one output, many candidate inputs.2) Map to hardware: the rotary switch wiper corresponds to the MUX output; each throw is an input.3) Selection action: rotating selects one throw at a time, like asserting select lines.4) Therefore, a rotary switch best demonstrates basic multiplexing. Verification / Alternative check: Electronics labs often use rotary selectors to choose among channels, identical in concept to a 1-of-N selector implemented in silicon. Why Other Options Are Wrong: Single-pole relay: on/off control, not 1-of-N selection. DPDT: switches two lines simultaneously, not arbitrary N-way selection. Linear stepper/potentiometer: not discrete 1-of-N routing devices. Common Pitfalls: Confusing multi-throw selection with multi-pole switching. A MUX is about choosing exactly one input path to the output. Final Answer: rotary switch (single-pole, multi-throw)

Question 3

Which statement best describes the parity method of error detection used in digital communication links?

Accepted Answer

Introduction / Context: Parity is a classic, low-overhead error-detection technique. Systems append one parity bit to a data word to enforce an overall even or odd count of 1s. Understanding what parity can and cannot detect is essential for selecting appropriate integrity checks. Given Data / Assumptions: We consider single parity (even or odd), not more advanced codes. Transmission errors are modeled as bit flips. Goal is detection, not correction. Concept / Approach: With even parity, the transmitter sets the parity bit so the total number of 1s is even. The receiver recomputes parity; a mismatch indicates an error. Single-bit errors flip parity from even to odd (or vice versa) and are always detected. However, two-bit errors restore the original parity and therefore evade detection. Parity does not provide error correction; it only flags potential corruption. Step-by-Step Solution: 1) Define parity rule (even or odd) across data + parity bit.2) Transmit data; compute parity at receiver.3) If exactly one bit flips, parity mismatches → error detected.4) If two bits flip, parity may match → error not detected. Verification / Alternative check: Truth tables show that parity detects all odd-numbered bit errors and misses even-numbered bit errors. Therefore, it is best for single-bit error detection but not double-bit detection. Why Other Options Are Wrong: (b) Double-bit errors are not reliably detected. (c) False; parity excels at single-bit detection. (d) Parity does not correct errors; codes like Hamming are needed for correction. (e) It does not correct automatically; it only detects odd-error counts. Common Pitfalls: Overestimating parity's power. For stronger guarantees, use CRCs or ECC like Hamming, BCH, or Reed–Solomon. Final Answer: Parity checking is best suited for detecting single-bit errors in transmitted codes.

Question 4

Which digital subsystem converts coded input characters (for example, BCD or 7-bit ASCII) into a human-readable or device-usable form such as segment drives or control lines?

Accepted Answer

Introduction / Context: Code translation is pervasive in digital electronics. Systems often produce compact coded representations (e.g., BCD, Gray, ASCII) that must be translated into a format understood by displays or actuators. Knowing which block performs this conversion is foundational. Given Data / Assumptions: Input is a coded representation of information. Output should be a more intelligible form (e.g., seven-segment lines, control signals, or readable symbols). Focus on functional role, not a specific IC part number. Concept / Approach: A decoder maps coded inputs to a set of outputs representing the decoded meaning. Examples include BCD-to-7-segment decoders that translate a 4-bit BCD value into seven segment drive lines, or address decoders that convert binary addresses into one-hot select lines for memory chips. Encoders perform the opposite transformation, compressing many inputs into a code. Step-by-Step Solution: 1) Identify data form: coded inputs.2) Determine desired output: human-readable or device-specific drive signals.3) Functional mapping: decoder expands or translates code to meaningful outputs.4) Conclude that the correct subsystem is a decoder. Verification / Alternative check: Common ICs like BCD-to-7-seg decoders (e.g., classic parts) exemplify this function, turning numeric codes into display segments that humans can read. Why Other Options Are Wrong: Encoder: opposite function (many inputs to fewer coded outputs). Display: a sink device; it does not perform the translation. Counter: produces sequences; no code translation implied. Latch: stores state; does not translate codes. Common Pitfalls: Assuming displays inherently decode; they only render signals they receive. The decoder must drive them correctly. Final Answer: decoder

Question 5

In instrumentation and embedded systems, what does it mean when a numeric or alphanumeric display is “multiplexed,” and which description best matches that behavior?

Accepted Answer

Introduction / Context: Multiplexed displays reduce pin count and wiring by sharing segment or digit lines among multiple characters. Microcontrollers rapidly scan or time-share the drive signals so that, due to persistence of vision, users perceive a steady readout. Given Data / Assumptions: Multiple digits or symbols share common segment lines. A controller activates one digit at a time at a high refresh rate. Human vision integrates the rapid updates. Concept / Approach: In multiplexing, the controller presents the appropriate segment pattern for one digit, enables that digit momentarily, then moves to the next, repeating quickly. The effect is a continuous multi-digit display with fewer physical connections than a fully parallel (non-multiplexed) solution, lowering cost and easing routing. Step-by-Step Solution: 1) Partition the display into digits sharing segment lines.2) For each refresh slice, output the segment pattern for one digit and enable its common line.3) Cycle through all digits at, for example, hundreds of hertz.4) Net effect: a single display assembly presents multiple values or digits via time-sharing. Verification / Alternative check: Measure segment currents with an oscilloscope: each digit sees pulsed drive while the average brightness remains steady if refresh is fast enough. Why Other Options Are Wrong: (a) Describes a demultiplexer, not a multiplexed display. (c) Generic switching statement; not about time-shared display driving. (d) Arbitrary BCD limitation; multiplexing is not confined to four BCD lines. (e) Opposite of multiplexing; dedicated continuous drive is non-multiplexed. Common Pitfalls: Driving digits too slowly causes flicker; driving too fast may reduce brightness due to duty cycle. Proper current and timing are essential. Final Answer: uses one display to present two or more pieces of information (time-shared driving of digits/segments)

Question 6

In digital systems, one common application of a multiplexer (MUX) is to route multiple parallel data lines onto a single shared path. Which task does a digital multiplexer directly facilitate for data handling?

Accepted Answer

Introduction / Context: A digital multiplexer (MUX) is a combinational logic device that selects one of many inputs and forwards it to a single output line. This selection is controlled by binary select inputs. Understanding the core function of a MUX helps explain how parallel data can efficiently share a single channel, a pattern seen in communication buses and serializer stages. Given Data / Assumptions: There are N data inputs and one output. Log2(N) select lines choose which input reaches the output at any instant. Selection can be changed each clock or control interval. Concept / Approach: A multiplexer performs input selection. If we have several parallel bits or channels that need to traverse a single wire or path, a MUX can time-division-route each input sequentially to the output. Paired with a clocked control sequence, this creates a serial stream that represents the original parallel words, i.e., a parallel-to-serial conversion. A demultiplexer or serial-to-parallel register on the receiving end can reconstruct the parallel word. Step-by-Step Solution: Let inputs be D0..D7 and select lines S2..S0.At time t0, set S=000 so output Y=D0.At time t1, set S=001 so Y=D1; continue cycling through selects.Collecting Y over time yields a serial sequence [D0,D1,...,D7], implementing parallel-to-serial conversion. Verification / Alternative check: Standard serializer circuits use a MUX to step through bit positions under control of a counter or shift-register based state machine, confirming that a MUX implements the selection needed for serialization. Why Other Options Are Wrong: Code conversion: Typically done by dedicated encoders/decoders or ROMs, not a plain MUX alone. Parity checking: Uses XOR trees, not selection logic. Data generation: Requires counters/LFSRs, not just a selector. ECC: Needs specialized encoders/decoders beyond simple multiplexing. Common Pitfalls: Confusing a MUX with an encoder; an encoder reduces many active lines to a binary code, while a MUX passes one selected line. Forgetting the role of the clock/control to make the serialization deterministic and synchronous. Final Answer: parallel-to-serial data conversion

Question 7

Regarding demultiplexers (DeMUX) in digital electronics, which statement best describes their typical data-routing function?

Accepted Answer

Introduction / Context: A demultiplexer (DeMUX) is the conceptual inverse of a multiplexer. Whereas a MUX funnels multiple inputs to a single output, a DeMUX takes a single input and routes it to one of many outputs based on select lines. Mastering this relationship is foundational for data distribution, memory addressing, and bus steering. Given Data / Assumptions: One data input line. Multiple output lines. Log2(N) select lines determine which output is active. Concept / Approach: A DeMUX implements controlled data distribution: data_in appears at exactly one of the N outputs at a time. This makes it ideal for tasks like writing to one of many registers or enabling one device on a shared line. In practice, address decoders used for memory chip selection behave as demultiplexers that assert a single chip-enable line among many. Step-by-Step Solution: Let input be D and outputs Y0..Y7 with selects S2..S0.When S=101, the DeMUX drives Y5 with D; all other Yk are inactive.Changing S redirects the same single input to a different output line as needed.Thus, the function is single input routed to one of many outputs. Verification / Alternative check: Truth tables of 1-to-4 or 1-to-8 DeMUX ICs confirm that exactly one output follows the input for any select code, validating the description. Why Other Options Are Wrong: Decimal to hexadecimal / parity conversions: These are code conversions performed by encoders/decoders, not DeMUX routing. AC to DC: Power conversion, not a logic routing function. Parallel-to-parallel conversion: May be achieved by decoders/ROMs, not the core DeMUX behavior. Common Pitfalls: Assuming multiple outputs are driven simultaneously; a DeMUX selects exactly one (unless specifically designed for multiple enables). Confusing enable polarity and output active levels (active-high vs active-low). Final Answer: single input, multiple outputs

Question 8

Which decoder type selects exactly one of sixteen output lines as active, based solely on the binary value of a 4-bit input word?

Accepted Answer

Introduction / Context: Decoders translate binary codes into one-hot outputs. A classic example is using a 4-bit input to activate one of sixteen lines, a building block for address decoding and device selection in digital systems. This is often referred to as a 4-to-16 or binary-to-hexadecimal decoder because sixteen distinct outputs correspond to the sixteen hexadecimal symbols (0–F). Given Data / Assumptions: Input width = 4 bits. Output count = 16 lines. Exactly one output should be asserted for each input pattern. Concept / Approach: A 4-to-16 decoder maps the 4-bit input to a one-hot 16-bit output. For input N (0..15), only YN is active. This functionality is commonly used for memory address line decoding, selecting registers, or enabling peripherals where only one device should respond to a given code. Step-by-Step Solution: Let input be A3..A0 and outputs Y0..Y15.For input 0101 (decimal 5), assert Y5; all others deasserted.Repeat for all 16 combinations to cover 0x0 through 0xF.Thus, a binary-to-hexadecimal (4-to-16) decoder is required. Verification / Alternative check: Commercial parts like the 74HC154 provide 4-to-16 decoding with active-low outputs and enable pins, matching the described behavior and confirming the mapping from 4-bit binary to sixteen one-hot outputs. Why Other Options Are Wrong: Hexadecimal (alone): Not a functional description. Dual octal outputs: Suggests two 3-to-8 decoders, not one 4-to-16. Hexadecimal-to-binary: The opposite direction of decoding. 4-to-8 with enable: Only eight outputs, not sixteen. Common Pitfalls: Overlooking active-low output conventions that invert logic levels. Forgetting enable pins must be set correctly for decoding to operate. Final Answer: binary-to-hexadecimal

Question 9

A digital circuit that observes an applied coded input pattern and asserts exactly one related output line (often one-hot) is best described as which device?

Accepted Answer

Introduction / Context: In digital logic, encoders and decoders perform opposite roles. A decoder observes a compact binary input and activates a corresponding output line, commonly as a one-hot signal. Recognizing this behavior is essential in address decoding, chip select schemes, and display selection. Given Data / Assumptions: The input is a coded binary value. Only one output line should be active for any valid input. Outputs may be active-high or active-low depending on implementation. Concept / Approach: A decoder translates an n-bit input into 2^n mutually exclusive outputs. For example, a 3-to-8 decoder maps 3 input bits to one of 8 outputs. Display drivers often include decoding logic internally, but the generic device that directly performs code-to-line activation is a decoder. Step-by-Step Solution: Let the input be A..D representing a binary number N.The decoder asserts output YN corresponding to N; all other Yk remain inactive.Thus the circuit responds to a specific input code and produces a related digital output line.Hence, the correct identification is a decoder. Verification / Alternative check: Datasheets for 74HC138 (3-to-8) and 74HC154 (4-to-16) demonstrate one-hot activation controlled by enables and inputs, validating the functional definition. Why Other Options Are Wrong: BCD matrix: Not a standard logic device category. Display driver: A broader class; may include decoding but is not the generic name. Encoder: Performs the inverse mapping (many inputs to compact binary output). Priority multiplexer: Not a standard term; multiplexers select one of many inputs to one output. Common Pitfalls: Confusing decoders with demultiplexers; a DeMUX routes signals, while a decoder generates one-hot control signals from codes. Ignoring enable pins that gate the decoder outputs. Final Answer: decoder

Question 10

For a 1-of-10 BCD (binary-coded decimal) decoder that selects one decimal output line (0–9), how many binary input lines are required?

Accepted Answer

Introduction / Context: BCD represents decimal digits 0–9 using 4-bit binary words. A 1-of-10 BCD decoder asserts exactly one of ten outputs according to the BCD input. Determining the number of input lines helps with pin budgeting and logic design for display and selection circuits. Given Data / Assumptions: Digits 0 through 9 are encoded in BCD. Each BCD digit requires four bits (0000 to 1001). Six combinations (1010 to 1111) are invalid and typically blanked or treated as don’t-care. Concept / Approach: Since BCD uses 4 bits per digit, the decoder must accept four input lines in order to uniquely represent the ten valid decimal values. The decoder then activates one corresponding output line among ten, often with additional blanking or error handling for invalid codes. Step-by-Step Solution: Recognize BCD width: 4 bits.Map valid codes: 0000..1001 → outputs 0..9.Provide four input pins to convey these bit values.Hence, the required inputs = 4. Verification / Alternative check: Standard ICs such as the 7442/74LS42 (BCD-to-decimal decoder) accept four inputs and produce ten active-low outputs, confirming the four-input requirement. Why Other Options Are Wrong: 8 or 10 inputs: Unnecessary for encoding a single decimal digit. 1 input: Insufficient to represent ten possibilities. 5 inputs: Would represent up to 32 values, exceeding BCD needs. Common Pitfalls: Treating invalid BCD inputs as valid; proper designs blank displays or signal error on 1010..1111. Confusing BCD with straight binary for 0–15 which would be a 4-to-16 decoder. Final Answer: 4

Question 11

In encoder design, when two or more inputs become active at the same time, what is the process used to determine which input takes precedence?

Accepted Answer

Introduction / Context: Encoders convert many input lines into a compact binary representation. In real systems, more than one input may assert simultaneously (e.g., multiple keys pressed). Priority handling is crucial to ensure deterministic output without ambiguity, which is why priority encoders are a standard logic block. Given Data / Assumptions: Multiple input lines may be active concurrently. The encoder must output one binary code. A defined precedence rule is required. Concept / Approach: A priority encoder assigns an ordering to inputs (e.g., highest-numbered input wins). When several inputs are asserted, the encoder outputs the code corresponding to the highest-priority input and may provide a valid/enable flag. This avoids metastability or ambiguous codes that a simple encoder might produce. Step-by-Step Solution: Define priority: I7 > I6 > ... > I0.If I3 and I6 are high, encoder outputs the code for I6.Output may include a group signal (GS) or enable output (EO) to cascade devices.Thus, the correct process is priority encoding. Verification / Alternative check: ICs such as 74HC148 (8-to-3 priority encoder) implement specified priority rules and demonstrate predictable outputs in multi-assert conditions. Why Other Options Are Wrong: FIFO: A buffering/queuing concept, not instantaneous priority resolution. Ripple blanking: Used in display chains to suppress leading zeros, unrelated to encoders. Priority decoding: Not the conventional term; decoding is the inverse function. TDM: A multiplexing method over time, not a logic priority scheme. Common Pitfalls: Using a simple encoder where a priority encoder is required can lead to undefined outputs. Forgetting to handle the no-input-active case with a valid flag or default code. Final Answer: priority encoding

Question 12

In a BCD-to-seven-segment display system, why is a code converter needed between the 4-bit BCD input and the LED segment lines?

Accepted Answer

Introduction / Context: Seven-segment displays require one control signal per segment (usually a–g). A BCD digit (0–9) is encoded with four bits, but to light the proper pattern, the system must translate that 4-bit value into seven on/off signals. This translation is the role of a BCD-to-seven-segment code converter/driver (e.g., 7447, 4511). Given Data / Assumptions: Input: 4-bit BCD representing 0..9. Output: 7 control lines for segments a–g (plus optional decimal point). Display type: common-anode or common-cathode determines active polarity. Concept / Approach: The converter implements a truth table mapping each BCD code to a specific seven-bit pattern. For example, the digit 0 lights segments a,b,c,d,e,f and leaves g off; the digit 1 lights only b and c. Invalid BCD codes (10–15) are usually blanked or show a defined pattern depending on the IC. Step-by-Step Solution: Accept BCD input XXXX (4 bits).Use combinational logic/ROM to compute a–g outputs.Drive the LED segments with correct polarity and current limiting.Thus, a 4→7 code conversion is required. Verification / Alternative check: Datasheets for 7447/7448 or 4511 show explicit BCD input to segment output tables, confirming that seven control lines are derived from four input bits and that polarity differs by display type. Why Other Options Are Wrong: No conversion: Without a mapping, segments cannot display the intended digit. BCD→gray or two's complement: Different code families, not needed for seven-seg control. BCD→10-bit: A decimal one-hot output is a different function (BCD-to-decimal decoder). Common Pitfalls: Mixing common-anode with common-cathode drivers; logic polarity must match. Ignoring segment current limits, leading to dim or damaged displays. Final Answer: to convert the 4-bit BCD into 7-bit code

Question 13

Magnitude comparator vs selector: Does a magnitude comparator output the highest or lowest numeric value of its inputs based on control signals, or is that the role of a different device?

Accepted Answer

Introduction / Context: Combinational building blocks have specialized roles. A magnitude comparator takes two binary numbers and asserts flags indicating A > B, A = B, or A < B. A multiplexer or dedicated min/max selector, not the comparator, forwards one of the operand values to the output. Confusing these blocks causes functional errors in datapaths and control logic. Given Data / Assumptions: Inputs are two binary words A and B. Magnitude comparator outputs are relational flags only. Selectors (MUX/min–max units) use flags or control lines to route values. Concept / Approach: A magnitude comparator does not drive out a numeric operand. It asserts logic-high on one or more of its relational outputs: A>B, A=B, AB is true, select A, else select B. Therefore, the statement that a comparator “outputs the highest or lowest value depending on control signals” incorrectly attributes selector behavior to the comparator itself. Step-by-Step Solution: Identify primitive: comparator ⇒ relational flags only.Identify selection function: MUX/min–max ⇒ routes operand to output.Map the claim: it describes a selector, not a comparator.Therefore, the statement is incorrect. Verification / Alternative check: Review standard ICs: 74x85 outputs A>B, A=B, A Why Other Options Are Wrong: “Correct” contradicts device definitions. Bit-width or two’s-complement representation do not change the role separation; tri-state buses are unrelated to comparator core behavior. Common Pitfalls: Assuming any block that “compares” will also select; in modular design, comparison and selection are distinct steps wired together by control logic. Final Answer: Incorrect

Question 14

Decoder outputs vs inputs: For a binary decoder, does having 2 select inputs imply only 2 outputs for the decoded value, or should it produce 2^n outputs?

Accepted Answer

Introduction / Context: Decoders are one-hot generators: they convert an n-bit binary input into one of 2^n active outputs. They are used for address decoding, memory selection, and instruction demultiplexing. The stem claims a 2-input decoder has only 2 outputs; we will verify the general n-to-2^n rule and correct this misconception. Given Data / Assumptions: Ideal binary decoder with n input (select) lines. Exactly one output is asserted for each input code when enabled. Active-high outputs assumed (active-low variants behave analogously). Concept / Approach: The defining property is exponential fan-out: an n-to-2^n decoder. For n = 2, outputs = 2^2 = 4. Typical parts: 2-to-4, 3-to-8, 4-to-16 decoders. Therefore, the claim of “two outputs” is incorrect. Confusing decoders with demultiplexers or simple selectors can cause wiring mistakes in address maps and control logic. Step-by-Step Solution: Use the rule: outputs = 2^n.Substitute n = 2 ⇒ outputs = 4.Hence, a 2-input decoder has four outputs (00, 01, 10, 11 one-hot).Therefore, the statement is incorrect. Verification / Alternative check: Look up a standard 74HC139/138 family: for n = 3, 3-to-8 outputs; for n = 2, 2-to-4 outputs. Datasheets reaffirm the 2^n relation. Why Other Options Are Wrong: Enable polarity, Gray coding, or encoder terminology do not change the fundamental output count. “Correct” contradicts the definition. Common Pitfalls: Mixing up decoder (n→2^n) with demultiplexer (routes one input to 1 of 2^n outputs but still has 2^n outputs). Ensure device roles and counts are clear before schematic capture. Final Answer: Incorrect

Question 15

Multiplexer function clarity: Does a multiplexer (MUX) choose which output to send an input to, or does it choose which input is forwarded to a single output?

Accepted Answer

Introduction / Context: Multiplexers and demultiplexers are duals but not identical. A multiplexer selects exactly one of many inputs and forwards it to a single output based on select lines. A demultiplexer takes a single input and routes it to one of many outputs. The stem incorrectly describes a demultiplexer as if it were a multiplexer. Clarifying this prevents common wiring errors in datapaths and I/O selection networks. Given Data / Assumptions: MUX: many-to-one (N inputs, 1 output). DEMUX: one-to-many (1 input, N outputs). Select lines determine which path is active. Concept / Approach: A k-select-line MUX chooses one of 2^k inputs to appear at a single output. Conversely, a k-select-line DEMUX activates one of 2^k outputs to receive the single input. Hence the statement “chooses which output to send an input to” describes a DEMUX, not a MUX. Therefore, as a definition of a multiplexer, the statement is incorrect. Step-by-Step Solution: Recall device roles: MUX = many→one; DEMUX = one→many.Map the stem: “choose which output an input goes to” ⇒ DEMUX.Therefore, the stem does not define a MUX correctly.Conclude: the statement is incorrect for a multiplexer. Verification / Alternative check: Typical parts: 74HC157 (2:1 quad MUX) selects between inputs for a single output per channel. 74HC138 (3:8 decoder/DEMUX) routes one enable/input to one of eight outputs—distinct functions. Why Other Options Are Wrong: Limiting to 2:1 or invoking tri-state buses does not change the core definition. “True for demultiplexers” acknowledges the dual but confirms the statement is not correct for MUX. Common Pitfalls: Using the wrong symbol in schematics; confusing enable pins with select lines; forgetting that MUX outputs are singular per channel. Final Answer: Incorrect

Question 16

Error-detection capability of single-parity schemes: Can simple parity checking detect only an odd number of bit errors in a codeword (and miss even numbers of bit flips)?

Accepted Answer

Introduction / Context: Parity bits are the simplest error-detection mechanism used in memory systems, serial links, and legacy protocols. A single parity bit forces the total number of 1s in a codeword to be either even (even parity) or odd (odd parity). Understanding exactly what error patterns parity detects—and which it cannot—guides the selection of stronger codes when needed, such as checksums, CRCs, or Hamming codes. Given Data / Assumptions: Single parity bit appended to a data word. Even or odd parity convention is known to both transmitter and receiver. Independent bit-flip error model (no burst-correction mechanisms assumed). Concept / Approach: Let w be the number of 1s in the transmitted data. The parity bit is set so that w + p has a fixed parity (even or odd). If an odd number of bits flip during transmission, the parity of the received word toggles, producing a mismatch flag. If an even number of bits flip, parity returns to the original parity class and the simple parity check fails to detect the error. Thus, parity detects any odd-weight error pattern (1, 3, 5, … flips) and misses all even-weight error patterns (2, 4, 6, … flips). The minimum Hamming distance of a single-parity code is 2, enabling detection of all single-bit errors but not correction and not detection of double-bit errors. Step-by-Step Solution: Define parity rule: choose p so that total ones count has fixed parity.Consider one-bit error: parity flips ⇒ detected.Consider two-bit errors: parity flips twice ⇒ original parity restored ⇒ undetected.Generalize to any odd vs even number of flips. Verification / Alternative check: Compute Hamming distance: with one parity bit, any valid codeword differs from any other by at least 2, confirming detect-1 capability and failure to detect all double-bit errors. Why Other Options Are Wrong: Odd vs even parity choice does not affect the odd-error detection rule; both detect odd numbers of flips. Hamming distance > 2 requires more redundancy than single parity. Applicability is general to binary data, not restricted to ASCII. Common Pitfalls: Assuming parity can correct errors (it cannot); assuming it detects double-bit errors (it does not); mixing parity with CRC behavior, which has different detection guarantees. Final Answer: Correct

Question 17

Digital design — encoder fundamentals: in combinational logic, is it accurate that an encoder circuit is specifically designed to generate a coded output (e.g., binary or BCD) corresponding to which single input line is active?

Accepted Answer

Introduction / Context: An encoder is a standard combinational logic block used in digital systems to compress multiple input lines into a smaller number of output bits. Typical examples include 8-to-3 binary encoders and keyboard encoders. This question checks the core definition: does an encoder generate a specific code on its outputs based on which input line is asserted? Given Data / Assumptions: One-hot or priority-encoded inputs are considered. Exactly one valid input is active at a time unless a priority encoder is used. Outputs are binary-coded representations (binary/BCD etc.). Concept / Approach: An N-to-m encoder maps N input lines to m outputs, where m = ceil(log2 N). The function is the inverse of a decoder: instead of expanding a coded input into one-of-N outputs, an encoder compresses one-of-N inputs into a code. Priority encoders add logic to resolve multiple simultaneous inputs according to a defined priority, ensuring a valid coded result. Step-by-Step Solution: 1) Identify the definition: encoder = device that converts active input line number into a code.2) Note the coding scheme (e.g., 8 inputs → 3-bit binary output).3) Recognize enhancements (priority, enable, valid) that keep the core behavior the same.4) Conclude the statement is an accurate summary of encoder purpose. Verification / Alternative check: Truth tables for standard 4-to-2 or 8-to-3 encoders show unique coded outputs for each asserted input line. Priority encoder datasheets confirm the same with added priority/valid flags. Why Other Options Are Wrong: Does not apply: contradicts the device definition. Only for parity encoders: parity generation is a different function (error checking), not line-to-code encoding. Applies only when all inputs are active: encoders assume one active input; all-active yields invalid unless priority or masking is used. Common Pitfalls: Confusing encoders with decoders or multiplexers; ignoring the need for priority when simultaneous inputs can occur. Final Answer: Applies

Question 18

Decoder realization with minimal gates: can a single AND gate plus two inverters act as a functional “basic decoder,” i.e., uniquely select one-of-N outputs from coded inputs?

Accepted Answer

Introduction / Context: Decoders expand a coded input (e.g., 2 bits) into one-of-N outputs (e.g., 4 lines). This item probes whether an extremely small gate set—one AND gate and two inverters—can truly perform the generic decoder function, which requires producing uniquely asserted output lines for each input code. Given Data / Assumptions: “Basic decoder” refers to standard one-of-N selection (e.g., 2-to-4, 3-to-8). Inputs are the coded lines; outputs are mutually exclusive selects. No ROM or PLA structures are assumed. Concept / Approach: A k-to-2^k decoder uses product terms (minterms) of the inputs and their complements. For k = 2, four AND terms are required, each AND-ing either the true or complemented inputs. Two inverters provide complements, but a single AND gate cannot generate all required minterms. Thus, the proposed gate count is insufficient for one-of-N decoding. Step-by-Step Solution: 1) For 2-to-4 decode: outputs D0 = ~A * ~B, D1 = ~A * B, D2 = A * ~B, D3 = A * B.2) Count required gates: four 2-input AND gates plus two inverters.3) Given only one AND gate and two inverters, you can realize at most one minterm.4) Therefore the gate set cannot implement a full decoder. Verification / Alternative check: Truth table inspection shows that a single AND gate yields only one of the minterms; additional AND gates are needed to cover all code combinations. Why Other Options Are Wrong: Applies: overclaims capability. Applies only with enable: an enable simply gates all outputs; it does not create missing minterms. Applies only for one-to-two decoding: even 1-to-2 decoding typically uses a buffer and an inverter (or two ANDs with enable), not a lone AND plus two inverters to realize “decoder” semantics. Common Pitfalls: Confusing “some decoding” (one minterm) with a full decoder; underestimating the number of product terms needed. Final Answer: Does not apply

Question 19

Multiplexer function check: is a multiplexer (MUX) a device that generates a fixed sequence of binary states on each clock pulse, regardless of its data inputs?

Accepted Answer

Introduction / Context: A multiplexer is often called a “data selector.” It forwards one of several input lines to a single output based on select inputs. This question tests whether a MUX inherently produces a fixed output sequence on each clock pulse, which would actually describe a counter or sequence generator, not a MUX. Given Data / Assumptions: Standard n-to-1 MUX with data inputs D0…Dn−1 and select lines S. No internal clocked memory in a simple combinational MUX. Any clocking pertains to external logic driving the select lines, not the MUX core. Concept / Approach: A MUX is purely combinational: Output Y = Dk where k is the index set by S. If a clock drives the select lines through a counter, the observed output may change in a pattern—but the MUX itself is not the sequence generator. The “fixed sequence on each clock” description fits counters or shift registers, not multiplexers. Step-by-Step Solution: 1) Define MUX behavior: selects one input to pass to output.2) Recognize sequence generation requires state (flip-flops, counters).3) Conclude the statement confuses the roles of selector vs sequencer.4) Therefore, it does not apply to a MUX by itself. Verification / Alternative check: Datasheets for basic MUX ICs (e.g., 74HC151) list propagation delay and truth table only—no clock, no internal state. Why Other Options Are Wrong: Applies: misidentifies the device function. “Only if select lines are clocked”: even then, the pattern comes from the external counter, not from the MUX. Common Pitfalls: Assuming “clocked” equals “sequential”; forgetting a MUX is combinational. Final Answer: Does not apply

Question 20

Decoder fundamentals: does the general function of a decoder involve asserting one or more specific outputs when its input lines match a particular digital state (code)?

Accepted Answer

Introduction / Context: Decoders are the counterpart to encoders: they expand a compact code into one-of-N (or sometimes multiple) outputs. They are used in address decoding, display driving, and memory chip selection. The question checks the canonical role of decoders in activating outputs when an input code is recognized. Given Data / Assumptions: K input lines represent a binary code. Up to 2^K distinct outputs are possible (or grouped outputs). Active-high or active-low conventions may apply. Concept / Approach: A decoder generates minterms of the inputs and asserts the output(s) corresponding to the input pattern. Examples include the 3-to-8 decoder (one of eight outputs goes active) and 4-to-16 address decoders. Some variants include enable inputs and multiple active outputs for special coding schemes, but the essence remains detection and activation based on input states. Step-by-Step Solution: 1) Model input code as a K-bit vector.2) Implement minterms with AND gates and input complements.3) Assert the matching output line(s) for the given code.4) Optional: gate the entire decoder with an enable pin. Verification / Alternative check: Standard truth tables (e.g., 74HC138) show exactly one active output for each 3-bit input when enabled, confirming the definition. Why Other Options Are Wrong: Does not apply: contradicts core functionality. Active-low only / all-ones-only: output polarity and specific codes are implementation details; the function is general detection and activation. Common Pitfalls: Confusing decoders with demultiplexers; overlooking enable and polarity conventions. Final Answer: Applies

Combinational Logic Circuits Questions