Question 1

Up/Down Counters — Next State in DOWN Mode A 4-bit up/down binary counter is operating in the DOWN mode and currently in state 1100 (decimal 12). What state will it go to on the next active clock pulse?

Accepted Answer

Introduction / Context: Binary counters are ubiquitous in timing and sequencing. Correctly predicting the next state of an up/down counter reinforces understanding of binary arithmetic and counter direction control. Here, we analyze the DOWN mode behavior from a given 4-bit state. Given Data / Assumptions: Counter width: 4 bits (Q3 Q2 Q1 Q0). Present state: 1100 (binary) = 12 (decimal). Counter direction: DOWN (decrement by 1 each count). No terminal count reload or modulus less than 16 is implied. Concept / Approach: In DOWN mode, the next state equals current state minus one, computed in binary with borrow as needed. For a straight 4-bit binary counter without truncation, the sequence near 12 goes: 1100 → 1011 → 1010 ... down to 0000, then wraps to 1111 on the subsequent count. Step-by-Step Solution: Interpret 1100 as decimal 12.Compute 12 − 1 = 11.Convert 11 to binary: 1011.Therefore, next state is 1011. Verification / Alternative check: Subtract one in binary directly: 1100 − 0001 → borrow from Q2 into Q1 Q0 yields 1011, confirming the arithmetic. Why Other Options Are Wrong: 1101: That is +1 (UP mode), not −1. 1111: That is the wrap state after 0000 in DOWN counting, not immediately after 1100. 0000: Many counts away (12 steps) from 1100 in DOWN mode. Common Pitfalls: Adding instead of subtracting, or assuming immediate wrap without reaching 0000 first. Final Answer: 1011

Question 2

Asynchronous (Ripple) Counter — Number of States How many distinct states are available in a 2-bit asynchronous (ripple) binary counter?

Accepted Answer

Introduction / Context: The number of unique states in a counter determines its modulus and how often it repeats. Whether synchronous or asynchronous, an N-bit binary counter can represent 2^N distinct states. Recognizing this quickly is a core digital logic skill. Given Data / Assumptions: Counter type: binary asynchronous (ripple) counter. Width: 2 bits (Q1 Q0). No truncation or preset modulus less than 2^N is specified. Concept / Approach: A binary counter with N flip-flops cycles through all binary combinations from 0 to (2^N − 1) unless gating trims the count. For N = 2, the set is {00, 01, 10, 11}, which totals four distinct states and constitutes a MOD-4 counter. Step-by-Step Solution: Compute 2^N with N = 2 → 2^2 = 4.Enumerate states: 00, 01, 10, 11.Confirm wrap: after 11, the next count wraps back to 00.Therefore, there are 4 distinct states. Verification / Alternative check: Simulate a ripple counter with two T flip-flops toggling on the preceding Q. The observed sequence shows four unique patterns before repeating. Why Other Options Are Wrong: 1, 2: Underestimate the state space; even a single flip-flop has 2 states. 8: Would require 3 bits (2^3). Common Pitfalls: Confusing number of states with number of flip-flops; forgetting the 2^N relationship. Final Answer: 4

Question 3

Synchronous vs. Ripple Counters — Effective Delay Synchronous construction reduces a counter’s observable propagation delay to approximately the delay of which elements?

Accepted Answer

Introduction / Context: Ripple (asynchronous) counters suffer cumulative delays because each flip-flop toggles the next. Synchronous counters clock all flip-flops in parallel, so the long chain of sequential delays is eliminated. Understanding what limits timing in the synchronous case is key to high-speed design. Given Data / Assumptions: Synchronous counter: all FFs share the same clock edge. Next-state logic is combinational (gates) driving each D/T input. Interest: worst-case path from the clock edge to valid outputs or terminal-count decode. Concept / Approach: In a synchronous counter, on the clock edge, all FFs update simultaneously with a clock-to-Q delay (tCQ). The decode or next-state decision typically passes through a small amount of combinational logic before being observed externally or used internally. Hence, the effective delay is dominated by a single FF delay plus the propagation of a small gate network, not a cascade of FF-to-FF delays. Step-by-Step Solution: At CLK edge → FF outputs update after tCQ.Signals then propagate through minimal combinational gates (e.g., increment logic, decode).The critical path is approximately tCQ + tGate.Therefore, the delay is effectively that of a single flip-flop and a gate. Verification / Alternative check: Timing diagrams and datasheets for synchronous counters (e.g., 74161) show specified clock-to-output and decode delays, without per-stage rippling as in 7490/7493 ripple counters. Why Other Options Are Wrong: All flip-flops and gates in series: Describes ripple behavior, not synchronous. After a 3-count boundary: Arbitrary and not a general principle. A single gate: Omits the unavoidable clock-to-Q of at least one flip-flop. Common Pitfalls: Assuming synchronous counters eliminate all delay; they reduce chain delay but still exhibit tCQ and small logic delay. Final Answer: a single flip-flop and a gate

Question 4

BCD Counters — Interpreting the Term A BCD counter is best described as which type of modulus counter for digital systems?

Accepted Answer

Introduction / Context: BCD (Binary-Coded Decimal) counters are common in time and frequency instrumentation because they align with decimal digits. Unlike pure binary counters, BCD counters restrict the state space to ten valid patterns per digit, simplifying decimal readouts on displays and printouts. Given Data / Assumptions: Single BCD digit uses 4 bits to encode 0–9. Illegal states 1010–1111 are skipped or corrected by internal reset logic. Each decade stage divides frequency by 10. Concept / Approach: A BCD counter is, by definition, a decade counter with modulus 10. It cycles through 0000 (0) to 1001 (9) and then resets to 0000, dividing the input frequency by 10. Multi-digit BCD counters cascade decades to form decimal numbers (tens, hundreds, etc.). Step-by-Step Solution: Define BCD digit: 4-bit code for 0–9 only.Identify modulus: number of valid states = 10 → MOD-10.Count sequence: 0000→0001→…→1001→wrap to 0000.Therefore, a BCD counter is a decade (mod-10) counter. Verification / Alternative check: Examine common TTL/CMOS parts (e.g., 7490 as decade with appropriate wiring, 4510 CMOS BCD up/down): datasheets specify divide-by-10 behavior and show invalid state handling. Why Other Options Are Wrong: Binary counter of unspecified modulus: Too vague; BCD specifically implies ten states. Full-modulus counter using all 16 4-bit combos: That would be a MOD-16 binary counter, not BCD. Divide-by-10 using 0000–1111: Contradiction; BCD excludes 1010–1111. Common Pitfalls: Assuming BCD equals binary; in BCD, some 4-bit codes are invalid and must be handled. Final Answer: a decade (modulo-10) counter that cycles through 0000 to 1001

Question 5

Ripple Counters — Natural (Maximum) States for 4 Bits How many natural states (untrimmed combinations) exist in a 4-bit ripple counter?

Accepted Answer

Introduction / Context: Ripple counters advance through all binary combinations defined by their width unless additional gating trims the sequence. The number of natural states equals the maximum count before wrapping back to zero. This determines both the modulus and the frequency division ratio. Given Data / Assumptions: Counter width: 4 flip-flops (Q3..Q0). No external reset logic to skip states. Binary counting (not Gray or BCD). Concept / Approach: For N bits, the number of natural states is 2^N. Thus a 4-bit counter cycles through 16 distinct states (0000 to 1111) and divides the input frequency by 16 at the MSB output. If a lesser modulus is required (e.g., MOD-10), extra logic is used to asynchronously or synchronously reset at the desired terminal count. Step-by-Step Solution: Compute 2^N for N = 4 → 16.Enumerate conceptually: 0000 … 1111 (16 total patterns).Wrap behavior: next count after 1111 returns to 0000.Therefore, the 4-bit ripple counter has 16 natural states. Verification / Alternative check: Simulation or truth-table expansion verifies that 16 unique states occur before repetition. The MSB toggles at fin/16, confirming the divide ratio. Why Other Options Are Wrong: 4 or 8: Correspond to 2-bit or 3-bit counters, not 4-bit. 32: Would require 5 bits. Common Pitfalls: Confusing “natural states” with “desired modulus”; trimming requires extra logic beyond the natural 2^N count. Final Answer: 16

Question 6

TTL Counter ICs — 7490 vs. 7493 What is the key difference in modulus between the TTL counters 7490 and 7493?

Accepted Answer

Introduction / Context: Classic 74xx counters provide fixed divide ratios without extra logic. Selecting the correct device for a decade or binary division requires knowing each chip’s modulus. Two frequently referenced parts are the 7490 and 7493. Given Data / Assumptions: 7490: commonly used as a decade counter. 7493: commonly used as a binary divide-by-16 counter. Standard wiring per datasheets is assumed. Concept / Approach: Modulus (MOD-N) indicates how many input pulses occur per full cycle of the counter and equals the frequency division factor. The 7490 provides MOD-10 (decade). The 7493 is a 4-bit binary (MOD-16) counter. They are often cascaded to form higher decimal or binary divisions respectively. Step-by-Step Solution: Identify 7490 behavior: decade sequence 0–9 then reset → divide-by-10.Identify 7493 behavior: binary 0–15 then wrap → divide-by-16.Map to choice: 7490 MOD-10, 7493 MOD-16.Hence, option A is correct. Verification / Alternative check: Back-of-envelope: cascade four 7490 decades → decimal clocks; cascade N 7493s → binary scalers of 2^(4N). Datasheets confirm the intended moduli. Why Other Options Are Wrong: Other pairings swap or misstate the true moduli. Common Pitfalls: Confusing 7492 (divide-by-12) with 7493 (divide-by-16); both are popular but serve different roles. Final Answer: 7490 is a MOD-10, 7493 is a MOD-16

Question 7

Synchronous Up/Down Counters — Reversibility During Operation Which statement best describes how a synchronous up/down counter can change direction during its counting sequence?

Accepted Answer

Introduction / Context: Up/down counters are frequently used for position tracking, incremental measurement, and reversible state machines. Whether you can switch direction on-the-fly affects control logic design and responsiveness to user inputs such as direction switches or encoder polarity changes. Given Data / Assumptions: Synchronous counter: all flip-flops clocked together. Direction input (UP/DOWN) selects increment or decrement logic in the combinational network. No special lockout or reset requirement is imposed. Concept / Approach: Because next-state logic is evaluated every clock and can include the direction signal, changing the UP/DOWN control prior to a clock edge alters the next transition from +1 to −1 (or vice versa). Therefore, reversal can occur at any count value without a reset, as long as setup/hold timing for the direction control is met. Step-by-Step Solution: Direction input = 1 → increment on next clock.Direction input = 0 → decrement on next clock.Toggle direction before the next clock while meeting setup/hold.Counter reverses immediately at the next tick, regardless of current state. Verification / Alternative check: Reference synchronous counter parts (e.g., 74191/74193). Datasheets and timing diagrams show immediate directional effect on the next active edge when the control input is changed in time. Why Other Options Are Wrong: Must continue once started / must reset first: Not required for synchronous designs. Cannot be reversed: Contradicts standard up/down counter operation. Common Pitfalls: Changing direction too close to the clock edge and violating setup/hold, leading to metastability or a missed reversal. Final Answer: In general, the counter can be reversed at any point in its counting sequence.

Question 8

8421 BCD Counter — Identify an Invalid Output State Which of the following is an invalid output state for a 4-bit 8421 BCD counter stage?

Accepted Answer

Introduction / Context: An 8421 BCD counter encodes decimal digits 0 through 9 using a 4-bit binary code. Only ten patterns are valid (0000 to 1001). Recognizing invalid states is essential for designing decode logic and for ensuring that counters recover correctly from power-up or noise-induced illegal states. Given Data / Assumptions: Valid BCD codes: 0000–1001. Invalid BCD codes: 1010–1111. 8421 weighting implies standard BCD, not excess-3 or other variants. Concept / Approach: To identify an invalid state, check whether the 4-bit pattern represents a decimal digit greater than 9. Any pattern with the two MSBs equal to 11 (i.e., 12–15) is invalid for 8421 BCD. Likewise, 1010 (10) through 1101 (13) are also invalid. Step-by-Step Solution: List options: 1110, 0000, 0010, 0001.Evaluate validity: 0000 (0), 0001 (1), 0010 (2) are valid BCD codes.Evaluate 1110: equals decimal 14, which is not a valid BCD digit.Thus, 1110 is an invalid BCD counter output. Verification / Alternative check: Consult any BCD truth table: codes from 0000 to 1001 are valid; 1110 falls outside the permitted range. Why Other Options Are Wrong: 0000: valid BCD for 0. 0010: valid BCD for 2. 0001: valid BCD for 1. Common Pitfalls: Confusing 8421 BCD with other decimal codes (e.g., Gray or excess-3), or assuming all 4-bit patterns are acceptable for BCD. Final Answer: 1110

Question 9

Implementing a Digital One-Shot in HDL Which approach correctly describes how to implement a one-shot (single pulse per trigger event) using a hardware description language?

Accepted Answer

Introduction / Context: A one-shot (monostable) generates a single, time-limited pulse for each qualifying trigger. In HDL for FPGAs or CPLDs, this is accomplished digitally using logic and flip-flops, not analog RC components. The design must respond once per edge and produce a controlled pulse width in clock cycles. Given Data / Assumptions: A synchronous clock domain is available. The trigger input may be asynchronous and should be synchronized. Pulses are measured in integer clock cycles. Concept / Approach: Use an edge detector to convert a rising transition into a one-clock strobe, then start a counter or timer that holds the output HIGH for a programmed number of cycles. This ensures exactly one output pulse per trigger edge, regardless of how long the trigger level persists. Step-by-Step Solution: Synchronize trigger with two flip-flops to avoid metastability.Edge detect: pulse_start = sync_trig and (not sync_trig_d1).When pulse_start = 1, load a down-counter with N (pulse width in cycles).While counter > 0, assert output and decrement each clock.When counter reaches 0, deassert output and re-arm for the next edge. Verification / Alternative check: Simulation with long trigger levels and closely spaced edges shows one output pulse per 0→1 transition and a consistent pulse width of N cycles. Hardware timing reports confirm that the logic is purely digital and synthesizable. Why Other Options Are Wrong: RC network in HDL: Analog RC cannot be described/synthesized meaningfully in standard FPGA logic. Generic “one-shot” library function: Not a universal primitive; vendors provide counters/timers instead. Level trigger: Produces level-sensitive behavior, not a single pulse per edge. Common Pitfalls: Failing to synchronize the trigger, neglecting edge detection (causing retriggers), or allowing retriggering while the pulse is active without explicit design intent. Final Answer: Apply the concept of a counter driven by a rising-edge detector to generate a fixed-width pulse.

Question 10

Modulus-10 (decade) counter — minimum hardware requirement For a MOD-10 (decade) counter that counts 0 through 9 and then recycles to 0, how many flip-flops are required at minimum (irrespective of synchronous or ripple style)?

Accepted Answer

Introduction / Context: A decade (MOD-10) counter is a sequential circuit that steps through ten distinct states (0 to 9) and then resets to 0. Determining the minimum number of flip-flops focuses on state capacity (2^n) rather than on whether the design is synchronous or ripple. This is a core idea in digital design when matching required modulus to available binary storage. Given Data / Assumptions: Required modulus: 10 states. Binary storage uses n flip-flops giving up to 2^n states. Non-power-of-two modulus achieved via decode/reset logic. Concept / Approach: Find the smallest n such that 2^n ≥ 10. Then, add simple combinational decoding to reset the counter after reaching decimal 9 (binary 1001). The rest of the 2^n state space is unused and prevented by the reset action. Step-by-Step Solution: Compute capacities: 2^3 = 8 (insufficient), 2^4 = 16 (sufficient).Minimum n = 4 flip-flops to represent at least 10 states.Use decode of 1010 (decimal 10) to generate reset back to 0000.Therefore, minimum hardware is 4 flip-flops (plus small decode logic). Verification / Alternative check: Simulating a 4-bit counter with reset-on-10 shows the sequence 0000→…→1001 then reset to 0000, giving exactly 10 states per cycle. Why Other Options Are Wrong: 10 flip-flops and 5 flip-flops greatly exceed the minimum for MOD-10. 2 flip-flops can represent only 4 states. “Synchronous clocking” is a style, not a quantity of flip-flops; it does not answer the question. Common Pitfalls: Assuming a non-power-of-two modulus needs that many flip-flops; forgetting that decoding unused states yields the desired modulus with the minimal n. Final Answer: 4 flip-flops

Question 11

Synchronous vs. ripple counters — speed advantage Why can a synchronous (parallel-clocked) counter operate at a higher maximum clock frequency than a ripple (asynchronous) counter?

Accepted Answer

Introduction / Context: Counter speed is limited by how state changes propagate. Ripple counters clock each flip-flop from the previous stage's output, introducing cumulative delays. Synchronous counters apply the same clock to all stages, so outputs settle simultaneously after one stage of combinational logic. Recognizing this difference explains why synchronous counters achieve higher clock rates. Given Data / Assumptions: Synchronous counters share a common clock (parallel clocking). Ripple counters chain the clock through toggling outputs. Propagation delay through flip-flops and logic limits f_max. Concept / Approach: In ripple counters, a transition must ripple through N flip-flops, so worst-case settling time ≈ N * t_pd_ff. In synchronous counters, all flip-flops sample together, and delay is dominated by logic depth + one flip-flop t_pd, typically far smaller than N * t_pd_ff. Step-by-Step Solution: Ripple: sequential toggles → cumulative delay across stages.Synchronous: common clock edge → simultaneous state change.Result: synchronous architecture supports higher f_max. Verification / Alternative check: Timing diagrams show ripple outputs changing at staggered times, whereas synchronous outputs change nearly together after the same edge, enabling tighter timing closure. Why Other Options Are Wrong: “One after the other” describes ripple, which is slower. Claiming synchronous cannot be faster contradicts practice. “Ripple is faster” is false for typical technologies. Common Pitfalls: Ignoring combinational decode delay in synchronous designs; reading counter outputs during ripple transitions causing glitches. Final Answer: The flip-flops change at the same time.

Question 12

Terminal count of a decade (MOD-10) binary counter In a typical binary decade counter that counts 0–9 and then resets, what is the terminal count pattern just before recycling?

Accepted Answer

Introduction / Context: The term “terminal count” refers to the last valid state in the counting sequence before the counter recycles to 0. For a MOD-10 (decade) counter implemented with binary flip-flops and reset decode logic, understanding which pattern is the terminal count avoids confusion with the reset-detect pattern itself (which is not a state in the sequence). Given Data / Assumptions: Counter counts 0000 (0) up to 1001 (9). Upon reaching 1010 (10), reset logic forces 0000. Binary outputs are active-high and standard order Q3..Q0. Concept / Approach: Enumerate valid states and identify the last one before reset occurs. In a binary decade, states 0000..1001 are valid; the detection of 1010 asserts reset. Thus, the terminal count is 1001 (decimal 9). Step-by-Step Solution: List sequence: 0000, 0001, …, 1001.Next binary value is 1010, which is decoded to reset.Therefore, terminal count (last valid) = 1001. Verification / Alternative check: Check typical 74xx90/92/160-series decades: documentation shows reset gates wired to detect 1010 (or equivalent), confirming 1001 is the terminal state. Why Other Options Are Wrong: 0000 is the first state, not the last. 1010 is the reset-detect pattern and not part of the normal sequence. 1111 is unrelated to decade counting and appears in straight binary MOD-16 sequences, not in a decade counter. Common Pitfalls: Confusing “terminal count” with “reset code,” and assuming the counter actually enters 1010. Properly designed decades skip 1010 by resetting immediately. Final Answer: 1001

Question 13

Combinational vs. sequential logic — key difference Which statement best captures the difference between combinational logic and sequential logic in digital systems?

Accepted Answer

Introduction / Context: Digital subsystems are broadly divided into combinational logic and sequential logic. Combinational circuits compute outputs purely from present inputs, while sequential circuits store state and usually change outputs in response to clock (timing) events. Distinguishing these categories is foundational for timing analysis, hazard mitigation, and state-machine design. Given Data / Assumptions: Combinational logic: no memory, outputs = f(current inputs). Sequential logic: has memory (flip-flops/latches), typically clocked. Positive logic conventions and idealized devices assumed. Concept / Approach: Because sequential circuits store prior information, they need an event to update state. In synchronous systems this is a clock edge; in asynchronous sequential designs, internal conditions cause transitions, but practical mainstream designs are clocked. Combinational logic does not require a clock; it reacts immediately (after propagation delay) to changes at its inputs. Step-by-Step Solution: Identify memoryless vs. memory-based behavior.Associate memory updates with timing pulses (clocks).Conclude the provided statement correctly differentiates the two. Verification / Alternative check: Truth tables suffice for combinational blocks; sequential blocks require state tables/diagrams indicating transitions on clock edges or conditions. Why Other Options Are Wrong: “Both triggered by timing pulses” is incorrect; only sequential logic inherently needs timing to update state. “Neither is triggered” ignores the role of the clock in sequential systems. Common Pitfalls: Equating asynchronous sequential circuits with combinational logic; forgetting that even combinational blocks exhibit propagation delay but do not require a clock to function. Final Answer: Combinational circuits are not triggered by timing pulses, sequential circuits are triggered by timing pulses.

Question 14

Meaning of the parallel outputs of a counter In a digital counter, the parallel output lines Qn..Q0 represent the:

Accepted Answer

Introduction / Context: Counters are registers that advance through a sequence of states. The most common way to observe the current state is via parallel output pins (Q lines). Knowing exactly what these lines convey avoids misinterpretation when interfacing counters with displays, microcontrollers, or comparators. Given Data / Assumptions: Counter implemented with flip-flops providing parallel outputs. Binary (or BCD/Gray) encoding as designed. Outputs are sampled after settling to avoid ripple glitches (if asynchronous). Concept / Approach: The Q lines collectively form the present state word of the counter. In straight binary counters this word equals the numeric count value. Other encodings (BCD, Gray) still present a multi-bit word representing the state. It is not the clock frequency; rather, it is data whose value changes once per count event. Step-by-Step Solution: Interpret Q lines as bus bits: Qn..Q0 = current count code.Treat this as a parallel data word suitable for decoding or display.Use downstream logic to convert or compare as needed. Verification / Alternative check: Hook Q lines to a binary display or microcontroller port; readings match the instantaneous count value (subject to propagation delay for ripple types). Why Other Options Are Wrong: Clock frequency is a property of the input clock, not the parallel outputs. Counter modulus is a design parameter (maximum states), not what the outputs directly present. “Clock count” is vague; the precise term is the present count value as a data word. Common Pitfalls: Sampling ripple counters during transitions; ignoring encoding differences (BCD vs binary). Final Answer: parallel data word

Question 15

Synchronous vs. asynchronous events — identifying true statements Which of the following statements is true regarding synchronous and asynchronous events in digital systems?

Accepted Answer

Introduction / Context: “Synchronous” implies timing with respect to a shared clock; “asynchronous” implies independence from a common timing reference. Distinguishing these categories is essential for designing safe interfaces and for analyzing metastability risks when crossing clock domains. Given Data / Assumptions: Synchronous events are coordinated by a clock edge or phase. Asynchronous events are not guaranteed to align to a single clock. We use conventional positive-logic, edge-sensitive clocking assumptions. Concept / Approach: Synchronous events in one clock domain occur “together” in the sense of being referenced to the same edge, while asynchronous events can arrive at arbitrary times relative to that edge. Thus, stating that asynchronous events “do not occur at the same time” (i.e., are not clock-aligned) captures the correct essence better than the other options. Step-by-Step Solution: Define synchronous: governed by a common clock → aligned activity.Define asynchronous: no common clock → unaligned activity.Select statement reflecting lack of alignment for asynchronous events. Verification / Alternative check: Consider an external button (asynchronous) into a CPU clock domain; arrivals are not clock-aligned and need synchronization. Why Other Options Are Wrong: Asynchronous events are not clock-controlled. Synchronous events inherently need a clock. “Only asynchronous events need a control clock” is backwards. Common Pitfalls: Interpreting “do not occur at the same time” too literally; the intent is “not aligned to a common clock.” Always add synchronizers for asynchronous inputs. Final Answer: Asynchronous events do not occur at the same time.

Question 16

Truncated modulus — identify the non-truncated case Which of the following is not an example of a truncated modulus in a binary counter design?

Accepted Answer

Introduction / Context: A “truncated modulus” results when a binary counter, which naturally cycles through 2^n states, is forced to recycle earlier using decode/reset logic to achieve a non-power-of-two modulus (e.g., 9, 11). Identifying which modulus is not truncated reinforces the relationship between natural binary capacity and custom count lengths. Given Data / Assumptions: Binary counters natively implement moduli of 2^n. Any other modulus requires decoding and resetting. We compare 8, 9, 11, and 15. Concept / Approach: Check if each choice equals 2^n for an integer n. If yes, it is a natural modulus and therefore not truncated. If not, it must be truncated from a higher power-of-two sequence by early reset. Step-by-Step Solution: Evaluate powers of two: 2^3 = 8 (natural), 2^4 = 16.9, 11, 15 are not powers of two.Therefore, 8 is the only non-truncated modulus; others are truncated. Verification / Alternative check: Design examples: MOD-9 or MOD-11 counters are made by decoding a specific state and resetting; MOD-8 requires simply three flip-flops with no extra decode. Why Other Options Are Wrong: 9, 11, and 15 require truncation from 16 (2^4) using reset logic. Common Pitfalls: Confusing “MOD-15” with “4-bit maximum” (which is 16). MOD-15 is indeed truncated; the natural 4-bit modulus is 16. Final Answer: 8

Question 17

Ripple counter worst-case delay with unequal tPHL/tPLH Four flip-flops form a ripple counter. Each has tPHL = 22 ns and tPLH = 15 ns. What is the maximum total delay that can occur through the chain?

Accepted Answer

Introduction / Context: In ripple (asynchronous) counters, each stage is clocked by the previous stage’s output, so propagation delays accumulate. When rise and fall delays differ (tPLH vs tPHL), the worst-case total chain delay uses the larger per-stage delay because any transition may propagate through the polarity that is slowest at each step. Estimating this upper bound is key to deciding maximum safe clock rates and decode timing windows. Given Data / Assumptions: Four cascaded flip-flops (4-bit ripple counter). Per-stage delays: tPHL = 22 ns, tPLH = 15 ns. Worst-case chain delay sought. Concept / Approach: The total worst-case ripple time ≈ number_of_stages * max(tPHL, tPLH). That ensures coverage regardless of edge polarities encountered along the chain. For this device, tPHL dominates at 22 ns. Step-by-Step Solution: Determine dominant delay per stage: max(22, 15) = 22 ns.Multiply by number of stages: 4 * 22 ns.Compute result: 88 ns maximum ripple delay. Verification / Alternative check: Timing diagrams for transitions like 1111→0000 illustrate sequential toggling with per-stage worst-case delays accumulating to roughly 88 ns before all bits settle. Why Other Options Are Wrong: 15 ns, 22 ns: single-stage delays, not the full chain. 60 ns: assumes 4 * 15 ns; ignores the slower direction tPHL. Common Pitfalls: Using average delay or the faster edge; ignoring that decode logic must wait for the MSB to settle to avoid glitches. Final Answer: 88 ns

Question 18

State capacity of a 3-bit asynchronous counter How many distinct count states does a 3-bit (three-flip-flop) asynchronous binary counter provide?

Accepted Answer

Introduction / Context: Each flip-flop holds one binary digit. Regardless of ripple or synchronous style, n flip-flops can encode up to 2^n distinct states. This question checks basic recall of binary capacity for a 3-bit counter, a recurring building block in larger designs and in divide-by-N frequency generation. Given Data / Assumptions: Three flip-flops (n = 3). Binary counting (no truncation/reset early). Idealized behavior without illegal states. Concept / Approach: The number of representable states equals the number of distinct combinations of 3 bits: 2 * 2 * 2 = 8. In free-running counters, these states cycle naturally from 000 to 111 and back to 000. Step-by-Step Solution: Apply formula: states = 2^n.Compute: 2^3 = 8.Therefore, there are eight unique count states. Verification / Alternative check: Enumerate explicitly: 000, 001, 010, 011, 100, 101, 110, 111 → 8 states. Why Other Options Are Wrong: 2 and 4 correspond to 1-bit and 2-bit capacities. 16 corresponds to 4 bits (2^4). Common Pitfalls: Confusing modulus with number of flip-flops; forgetting that truncation (e.g., MOD-6) requires extra decode beyond the natural 2^n states. Final Answer: 8

Question 19

Common applications of MOD-6 / MOD-12 counters MOD-6 and MOD-12 counters (and their multiples) are most commonly applied as:

Accepted Answer

Introduction / Context: Time-keeping divides seconds, minutes, and hours into bases of 6, 10, and 12 (e.g., 60 seconds per minute, 60 minutes per hour, 12 hours per half-day). Digital clocks exploit counters whose moduli align with these bases. Recognizing why MOD-6 and MOD-12 show up in clock designs cements understanding of counter selection for system-level requirements. Given Data / Assumptions: Seconds and minutes: 0–59 (requires MOD-60 = MOD-6 × MOD-10). Hours: 1–12 or 0–23 (MOD-12 often used for 12-hour format). Counters can be cascaded to achieve products of moduli (e.g., MOD-6 with MOD-10). Concept / Approach: Using a MOD-6 counter for the units-of-tens (0–5) and a MOD-10 for ones (0–9) yields a natural 00–59 range. Similarly, MOD-12 provides 1–12 hour cycles when combined with appropriate display/offset logic. These counters are thus staple components of digital clocks. Step-by-Step Solution: Select MOD-6 for the tens-of-seconds/minutes position.Pair with a MOD-10 for the ones position → 6 × 10 = 60.Use MOD-12 for hours in 12-hour clocks. Verification / Alternative check: Examine common clock ICs or reference designs: seconds are obtained via divide-by-60 chains built from MOD-6 and MOD-10 counters; hours often via MOD-12. Why Other Options Are Wrong: Frequency counters generally use large binary/divide-by-N chains not specifically MOD-6/12 focused. Multiplexed displays concern scanning, not count modulus choice. Power meters do not inherently rely on MOD-6 or MOD-12 divisions. Common Pitfalls: Assuming one counter alone makes a clock; in practice, cascaded moduli (e.g., MOD-6 then MOD-10) are used to form 60-base divisions. Final Answer: digital clocks

Question 20

Up/down counter control — can the count direction be reversed once counting has started? Consider a digital up/down counter with a dedicated UP/DOWN (or U/D¯) control input. After the device has already begun its counting sequence, is it possible to…

Accepted Answer

Introduction / Context: Up/down counters are widely used whenever a system must increment and decrement a value under digital control. A common misconception is that once the counter has started to count in one direction, it cannot reverse until the sequence completes or the circuit is reset. In reality, most standard up/down counters include a direction control pin that can be toggled at run time to change the direction of counting without losing the current value. Given Data / Assumptions: A standard synchronous or asynchronous up/down counter with a direction control input (labeled UP/DOWN, U/D, or DIR). Clocking continues while direction may change. No special lockout or one-way gating is present. Concept / Approach: The counter's next-state logic uses the direction input to determine whether to add 1 or subtract 1 from the present state at the next active clock edge. Because the current state is stored in flip-flops, changing the direction simply alters the arithmetic performed on the next edge. The stored count is preserved, and subsequent counts proceed in the new direction. Step-by-Step Solution: Assume the counter is at state N and is currently counting up (DIR = UP).Toggle the direction input to DOWN while continuing to apply clock pulses.On the next active clock edge, the next state becomes N − 1 rather than N + 1.Counting continues downward until the direction is changed again or a reset/preset is applied. Verification / Alternative check: Examine typical datasheets (e.g., 74191/74193, 74HC190/191) where the DIR/U¯D pin explicitly selects increment or decrement. Timing diagrams show that the device will change direction as soon as the control meets setup/hold requirements relative to the clock edge. Why Other Options Are Wrong: True: incorrect, because direction can be reversed dynamically. Only with power cycling or after asynchronous reset: unnecessary; these actions clear/preset the count, but are not required merely to reverse direction. Only if the modulus is a power of two: modulus does not constrain direction control. Common Pitfalls: Violating setup/hold on the DIR pin, which can create one-cycle ambiguity. Always change DIR well before the active clock edge. Confusing counters that include separate up and down clock pins; when both are used, ensure only one is active at a time. Final Answer: False

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