Q: Wiring a 7493 as a MOD-12 (divide-by-12) counter Which pins of the 7493 should be connected together to configure the counter for modulus 12 operation?

Introduction / Context: The 7493 is a 4-bit ripple counter with separate divide-by-2 and divide-by-8 sections. By wiring its outputs back to the asynchronous reset inputs, you can truncate the natural modulus-16 sequence to achieve a desired modulus such as 12 (counts 0 through 11). Correct pin connections are crucial to reset the counter exactly at the intended terminal count. Given Data / Assumptions: Pin roles (TTL 7493): QA=12, QB=9, QC=8, QD=11. CLK B (higher stages) = pin 1; CLK A (LSB) = pin 14. Asynchronous reset inputs: R01=2 and R02=3; both must be HIGH to clear. Goal: MOD-12 → reset at binary 1100 (decimal 12), i.e., QC=1 and QD=1. Concept / Approach: First, connect QA (pin 12) to CLK B (pin 1) so the higher stages count at QA/2, creating a standard 4-bit chain. To force modulus 12, detect count 12 (QD=1 and QC=1) and feed those signals to the two reset pins so that when the state reaches 1100, the counter asynchronously clears to 0000 on the very next instant. Step-by-Step Solution: Chain the sections: connect 12 → 1.Detect terminal count 12 (1100): use QD (pin 11) and QC (pin 8).Drive resets: connect 11 → 3 and 8 → 2 (both must be HIGH to clear).Verify on a scope or simulation: sequence repeats 0000…1011 then clears. Verification / Alternative check: List the count sequence and confirm that upon reaching 1100 both reset pins go HIGH, instantly clearing the counter to 0000, yielding exactly 12 distinct states per cycle. Why Other Options Are Wrong: 12 to 1, 11 to 3, 9 to 2: Uses QB instead of QC; would reset at 1010 (10), not 12. 12 to 1, 11 to 3, 12 to 2: Misuses QA for a reset input and breaks the chain. 12 to 1, 11 to 3, 1 to 2: Feeding the clock into reset is incorrect and unstable. Common Pitfalls: Forgetting both reset inputs must be asserted together; mixing up QC and QB pin numbers; or omitting the QA→CLK B link so upper stages never count. Final Answer: 12 to 1, 11 to 3, 8 to 2

Q: Asynchronous counter delay accumulation A 5-bit ripple (asynchronous) binary counter uses five flip-flops, each with propagation delay 12 ns. What is the total worst-case propagation delay tp(tot)?

Introduction / Context: In ripple counters, the clock signal propagates through cascaded flip-flops, so output bits do not change simultaneously. The worst-case propagation delay equals the sum of the individual stage delays up to the most significant bit used, which limits the maximum counting frequency and affects decoding hazards. Given Data / Assumptions: Number of stages (flip-flops): 5. Propagation delay per stage: 12 ns (worst case). Asynchronous (ripple) topology: each stage toggles on the previous stage’s output. Concept / Approach: Because the toggling ripples from the least significant to the most significant stage, the worst-case time for the final bit to settle is the sum of delays through all five flip-flops. Therefore, tp(tot) = N * t_pd for N cascaded stages in the ripple path. Step-by-Step Solution: Identify N = 5 stages.Use t_pd per stage = 12 ns.Compute tp(tot) = 5 * 12 ns = 60 ns.This is the worst-case settling time after a triggering clock edge. Verification / Alternative check: Compare to a 4-bit ripple counter: 4 * 12 ns = 48 ns. Extending to 5 bits adds another 12 ns, consistent with linear accumulation. Why Other Options Are Wrong: 12 ms: Milliseconds are three orders of magnitude too large and mismatch per-stage specs. 24 ns / 48 ns: Correspond to 2 or 4 stages, not 5. Common Pitfalls: Confusing ripple with synchronous counters (which do not accumulate delays in the same way), or forgetting worst-case analysis when decoding multiple bits immediately after a transition. Final Answer: 60 ns

Q: Applications of integrated counter ICs Integrated-circuit (IC) counter chips are commonly used in which types of applications?

Introduction / Context: Counters are fundamental building blocks in digital electronics. Off-the-shelf counter ICs appear in timers, event counters, digital clocks, and frequency-management circuits. Understanding their typical use-cases helps in selecting the right device and integrating it appropriately with oscillators and decoding logic. Given Data / Assumptions: Counters advance states in response to clock pulses. They can be cascaded and combined with decoders for sequencing. Frequency division (not multiplication) is a natural consequence of counting cycles. Concept / Approach: Counters inherently divide frequency: a toggle (divide-by-2) flip-flop halves frequency; chaining N such stages yields divide-by-2^N. Timing operations result from dividing a reference clock to produce time bases. Sequencing arises when decoded states drive control lines. Counting operations are, of course, the direct application. Frequency multiplication typically requires phase-locked loops or other techniques, not basic counters alone. Step-by-Step Solution: Start with a clock source (e.g., crystal oscillator).Feed into counter chain; obtain lower-frequency outputs at successive stages.Decode particular counts to generate sequences of control signals.Use output periods as timing intervals for digital systems. Verification / Alternative check: Examine a digital clock: counters divide 32.768 kHz to 1 Hz, then decode counts for seconds/minutes/hours. This showcases timing, counting, sequencing, and frequency division together. Why Other Options Are Wrong: Options with frequency multiplication: plain counters do not multiply frequency. Decoding operations are typically done by decoders, not counters themselves (though counters feed decoders). Common Pitfalls: Assuming counters can increase frequency; misusing asynchronous counters where synchronous division is required for tight timing. Final Answer: timing operations, counting operations, sequencing, and frequency division

Q: Identifying invalid states in an 8421 BCD counter Which of the following 4-bit codes is an invalid state for a natural 8421 BCD up-counter?

Introduction / Context: BCD (binary-coded decimal) in 8421 weighting represents decimal digits 0 through 9 using 4-bit codes from 0000 to 1001. States 1010 through 1111 are not valid BCD digits and are skipped or corrected in BCD counters. Recognizing valid versus invalid states is important for designing truncation and reset logic. Given Data / Assumptions: 8421 BCD valid range: 0000 (0) to 1001 (9). Invalid range: 1010 (10) to 1111 (15). We check the listed codes against these ranges. Concept / Approach: Compare each option to the valid set. Codes representing decimal 0–9 are valid; anything above 1001 is invalid in a pure BCD digit counter and must be corrected via synchronous clear or carry logic when designing counters or state machines that display decimal digits. Step-by-Step Solution: 0011 = 3 → valid.1001 = 9 → valid.1000 = 8 → valid.1100 = 12 → invalid (out of BCD digit range). Verification / Alternative check: Check any BCD truth table: only 0000–1001 are mapped to digits; 1100 is unmapped and thus invalid. Why Other Options Are Wrong: 0011, 1001, 1000: All within 0–9 and therefore legal BCD states. Common Pitfalls: Confusing 8421 with other BCD variants; forgetting that counters must skip or reset on reaching 1010 (decimal 10) to maintain decimal correctness. Final Answer: 1100

Q: Interpreting counter modulus A counter with modulus 16 will function as which kind of frequency divider?

Introduction / Context: The modulus (MOD) of a counter is the number of distinct states in its counting cycle. When used as a frequency divider, the output signal that toggles once per full cycle divides the input clock by the modulus. Understanding this relationship allows quick estimation of division factors in timing chains. Given Data / Assumptions: Counter modulus: 16 → 16 unique states per cycle. Each complete cycle corresponds to one output repetition. Assume a single output that indicates cycle completion (for example, decoded terminal count or MSB patterns). Concept / Approach: For N distinct states, the counter advances one state per clock pulse and repeats every N pulses. Therefore, the fundamental repetition period corresponds to dividing the clock frequency by N. With MOD=16, the division factor is 16, producing an output with frequency f_out = f_clk / 16 under standard use. Step-by-Step Solution: Define modulus N = 16.One complete count sequence requires 16 clock pulses.The cycle-based output repeats once per 16 pulses.Hence the device behaves as a divide-by-16 counter. Verification / Alternative check: Consider a synchronous 4-bit binary counter: its MSB toggles at f_clk/16, and its state sequence length is 16, matching the modulus definition. Why Other Options Are Wrong: divide-by-8/32/64: These correspond to moduli 8/32/64 respectively, not 16. Common Pitfalls: Confusing the MSB toggle rate with the total modulus in unusual wiring; generally, the modulus dictates the fundamental division ratio. Final Answer: divide-by-16 counter

Q: Cascading decade counters Four cascaded modulus-10 (decade) counters together will produce what overall modulus?

Introduction / Context: Counters are often cascaded to extend the range of counting. When you cascade counters, the total modulus is the product of the individual moduli, enabling decimal timekeeping and event-counting over large ranges using standard decade devices. Given Data / Assumptions: Each stage: modulus 10. Number of stages: 4 (units, tens, hundreds, thousands). Proper cascading: carry (or ripple) from one stage clocks the next. Concept / Approach: The overall modulus of cascaded counters equals the product of their individual moduli. Therefore, four decades produce 10 * 10 * 10 * 10 = 10,000 unique states before the sequence repeats. This principle generalizes to any set of cascaded counters with possibly different moduli (overall modulus = product of all). Step-by-Step Solution: Identify per-stage modulus M = 10.Compute product: 10^4 = 10,000.Interpretation: counter counts 0000–9999 (ten thousand states).Reset after 9999 back to 0000 completes the cycle. Verification / Alternative check: Observe a 4-digit decimal counter: units advances each pulse; tens advances each time units rolls over; and so on—clearly yielding 10,000 states. Why Other Options Are Wrong: 10, 100, 1,000: These are products for 1, 2, and 3 cascaded decades respectively. Common Pitfalls: Miscounting the number of stages; failing to ensure proper carry/ripple connections so that the theoretical modulus is actually realized in hardware. Final Answer: 10,000

Q: Deleting states for a target modulus You have four cascaded counters providing a total of 16 bits (overall natural count = 65,536 states). To realize an exact modulus of 50,000, how many states must be deleted (skipped)?

Introduction / Context: When the native modulus of a counter chain exceeds the required count range, designers implement truncation by decoding a terminal count and forcing a synchronous/asynchronous clear. Determining how many states to delete is a straightforward arithmetic exercise but must be done precisely to avoid off-by-one errors in the division ratio. Given Data / Assumptions: Total available states from 16 bits: 2^16 = 65,536. Desired modulus: 50,000. We delete states above the desired terminal state so the sequence repeats correctly. Concept / Approach: Deleted states = native_states − desired_modulus. After reaching the desired terminal count (49,999 if starting at 0), the counter is forced back to 0, skipping the remaining high states so that exactly 50,000 pulses form a complete cycle, giving a divide-by-50,000 output. Step-by-Step Solution: Compute native_states = 2^16 = 65,536.Compute deletion count = 65,536 − 50,000.Perform subtraction: 65,536 − 50,000 = 15,536.Implement by decoding the first unwanted state and asserting reset. Verification / Alternative check: Simulate the counter: confirm that after 50,000 input clocks, the output sequence repeats, demonstrating the correct modulus and hence the correctness of the deletion count. Why Other Options Are Wrong: 50,000 / 65,536: These are the desired and native states themselves, not the difference. 25,536: Arithmetic error (confuses difference with midpoint or mixes digits). Common Pitfalls: Off-by-one errors when the sequence starts at 1 instead of 0; neglecting synchronous clear timing which can add one extra count if not aligned with the clock edge. Final Answer: 15,536

Question 1

Seven-segment displays — behavior of a common-anode LED module A seven-segment, common-anode LED display is designed for which control behavior?

Accepted Answer

Introduction / Context: Seven-segment LED displays come in two wiring polarities: common-anode and common-cathode. Understanding their behavior is necessary when selecting driver ICs or building microcontroller interfaces, because the logic level required to illuminate a segment depends on the common node connection. Given Data / Assumptions: Common-anode type: all anodes of the segments are tied together internally. The common anode is typically connected to Vcc through a current-limiting path. Individual segment pins are the cathodes. Concept / Approach: For a common-anode display, to turn a segment ON you must sink current from its cathode to ground (logic LOW at the driver output). Conversely, applying a logic HIGH to the cathode stops current flow, turning the segment OFF. This is the opposite of common-cathode displays, where a logic HIGH at the segment pin lights the LED. Step-by-Step Reasoning: Tie the common anode to Vcc.To illuminate a segment, drive its cathode LOW to allow current from Vcc → LED → driver → ground.To extinguish a segment, drive its cathode HIGH (no voltage drop, no current flows). Verification / Alternative check: Consult a typical driver like the 74xx47 BCD-to-7-segment decoder for common-anode displays; its outputs are active-LOW, matching the sink-current requirement. A quick bench test with a resistor confirms that LOW lights a segment and HIGH turns it off. Why Other Options Are Wrong: All cathodes wired together: describes common-cathode devices. One common LED: each segment is its own LED; there is no single common LED. Disorientation of modules: not a technical behavior. A HIGH to turn on each segment: opposite of common-anode behavior. Common Pitfalls: Forgetting current-limiting resistors; each segment typically needs its own resistor. Using a source-only driver with a common-anode module; a sink-capable driver is preferred. Final Answer: a HIGH to turn off each segment

Question 2

Asynchronous (ripple) down counter — intermediate transitional states An asynchronous 4-bit binary down counter changes from count 2 (0010₂) to count 3 (0011₂). How many intermediate transitional states (glitches) occur at the outputs during this ch…

Accepted Answer

Introduction / Context: Ripple counters change state sequentially as each flip-flop toggles in response to the previous stage, which can create transient intermediate states at the multi-bit output. Understanding when such glitches occur is important when driving decoders or combinational logic that might respond to the brief incorrect patterns. Given Data / Assumptions: A 4-bit asynchronous (ripple) binary down counter. Transition considered: 2 (0010₂) → 3 (0011₂). Outputs observed directly at the counter pins. Concept / Approach: Transitional states occur when multiple bits need to change and do not toggle simultaneously. If only one bit changes for a given increment/decrement, then no intermediate invalid combination appears, because there is no propagation chain causing other stages to toggle during the event. Step-by-Step Reasoning: Represent 2 = 0010₂ and 3 = 0011₂.Only the least significant bit changes: from 0 to 1.Higher-order bits remain the same (no toggling is required), so there is no ripple through other stages.Therefore, no intermediate transitional states occur; the output goes directly from 0010 to 0011. Verification / Alternative check: Compare to a problematic boundary like 0000 → 1111 in a down counter (or 0111 → 1000 in an up counter), where multiple bits flip and glitches are expected. In contrast, 0010 → 0011 requires only one bit flip, so the transition is clean even in a ripple design. Why Other Options Are Wrong: One/Two/Three: imply additional bits toggling, which does not occur for this specific transition. Fifteen: misinterprets “modulus” or assumes spurious oscillation. Common Pitfalls: Assuming ripple counters always glitch; they glitch only when more than one bit changes. Confusing down vs. up transitions; the analysis hinges on which bits must toggle. Final Answer: None

Question 3

Synchronous vs. asynchronous counters — eliminating ripple delay Why do synchronous counters avoid the cumulative propagation delays seen in asynchronous (ripple) counters?

Accepted Answer

Introduction / Context: Asynchronous counters propagate state changes from one flip-flop to the next, leading to cumulative ripple delays and temporary incorrect outputs. Synchronous counters are designed to eliminate this behavior so that all bits update together, a crucial advantage in high-speed digital systems. Given Data / Assumptions: Synchronous counter implemented with edge-triggered flip-flops. Common system clock distributed to all stages. Proper gating logic derives each flip-flop’s next state from the present state. Concept / Approach: In synchronous designs, every flip-flop samples its input on the same clock edge. The combinational logic feeding each stage ensures that the correct next value is present at the sampling instant. Because no stage waits for another to toggle first, all outputs change simultaneously, eliminating ripple-through delays at the word output. Step-by-Step Reasoning: Distribute one clock to all flip-flops (common edge).Design logic so that D (or J/K) inputs represent the correct next count before the clock edge.At the edge, all flip-flops update together ⇒ no bit-by-bit cascade. Verification / Alternative check: Observe waveforms: in a synchronous counter, all Q outputs transition at the same edge. In a ripple counter, higher-order bits lag lower-order ones by multiple propagation delays, readily visible on a scope as skewed edges and intermediate codes. Why Other Options Are Wrong: First/last stage only or last stage only: still serializes updates and would not prevent ripple behavior. No clock used: counters by definition advance with a clock. “Faster process”: technology helps but does not fundamentally remove ripple; architecture does. Common Pitfalls: Assuming synchronous eliminates all delay; it eliminates ripple error at the word output, but setup/hold and logic delays still must meet timing. Final Answer: input clock pulses are applied simultaneously to each stage

Question 4

HDL ring counter coding practice In a hardware description language (HDL) implementation of a ring counter, many invalid (illegal) states can be safely handled in the code by which construct?

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Introduction / Context: Ring counters are sequential circuits that circulate a single 1 (or 0) through a shift register. In HDL (VHDL/Verilog), not all possible bit patterns are valid states for a given ring counter width. Good coding practice requires explicitly handling these illegal states so that the design recovers predictably if a fault or upset occurs. Given Data / Assumptions: Target device: an HDL-coded ring counter. Only a small subset of all state patterns are legal (one-hot in a typical ring counter). We want to include recovery behavior for all other patterns. Concept / Approach: HDLs offer selection constructs (for example, case in VHDL/Verilog). In VHDL, the when others branch (or default in other languages) catches any value not explicitly listed. This is the canonical place to funnel all illegal states back to a known reset state (for example, 0001). Using a bare elsif chain without a final catch-all often leaves unhandled conditions. A data pin such as ser_in is unrelated to state recovery. The idea is to write self-correcting code by coding the “others” branch to reinitialize the machine. Step-by-Step Solution: Write a case statement over the present_state vector.Enumerate legal one-hot states explicitly (e.g., 0001, 0010, 0100, 1000).For all remaining bit patterns, write when others => next_state <= RESET_STATE.Synthesize/simulate and verify that any injected illegal state returns to RESET_STATE in one clock. Verification / Alternative check: Perform fault injection in simulation by forcing an invalid state; observe that the others clause deterministically recovers to the reset state on the next tick. Why Other Options Are Wrong: using a case statement.: A case is necessary, but the others arm is what actually catches illegal states. using an elsif statement.: Without a catch-all, some illegal states remain unhandled. the ser_in line.: This is a data input, not a coding construct for illegal-state recovery. Common Pitfalls: Forgetting to specify the others branch; not resetting to a legal one-hot value; or allowing latches by incomplete assignments inside the case. Final Answer: including them under others.

Question 5

Wiring a 7493 as a MOD-12 (divide-by-12) counter Which pins of the 7493 should be connected together to configure the counter for modulus 12 operation?

Accepted Answer

Introduction / Context: The 7493 is a 4-bit ripple counter with separate divide-by-2 and divide-by-8 sections. By wiring its outputs back to the asynchronous reset inputs, you can truncate the natural modulus-16 sequence to achieve a desired modulus such as 12 (counts 0 through 11). Correct pin connections are crucial to reset the counter exactly at the intended terminal count. Given Data / Assumptions: Pin roles (TTL 7493): QA=12, QB=9, QC=8, QD=11. CLK B (higher stages) = pin 1; CLK A (LSB) = pin 14. Asynchronous reset inputs: R01=2 and R02=3; both must be HIGH to clear. Goal: MOD-12 → reset at binary 1100 (decimal 12), i.e., QC=1 and QD=1. Concept / Approach: First, connect QA (pin 12) to CLK B (pin 1) so the higher stages count at QA/2, creating a standard 4-bit chain. To force modulus 12, detect count 12 (QD=1 and QC=1) and feed those signals to the two reset pins so that when the state reaches 1100, the counter asynchronously clears to 0000 on the very next instant. Step-by-Step Solution: Chain the sections: connect 12 → 1.Detect terminal count 12 (1100): use QD (pin 11) and QC (pin 8).Drive resets: connect 11 → 3 and 8 → 2 (both must be HIGH to clear).Verify on a scope or simulation: sequence repeats 0000…1011 then clears. Verification / Alternative check: List the count sequence and confirm that upon reaching 1100 both reset pins go HIGH, instantly clearing the counter to 0000, yielding exactly 12 distinct states per cycle. Why Other Options Are Wrong: 12 to 1, 11 to 3, 9 to 2: Uses QB instead of QC; would reset at 1010 (10), not 12. 12 to 1, 11 to 3, 12 to 2: Misuses QA for a reset input and breaks the chain. 12 to 1, 11 to 3, 1 to 2: Feeding the clock into reset is incorrect and unstable. Common Pitfalls: Forgetting both reset inputs must be asserted together; mixing up QC and QB pin numbers; or omitting the QA→CLK B link so upper stages never count. Final Answer: 12 to 1, 11 to 3, 8 to 2

Question 6

Asynchronous counter delay accumulation A 5-bit ripple (asynchronous) binary counter uses five flip-flops, each with propagation delay 12 ns. What is the total worst-case propagation delay tp(tot)?

Accepted Answer

Introduction / Context: In ripple counters, the clock signal propagates through cascaded flip-flops, so output bits do not change simultaneously. The worst-case propagation delay equals the sum of the individual stage delays up to the most significant bit used, which limits the maximum counting frequency and affects decoding hazards. Given Data / Assumptions: Number of stages (flip-flops): 5. Propagation delay per stage: 12 ns (worst case). Asynchronous (ripple) topology: each stage toggles on the previous stage’s output. Concept / Approach: Because the toggling ripples from the least significant to the most significant stage, the worst-case time for the final bit to settle is the sum of delays through all five flip-flops. Therefore, tp(tot) = N * t_pd for N cascaded stages in the ripple path. Step-by-Step Solution: Identify N = 5 stages.Use t_pd per stage = 12 ns.Compute tp(tot) = 5 * 12 ns = 60 ns.This is the worst-case settling time after a triggering clock edge. Verification / Alternative check: Compare to a 4-bit ripple counter: 4 * 12 ns = 48 ns. Extending to 5 bits adds another 12 ns, consistent with linear accumulation. Why Other Options Are Wrong: 12 ms: Milliseconds are three orders of magnitude too large and mismatch per-stage specs. 24 ns / 48 ns: Correspond to 2 or 4 stages, not 5. Common Pitfalls: Confusing ripple with synchronous counters (which do not accumulate delays in the same way), or forgetting worst-case analysis when decoding multiple bits immediately after a transition. Final Answer: 60 ns

Question 7

Applications of integrated counter ICs Integrated-circuit (IC) counter chips are commonly used in which types of applications?

Accepted Answer

Introduction / Context: Counters are fundamental building blocks in digital electronics. Off-the-shelf counter ICs appear in timers, event counters, digital clocks, and frequency-management circuits. Understanding their typical use-cases helps in selecting the right device and integrating it appropriately with oscillators and decoding logic. Given Data / Assumptions: Counters advance states in response to clock pulses. They can be cascaded and combined with decoders for sequencing. Frequency division (not multiplication) is a natural consequence of counting cycles. Concept / Approach: Counters inherently divide frequency: a toggle (divide-by-2) flip-flop halves frequency; chaining N such stages yields divide-by-2^N. Timing operations result from dividing a reference clock to produce time bases. Sequencing arises when decoded states drive control lines. Counting operations are, of course, the direct application. Frequency multiplication typically requires phase-locked loops or other techniques, not basic counters alone. Step-by-Step Solution: Start with a clock source (e.g., crystal oscillator).Feed into counter chain; obtain lower-frequency outputs at successive stages.Decode particular counts to generate sequences of control signals.Use output periods as timing intervals for digital systems. Verification / Alternative check: Examine a digital clock: counters divide 32.768 kHz to 1 Hz, then decode counts for seconds/minutes/hours. This showcases timing, counting, sequencing, and frequency division together. Why Other Options Are Wrong: Options with frequency multiplication: plain counters do not multiply frequency. Decoding operations are typically done by decoders, not counters themselves (though counters feed decoders). Common Pitfalls: Assuming counters can increase frequency; misusing asynchronous counters where synchronous division is required for tight timing. Final Answer: timing operations, counting operations, sequencing, and frequency division

Question 8

Identifying invalid states in an 8421 BCD counter Which of the following 4-bit codes is an invalid state for a natural 8421 BCD up-counter?

Accepted Answer

Introduction / Context: BCD (binary-coded decimal) in 8421 weighting represents decimal digits 0 through 9 using 4-bit codes from 0000 to 1001. States 1010 through 1111 are not valid BCD digits and are skipped or corrected in BCD counters. Recognizing valid versus invalid states is important for designing truncation and reset logic. Given Data / Assumptions: 8421 BCD valid range: 0000 (0) to 1001 (9). Invalid range: 1010 (10) to 1111 (15). We check the listed codes against these ranges. Concept / Approach: Compare each option to the valid set. Codes representing decimal 0–9 are valid; anything above 1001 is invalid in a pure BCD digit counter and must be corrected via synchronous clear or carry logic when designing counters or state machines that display decimal digits. Step-by-Step Solution: 0011 = 3 → valid.1001 = 9 → valid.1000 = 8 → valid.1100 = 12 → invalid (out of BCD digit range). Verification / Alternative check: Check any BCD truth table: only 0000–1001 are mapped to digits; 1100 is unmapped and thus invalid. Why Other Options Are Wrong: 0011, 1001, 1000: All within 0–9 and therefore legal BCD states. Common Pitfalls: Confusing 8421 with other BCD variants; forgetting that counters must skip or reset on reaching 1010 (decimal 10) to maintain decimal correctness. Final Answer: 1100

Question 9

Interpreting counter modulus A counter with modulus 16 will function as which kind of frequency divider?

Accepted Answer

Introduction / Context: The modulus (MOD) of a counter is the number of distinct states in its counting cycle. When used as a frequency divider, the output signal that toggles once per full cycle divides the input clock by the modulus. Understanding this relationship allows quick estimation of division factors in timing chains. Given Data / Assumptions: Counter modulus: 16 → 16 unique states per cycle. Each complete cycle corresponds to one output repetition. Assume a single output that indicates cycle completion (for example, decoded terminal count or MSB patterns). Concept / Approach: For N distinct states, the counter advances one state per clock pulse and repeats every N pulses. Therefore, the fundamental repetition period corresponds to dividing the clock frequency by N. With MOD=16, the division factor is 16, producing an output with frequency f_out = f_clk / 16 under standard use. Step-by-Step Solution: Define modulus N = 16.One complete count sequence requires 16 clock pulses.The cycle-based output repeats once per 16 pulses.Hence the device behaves as a divide-by-16 counter. Verification / Alternative check: Consider a synchronous 4-bit binary counter: its MSB toggles at f_clk/16, and its state sequence length is 16, matching the modulus definition. Why Other Options Are Wrong: divide-by-8/32/64: These correspond to moduli 8/32/64 respectively, not 16. Common Pitfalls: Confusing the MSB toggle rate with the total modulus in unusual wiring; generally, the modulus dictates the fundamental division ratio. Final Answer: divide-by-16 counter

Question 10

Cascading decade counters Four cascaded modulus-10 (decade) counters together will produce what overall modulus?

Accepted Answer

Introduction / Context: Counters are often cascaded to extend the range of counting. When you cascade counters, the total modulus is the product of the individual moduli, enabling decimal timekeeping and event-counting over large ranges using standard decade devices. Given Data / Assumptions: Each stage: modulus 10. Number of stages: 4 (units, tens, hundreds, thousands). Proper cascading: carry (or ripple) from one stage clocks the next. Concept / Approach: The overall modulus of cascaded counters equals the product of their individual moduli. Therefore, four decades produce 10 * 10 * 10 * 10 = 10,000 unique states before the sequence repeats. This principle generalizes to any set of cascaded counters with possibly different moduli (overall modulus = product of all). Step-by-Step Solution: Identify per-stage modulus M = 10.Compute product: 10^4 = 10,000.Interpretation: counter counts 0000–9999 (ten thousand states).Reset after 9999 back to 0000 completes the cycle. Verification / Alternative check: Observe a 4-digit decimal counter: units advances each pulse; tens advances each time units rolls over; and so on—clearly yielding 10,000 states. Why Other Options Are Wrong: 10, 100, 1,000: These are products for 1, 2, and 3 cascaded decades respectively. Common Pitfalls: Miscounting the number of stages; failing to ensure proper carry/ripple connections so that the theoretical modulus is actually realized in hardware. Final Answer: 10,000

Question 11

Deleting states for a target modulus You have four cascaded counters providing a total of 16 bits (overall natural count = 65,536 states). To realize an exact modulus of 50,000, how many states must be deleted (skipped)?

Accepted Answer

Introduction / Context: When the native modulus of a counter chain exceeds the required count range, designers implement truncation by decoding a terminal count and forcing a synchronous/asynchronous clear. Determining how many states to delete is a straightforward arithmetic exercise but must be done precisely to avoid off-by-one errors in the division ratio. Given Data / Assumptions: Total available states from 16 bits: 2^16 = 65,536. Desired modulus: 50,000. We delete states above the desired terminal state so the sequence repeats correctly. Concept / Approach: Deleted states = native_states − desired_modulus. After reaching the desired terminal count (49,999 if starting at 0), the counter is forced back to 0, skipping the remaining high states so that exactly 50,000 pulses form a complete cycle, giving a divide-by-50,000 output. Step-by-Step Solution: Compute native_states = 2^16 = 65,536.Compute deletion count = 65,536 − 50,000.Perform subtraction: 65,536 − 50,000 = 15,536.Implement by decoding the first unwanted state and asserting reset. Verification / Alternative check: Simulate the counter: confirm that after 50,000 input clocks, the output sequence repeats, demonstrating the correct modulus and hence the correctness of the deletion count. Why Other Options Are Wrong: 50,000 / 65,536: These are the desired and native states themselves, not the difference. 25,536: Arithmetic error (confuses difference with midpoint or mixes digits). Common Pitfalls: Off-by-one errors when the sequence starts at 1 instead of 0; neglecting synchronous clear timing which can add one extra count if not aligned with the clock edge. Final Answer: 15,536

Question 12

Cascaded MOD-5 counters — overall counting range Three counters, each with modulus 5 (MOD-5), are cascaded in series. What is the overall modulus (maximum unique count before the sequence repeats)?

Accepted Answer

Introduction / Context: Cascading digital counters multiplies their individual moduli. This question checks whether you can determine the total counting range when multiple modulus-N stages are chained, a common design in timing dividers and sequence generators. Given Data / Assumptions: There are three cascaded counters. Each counter is modulus 5 (counts 0 through 4 and then rolls over). The counters are connected so that the overall count cycles through every unique combination. Concept / Approach: When counters are cascaded such that one stage advances the next on overflow, the total modulus equals the product of the individual moduli. Thus, MOD-A followed by MOD-B yields MOD-(A*B); extend this by multiplication for more stages. Step-by-Step Solution: Compute total modulus: M_total = 5 * 5 * 5.5 * 5 = 25.25 * 5 = 125.Therefore, the overall modulus is 125. Verification / Alternative check: List the ranges: the least significant stage has 5 states; for each of those, the second has 5; for each pair, the third has 5. That is 5 * 5 * 5 = 125 unique combinations before repeating. Why Other Options Are Wrong: 5: would be a single MOD-5 stage only. 25: corresponds to two MOD-5 stages (5 * 5). 500: not a power-of-5 product from three MOD-5 counters. Common Pitfalls: Adding moduli instead of multiplying; forgetting that each additional cascaded stage multiplies total states. Final Answer: 125

Question 13

Purpose of the CTR DIV 8 block in a serial data path (counter divides by 8) In a system using a divide-by-8 counter labeled “CTR DIV 8” along with a control flip-flop, data output register, and a one-shot, what is the function of the divide-by-8 sta…

Accepted Answer

Introduction / Context: Divide-by-N counters are often used in serial interfaces to count received bits and control when a byte-wide register is latched or transferred. A “CTR DIV 8” suggests a modulo-8 counter, ideal for 8-bit (one byte) data framing in many systems. Given Data / Assumptions: The counter divides by 8 (tracks 8 bit times). A control flip-flop, an output register, and a one-shot are present. Typical serial byte width is 8 bits (not counting start/stop/parity). Concept / Approach: As serial bits arrive, the divide-by-8 counter increments one count per bit time. After eight counts, it signals “byte complete,” enabling a transfer or load of the parallel output register. A one-shot can generate a precise strobe or reset pulse to reinitialize the counter and control logic for the next byte. Step-by-Step Solution: 1) Count incoming bits with CTR DIV 8: 0→7.2) When the count reaches 8, assert a terminal count signal.3) Use this signal to strobe the data output register and trigger the one-shot.4) One-shot pulse resets the control FF and the divide-by-8 counter to start the next frame. Verification / Alternative check: Observe timing: every eighth bit, a strobe occurs and the counter resets, yielding a repeating byte boundary. Why Other Options Are Wrong: Dividing to match serial input rate (a): generic and not specific to byte framing. Option (b): too convoluted and implies the counter enables storage before counting all bits. Parity verification (c): parity requires XOR logic, not just a divide-by-8 counter. Common Pitfalls: Confusing clock division with bit counting for framing; overlooking the role of a one-shot as a strobe/reset generator. Final Answer: It keeps track of the eight data bits, triggering the transfer of the data through the output register and the one-shot, which then resets the control flip-flop and divide-by-8 counter.

Question 14

Active-level designation for up/down counting Given a counter designation that specifies the active logic levels for counting direction, what does it mean if the notation states that the up count is active-LOW and the down count is active-HIGH?

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Introduction / Context: Many up/down counters have direction-control inputs whose active level determines the counting direction. Recognizing “active-LOW” or “active-HIGH” notation prevents wiring mistakes and logic inversions when designing control signals. Given Data / Assumptions: One control input selects up or down counting. Active level indicates which logic level causes that action. Positive-logic system is assumed (0 = LOW, 1 = HIGH). Concept / Approach: “Active-LOW up count” means the counter increments when the up-control input is at logic 0. “Active-HIGH down count” means the counter decrements when the down-control input is at logic 1, or when the same direction line (with defined polarity) selects down mode at logic 1. Step-by-Step Solution: 1) Interpret the notation given with the device.2) Map active-LOW to logic 0 and active-HIGH to logic 1.3) Conclude which level selects each direction.4) Apply when wiring the direction control to avoid unintended counting. Verification / Alternative check: Consult a truth table: check that the counter steps up when UP=0 and steps down when DOWN=1 (or when a single DIR line uses the stated polarity). Why Other Options Are Wrong: Options a, c, d contradict the specified active-level conditions. Common Pitfalls: Ignoring active-LOW labels and assuming all controls are active-HIGH; forgetting required pull-ups/pull-downs. Final Answer: up count is active-LOW, the down count is active-HIGH

Question 15

Designing a MOD-32 binary counter — number of flip-flops How many flip-flops are required to construct a MOD-32 binary counter (i.e., a counter that cycles through 32 distinct states)?

Accepted Answer

Introduction / Context: Binary counters implemented with flip-flops have a number of states equal to 2^n, where n is the number of flip-flops (bits). Determining the number of flip-flops needed for a target modulus is a foundational skill for digital timing and sequencing design. Given Data / Assumptions: We need a counter with 32 distinct states (MOD-32). Each flip-flop contributes one binary digit (bit). States grow as powers of two: 2^n. Concept / Approach: Find the smallest n such that 2^n ≥ 32. Because 2^5 = 32, five flip-flops are exactly sufficient and produce the required modulus without wasted states. Step-by-Step Solution: 1) Evaluate powers: 2^4 = 16 (insufficient).2) Next power: 2^5 = 32 (matches requirement).3) Therefore, n = 5 flip-flops.4) Implement as ripple or synchronous as needed for timing constraints. Verification / Alternative check: Simulate a 5-bit counter; it cycles through 00000 to 11111 (32 states) before repeating. Why Other Options Are Wrong: 3 and 6 do not yield 32 states (2^3=8, 2^6=64). 45 is unrelated and not a number of flip-flops. Common Pitfalls: Confusing decimal modulus with binary powers; forgetting that extra states appear if n is larger than necessary. Final Answer: 5

Question 16

Seven-segment display — segments required to show the digit 2 For a standard seven-segment display with segments a–g, which segments must be active to display the decimal digit 2?

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Introduction / Context: Seven-segment displays render decimal digits using combinations of the segments a through g. Knowing the correct segment activation pattern is essential for designing decoders and driving logic for numeric indicators in embedded systems and instrumentation. Given Data / Assumptions: Standard seven-segment labeling: a (top), b (upper-right), c (lower-right), d (bottom), e (lower-left), f (upper-left), g (middle). We want to display the decimal digit 2. Common-cathode/common-anode electrical polarity is irrelevant to the logical pattern. Concept / Approach: The digit 2 consists of the top bar, upper-right, middle, lower-left, and bottom bars illuminated. That corresponds to segments a, b, g, e, and d (order may vary). Segment naming confirms the exact set needed. Step-by-Step Solution: 1) Start with the top bar → segment a ON.2) Upper-right vertical → segment b ON.3) Middle bar → segment g ON.4) Lower-left vertical → segment e ON.5) Bottom bar → segment d ON. Verification / Alternative check: Compare with other digits: “3” would be a, b, c, d, g (no e), confirming that “2” uniquely uses e instead of c. Why Other Options Are Wrong: a, b, c, d, g: that shows “3,” not “2.” a, c, d, f, g: that shows “5” (left side segments differ). a, b, c, d, e, f: that would illuminate six segments and does not correspond to a standard single digit. Common Pitfalls: Mixing up e and c (left vs. right lower verticals) or forgetting the middle bar g for “2.” Final Answer: a, b, d, e, and g

Question 17

Minimum logic for a MOD-64 synchronous binary counter Which group of logic devices represents the minimum required to implement a MOD-64 synchronous binary counter?

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Introduction / Context: A synchronous binary counter advances all flip-flops in lockstep with the clock, using combinational logic to generate each stage’s toggle condition. Determining the minimum hardware helps optimize resource usage in ASICs, FPGAs, and discrete designs. Given Data / Assumptions: Target modulus is 64 → requires 6 bits since 2^6 = 64. We may use multi-input AND gates where helpful (common in practice). Counter style is synchronous (not ripple), so toggling is controlled by combinational conditions. Concept / Approach: For a binary counter with T-type behavior: T0 = 1 (LSB toggles every clock), T1 = Q0, T2 = Q1 * Q0, T3 = Q2 * Q1 * Q0, T4 = Q3 * Q2 * Q1 * Q0, T5 = Q4 * Q3 * Q2 * Q1 * Q0. Using one multi-input AND per stage that needs a product term yields four AND gates for stages 2 through 5; stages 0 and 1 need none beyond simple wiring. Step-by-Step Solution: List toggles: T0=1; T1=Q0; T2=Q1Q0; T3=Q2Q1Q0; T4=Q3Q2Q1Q0; T5=Q4Q3Q2Q1Q0.Provide ANDs: one each to form T2, T3, T4, and T5 (four total).Use six flip-flops: one per counter bit to achieve 2^6 states.Thus, minimum parts: six flip-flops and four AND gates. Verification / Alternative check: Synthesis tools for FPGAs commonly infer this structure with equivalent LUT usage; discrete logic implementations map directly to available multi-input AND gates. Why Other Options Are Wrong: Five flip-flops: can only reach 2^5 = 32 states (MOD-32). Seven flip-flops: unnecessary hardware for MOD-64; also AND count is not minimal. Four flip-flops: at most MOD-16. Common Pitfalls: Assuming each stage requires many pairwise 2-input ANDs; if multi-input ANDs are available, the count reduces to one per higher stage. Final Answer: Six flip-flops, four AND gates

Question 18

Understanding a multiplexed display interface A “multiplexed display” being driven by a logic circuit typically behaves like which of the following digital functions?

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Introduction / Context: In digital electronics, the word “multiplexed” often refers to the technique of selecting one of many inputs to drive a shared output resource for a short time slice. This is central to display scanning, where multiple digit modules share segment lines and are enabled one at a time in rapid succession. Given Data / Assumptions: A logic circuit time-shares resources among several display elements (digits). Only one source is selected to drive the common output bus at any instant. Human persistence of vision makes sequential updates appear simultaneous. Concept / Approach: The fundamental digital component that models this selection is the multiplexer (data selector). A multiplexer accepts many data inputs and, under control of select lines, routes exactly one input to the output. In displays, digit-select lines and segment busses implement the same concept at the system level. Step-by-Step Solution: Identify device behavior: multiple inputs → one chosen output at a time.Map to definition: a multiplexer allows one of several inputs to pass to the output.Relate to displays: the controller selects each digit in turn, applying its data to shared segment lines.Conclude that option (b) matches the multiplexed function. Verification / Alternative check: Contrast with a demultiplexer (one input to many outputs), which is not the typical function implied by “multiplexed display” selection of input data. Why Other Options Are Wrong: (a) describes a demultiplexer, not a multiplexer. (c) is a broadcast or bus-driver scenario, not selected routing. (d) is overly specific and not a generic definition. Common Pitfalls: Confusing the system-level display scanning (digit enabling) with the data-selection concept; both occur, but the term “multiplexed” aligns with selecting one of many inputs at a time. Final Answer: accepts data inputs from several lines and allows one of them at a time to pass to the output

Question 19

Cascaded modulus counters — lowest output frequency A 12 MHz clock is applied to a cascaded counter chain containing a modulus-5 stage, a modulus-8 stage, and a modulus-10 stage. What is the lowest output frequency available from the chain?

Accepted Answer

Introduction / Context: Cascading counters with different moduli multiplies the overall division factor. Determining the final output frequency after multiple stages is a routine step in clock-generation and timing applications. Given Data / Assumptions: Input clock fin = 12 MHz. Three cascaded stages with moduli 5, 8, and 10. Stages are cascaded so each divides the frequency presented by the previous one. Concept / Approach: The total division factor equals the product of the individual moduli. Therefore, fout = fin / (5 * 8 * 10). Convert units carefully to present the result in kilohertz for comparison to the options. Step-by-Step Solution: Compute total division: 5 * 8 * 10 = 400.Apply to input: fout = 12,000,000 Hz / 400.Perform division: 12,000,000 / 400 = 30,000 Hz.Convert to kHz: 30,000 Hz = 30 kHz. Verification / Alternative check: Stepwise: 12 MHz → /5 = 2.4 MHz → /8 = 0.3 MHz → /10 = 0.03 MHz = 30 kHz. Matches the calculation. Why Other Options Are Wrong: 10 kHz and 20 kHz: correspond to stronger division than the chain provides. 60 kHz: corresponds to halving the correct division factor (200 instead of 400). Common Pitfalls: Adding moduli or mis-converting units; forgetting to multiply all stage moduli. Final Answer: 30 kHz

Question 20

Counters — Meaning of a Parallel Load Operation In synchronous digital design, what is meant by a parallel load of a counter or register? Choose the best description that captures how data is applied and when it is captured by the flip-flops (FFs).

Accepted Answer

Introduction / Context: A fundamental capability of synchronous counters and registers is the ability to capture a multi-bit value in one operation. This is commonly called a parallel load. Understanding how and when a parallel load occurs helps students correctly wire control signals such as load, reset, and enable, and to predict timing behavior in finite-state machines and data paths. Given Data / Assumptions: The device is a synchronous counter or register built from edge-triggered flip-flops. The device provides dedicated parallel data inputs (e.g., D3..D0) and a load control input (e.g., LD or PL). The system uses a single system clock to coordinate state changes. Concept / Approach: Parallel load means the multi-bit value present on the external data inputs is transferred into all internal flip-flops simultaneously at the designated clocking event when the load control is asserted. This is different from serial loading (one bit per clock) and from asynchronous preset/clear (which forces 1s or 0s independent of the clock). Step-by-Step Solution: Identify control: the load input (active-HIGH or active-LOW) enables the parallel capture.Clocking: on the active clock edge, with load asserted, each FF captures its corresponding D input bit.Result: the N-bit register changes all bits concurrently to match the applied N-bit word.Contrast: with load deasserted, the device either counts (for counters) or holds (for registers) per its normal function. Verification / Alternative check: Datasheets for common counters (e.g., 74161/74163 synchronous counters) show a parallel load input (PL). When PL is active, Q takes D on the next clock; when PL is inactive, the device counts or holds according to enable signals. Simulation confirms that all bits update together at the clock edge. Why Other Options Are Wrong: Each flip-flop loaded on separate clocks: That describes a sequential or staged load, not parallel loading. The counter is cleared: That is reset, not load. All FFs are preset asynchronously: Asynchronous preset ignores the clock and forces 1s, not arbitrary data words. Common Pitfalls: Confusing “preset/clear” with “load,” and assuming load acts immediately without a clock; in synchronous parts, loading occurs at the clock edge when the load control is asserted. Final Answer: All flip-flops are simultaneously loaded from their parallel data inputs on a single active clock edge.

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