Question 1

Encoder vs. decoder fundamentals How does an encoder differ from a decoder in digital systems?

Accepted Answer

Introduction / Context: Encoders and decoders are complementary combinational circuits widely used in selection, addressing, and display systems. Being able to state their core function succinctly is key to choosing the correct device for a given signal-routing or code-translation task. Given Data / Assumptions: An N-to-n encoder maps a 1-of-N active input into an n-bit code, typically with n = log2(N). An n-to-2^n decoder maps an n-bit binary input to one active output line among 2^n outputs. Some devices include enable inputs and priority handling but their basic roles remain as above. Concept / Approach: An encoder compresses the identity of one active line among many into a compact binary word. Conversely, a decoder expands a binary word into a single asserted output among many. Remember: encoder = many-to-few (coding), decoder = few-to-many (selection). Step-by-Step Solution: For an 8-to-3 encoder: I0..I7 → Y2..Y0; exactly one input HIGH; output is the binary index.For a 3-to-8 decoder: A2..A0 → D0..D7; exactly one output HIGH corresponding to the binary value.Priority encoders resolve multiple simultaneous inputs by predefined priority rules.Enable pins can tri-state or disable outputs without changing the core mapping behavior. Verification / Alternative check: Truth tables in datasheets confirm the many-to-few vs few-to-many roles. Simulation of simple cases (e.g., I5 HIGH on an encoder) yields output 101 for Y2..Y0. Why Other Options Are Wrong: Decoder outputs a binary code (B): Backwards—decoders expand, encoders compress. Decoder compresses an n-bit word (C): Also backwards. Encoder drives all outputs HIGH on invalid inputs (D): Not generally true; behavior depends on device (some assert a validity or priority output instead). Common Pitfalls: Confusing enable polarity or priority behavior with the fundamental translation direction; mixing up tri-state output multiplexers with decoders. Final Answer: The output of an encoder is a binary code for 1-of-N input.

Question 2

Meaning of inequality symbols Interpret the mathematical relations A < B and A > B. What do these symbols indicate about the relative values of A and B?

Accepted Answer

Introduction / Context: Inequality symbols are foundational in mathematics, programming, and engineering specifications. They appear in constraints, comparator logic, sorting, and conditional branching. A clear understanding prevents logic errors and misinterpretations in formulas and code. Given Data / Assumptions: Two quantities: A and B (numbers, variables, or expressions). Standard mathematical meaning of inequality symbols. No special domain-specific overloading is assumed. Concept / Approach: The symbol “<” reads “is less than,” and the symbol “>” reads “is greater than.” Thus A < B places A to the left of B on the number line, while A > B places A to the right of B. These relations are strict (not equal). Non-strict relations use “≤” or “≥”. Step-by-Step Solution: A < B → A is less than B (A comes before B on the number line).A > B → A is greater than B (A comes after B on the number line).If equality is allowed, use A ≤ B or A ≥ B accordingly.In code, “<” and “>” are typically the same, though some languages offer combined operators like “<=” and “>=”. Verification / Alternative check: Example: with A = 3 and B = 5, 3 < 5 is true, while 3 > 5 is false. Swapping values (A = 7, B = 2) reverses truth values accordingly. Why Other Options Are Wrong: Options A and B invert the meanings, contradicting standard mathematical definitions. Common Pitfalls: Mixing up “<” and “>” in compound conditions, and confusing strict versus non-strict inequalities, especially when handling boundary cases in algorithms. Final Answer: A < B means A is less than B. A > B means A is greater than B.

Question 3

Selecting an input on the 74151 (8-to-1) multiplexer For a 74151 eight-line multiplexer, what must the select inputs S0, S1, and S2 be set to so that the output Y equals input I5 (assume standard select ordering)?

Accepted Answer

Introduction / Context: The 74151 is a classic 8-to-1 data selector/multiplexer. It routes one of eight data inputs (I0–I7) to its output Y based on a 3-bit select code on S2, S1, S0. Correctly mapping the desired input index to the select lines is a routine task in digital design and troubleshooting. Given Data / Assumptions: 74151 select lines are ordered S2 (MSB), S1, S0 (LSB). Desired input: I5. Assume enable is active and no inversion options are altering the basic selection. Concept / Approach: To select input Ik, load the binary representation of k on the select lines, with S2 as the most significant bit and S0 as the least significant bit. For k = 5, the binary code is 101, so S2 = 1, S1 = 0, S0 = 1. Some datasheets present the order as S2 S1 S0; the question provides the tuple in the order S0, S1, S2, so we assign accordingly. Step-by-Step Solution: Convert index: 5 → binary 101.Map to S2 S1 S0: 1 0 1.Report in the question's order S0, S1, S2 → 1, 0, 1.Therefore, S0 = 1, S1 = 0, S2 = 1 selects I5. Verification / Alternative check: Cross-check against the truth table in a 74151 datasheet: Y = Ii where i = S2S1S0 in binary when the enable pin allows selection. Why Other Options Are Wrong: 010, 001, 110: These select I2, I1, and I6 respectively, not I5. Common Pitfalls: Confusing bit order (S2 vs S0) or forgetting an active-LOW enable that forces Y to a fixed state regardless of S2–S0. Final Answer: S0 = 1, S1 = 0, S2 = 1

Question 4

Demultiplexer function Most demultiplexers (DEMUX) are used to facilitate which general kind of signal conversion in digital systems?

Accepted Answer

Introduction / Context: A demultiplexer routes a single input signal to one of many outputs based on select lines. It is the functional inverse of a multiplexer and is used in applications such as address decoding, time-division distribution, and controlled signal routing. Given Data / Assumptions: One data input line. Multiple output lines (typically 2^n for n select lines). Selection determined by binary control inputs. Concept / Approach: The DEMUX takes a single input and directs it to one of many output lines, leaving the others inactive. Therefore, the broad conversion is “1-to-N,” or single-input to multiple-outputs. It does not change number bases, perform analog power conversion, or parity transformation by itself (though it may be used within larger systems that do). Step-by-Step Solution: Define N outputs and n select lines (N = 2^n for a basic DEMUX).Apply a binary code on the select lines to choose the active output.The input signal is replicated only onto the selected output line.Use enable lines to gate the device on/off as needed. Verification / Alternative check: Consult a 1-to-8 DEMUX truth table: when S2S1S0 = k, only Yk follows the input; all other Y lines are inactive. Simulation will show the single signal appearing on different outputs as the select code changes. Why Other Options Are Wrong: decimal-to-hexadecimal: Number base conversion is done by encoders, decoders, or arithmetic logic, not a DEMUX. ac to dc: That is power conversion, not a logic function. odd parity to even parity: A parity generator/checker performs parity operations, not a DEMUX. Common Pitfalls: Confusing DEMUX with decoder: a decoder activates one output but does not route a data input; a DEMUX both selects and routes the data. Final Answer: single input, multiple outputs

Question 5

BCD (Binary-Coded Decimal) decoders — number of output lines In digital electronics, a standard BCD-to-decimal decoder accepts a 4-bit BCD input (0000 to 1001 for digits 0–9). How many distinct output lines does such a BCD decoder provide to represe…

Accepted Answer

Introduction / Context: A BCD (Binary-Coded Decimal) to decimal decoder converts a 4-bit BCD input into a one-of-ten output pattern where exactly one line is active for the digit being represented. This question checks basic decoder literacy used in counters, seven-segment drivers, and numeric multiplexed displays. Given Data / Assumptions: Input code is BCD: valid codes 0000 through 1001 represent 0–9. Invalid BCD inputs 1010–1111 are typically suppressed or treated as don’t-care. Output style is one-of-N (one line active at a time). Concept / Approach: A BCD-to-decimal decoder must generate a unique output for each decimal digit 0–9. Therefore there must be 10 outputs. Internally, combinational logic decodes the 4-bit input and drives the corresponding output line active, while all others remain inactive. Step-by-Step Solution: Identify decimal range for BCD: 10 digits (0–9).Map each digit to one line: requires 10 output lines.Invalid inputs: ignored or placed in a defined inactive state.Therefore total outputs = 10. Verification / Alternative check: Common ICs (e.g., 7442/7445 families) are 4-to-10 decoders/decoders-drivers, confirming the 10-line requirement. Why Other Options Are Wrong: 4: This is the number of BCD input bits, not outputs. 8: Would suit octal decoding, not decimal BCD. 16: Corresponds to full 4-to-16 binary decoding, not restricted to BCD 0–9. Common Pitfalls: Confusing a 4-to-16 binary decoder with a BCD-to-decimal decoder; BCD decoders restrict outputs to 10 valid digits. Final Answer: 10

Question 6

Interpreting logic symbols — determining active level from bubbles When reading a decoder's logic symbol, how can you determine whether an output is active-HIGH or active-LOW from the drawing alone?

Accepted Answer

Introduction / Context: Schematic symbols use small visual cues to convey polarity (active level). Decoders, encoders, and flip-flops often show bubbles on pins to indicate inversion. Correctly interpreting these “bubbles” is essential to avoid wiring a system with the wrong polarity and getting inverted behavior. Given Data / Assumptions: Standard ANSI/IEC logic symbolism applies. A small bubble (circle) denotes inversion at that pin. Active-HIGH means the function asserts at logic 1; active-LOW means it asserts at logic 0. Concept / Approach: A bubble indicates an inverting relationship. On an output, the presence of a bubble means the output is asserted when the internal “true” signal is LOW at the pin—i.e., the output is active-LOW. Similarly, a bubble on an input means that signal is interpreted in its complemented sense (active-LOW input). No bubble implies active-HIGH behavior. Step-by-Step Solution: Look for a small circle (bubble) on the output pin.Bubble present → output asserts at logic 0 → active-LOW.No bubble → output asserts at logic 1 → active-HIGH.Therefore, a bubble indicates active-LOW. Verification / Alternative check: Compare with truth tables of standard decoder ICs (e.g., 74xx138 with active-LOW outputs) whose symbols show bubbles on outputs. Why Other Options Are Wrong: Bubbles never denote active-HIGH; that would contradict the inversion meaning. “Square indicates …” is not a standard polarity marker. Common Pitfalls: Forgetting that a bubble flips the sense of the signal and that multiple bubbles in series can cancel the inversion. Final Answer: A bubble indicates active-LOW.

Question 7

Using 74184 BCD-to-binary converters — two-digit BCD to binary How many SN74184 BCD-to-binary converter ICs are required to convert two complete BCD digits (00–99) into a pure binary value for general-purpose decoding?

Accepted Answer

Introduction / Context: The classic SN74184 implements BCD-to-binary conversion using internal ROM-style tables. Practical converters for multi-digit BCD often require multiple devices to cover the full decimal range without invalid gaps. This question targets architectural understanding rather than memorizing a specific pinout. Given Data / Assumptions: We must handle two BCD digits (00–99). The 74184 device provides a 6-bit BCD-to-binary table designed around typical 0–63 ranges; wider ranges require staged or conditional conversion. The goal is a continuous binary output covering 0–99 (requires 7 bits). Concept / Approach: A common discrete-logic approach uses one converter network for the lower ranges and another (gated by the tens digit) to extend coverage to the higher ranges, then combines results. Rule-of-thumb designs use two 74184 devices per decimal digit for robust full-range conversion; thus, two digits generally require four devices. This scales with known reference designs where three digits use six devices (two per digit), maintaining uniform methodology and timing. Step-by-Step Solution: Determine required binary width: 0–99 needs 7 bits (since 2^7 = 128).Recognize 74184's table focus: efficient over limited ranges such as 0–63.Provide gating/combination to cover 64–99 using additional devices.Aggregate devices for two digits: 2 devices/digit → total 4 devices. Verification / Alternative check: Reference multi-digit implementations: three BCD digits (000–999) often employ six 74184 ICs (two per digit), which aligns with the two-digit case requiring four. Why Other Options Are Wrong: 1 or 2: insufficient to realize seamless 00–99 binary coverage with clean timing and decoding. 8: excessive for two digits and not minimal. Common Pitfalls: Assuming a single small converter IC always maps any number of BCD digits; multi-digit conversion needs either arithmetic (add/scale) or multiple table devices. Final Answer: 4

Question 8

Decoder sizing — number of outputs for a 6-bit binary input If a binary decoder accepts a 6-bit input (values 0–63), how many distinct output lines are available in a fully decoded one-of-N arrangement?

Accepted Answer

Introduction / Context: Binary decoders map an n-bit input to one-of-2^n outputs, activating exactly one output for each input code. Properly sizing decoders is fundamental when designing address decoders, channel selectors, and state decoders. Given Data / Assumptions: Number of input bits n = 6. Fully decoded, one-hot output behavior. No invalid codes because all 6-bit combinations are valid (0–63). Concept / Approach: The number of outputs in a full binary decoder equals 2^n. With n = 6, 2^6 = 64 outputs. Each output corresponds to one unique input value; only that line is asserted at any given time. Step-by-Step Solution: Compute 2^n for n = 6 → 2^6 = 64.Interpretation: one output per input code (0–63).Therefore, total outputs = 64. Verification / Alternative check: Compare with common decoder families: 3-to-8 (2^3), 4-to-16 (2^4). Extending the pattern to 6 bits yields 64 outputs. Why Other Options Are Wrong: 16 and 32 correspond to 4-bit and 5-bit decoders. 128 corresponds to 7-bit decoding. Common Pitfalls: Confusing a BCD-to-decimal decoder (10 outputs) with a full binary decoder (2^n outputs). Final Answer: 64

Question 9

Recognizing applications of digital multiplexers Which application correctly reflects a common, practical use of a digital multiplexer (data selector) in digital system design?

Accepted Answer

Introduction / Context: A multiplexer (MUX) routes one of many inputs to a single output based on select signals. It is often called a “data selector.” This role is ubiquitous in digital systems for bus sharing, input selection, and time-division multiplexed display driving. Given Data / Assumptions: Multiplexer has multiple data inputs, select lines, and one output. At any instant exactly one input is connected through to the output. We are not describing arithmetic or error-detection functions. Concept / Approach: The MUX’s primary use is selection of one input among many. Functions like serial-to-parallel conversion are typically performed by shift registers and demultiplexers, while parity checking uses XOR logic. Data generation suggests sources such as counters or LFSRs rather than a selector. Step-by-Step Solution: Identify multiplexer behavior: many-to-one selection.Match to application: “data selector.”Eliminate unrelated tasks (parity, format conversion, generation).Therefore, option (d) is correct. Verification / Alternative check: Look up 74HC151 (8-to-1 data selector) or similar: datasheets explicitly label these ICs as “multiplexer/data selector.” Why Other Options Are Wrong: Data generation: multiplexers select existing data, they do not generate new data. Serial-to-parallel conversion: primarily uses shift registers and demultiplexers. Parity checking: uses XOR/XNOR networks, not a selector. Common Pitfalls: Confusing multiplexers (many-to-one) with demultiplexers (one-to-many) and shift-register-based format converters. Final Answer: data selector

Question 10

Which digital system translates coded characters into a more useful form? Identify the subsystem that takes a coded binary input (such as BCD or 7-bit ASCII) and converts or expands it into a more directly usable set of output signals.

Accepted Answer

Introduction / Context: Many digital systems use compact codes for efficiency. A decoder translates these codes into broader, more directly useful output patterns, such as driving individual display segments or selecting one of many lines. Recognizing the role of decoders is fundamental in digital design. Given Data / Assumptions: Input is a coded representation (e.g., BCD 0000–1001 for 0–9). Output must be a more useful form (e.g., 1-of-10 lines, 7-segment patterns). We distinguish between encoders and decoders. Concept / Approach: An encoder compresses many input lines into a smaller coded output; a decoder performs the reverse, expanding coded input into a richer set of outputs. Therefore, the block that translates a compact code into actionable signals is a decoder. Step-by-Step Solution: Identify direction of conversion: code → expanded outputs.Match function: this is decoding.Hence, the correct subsystem is the decoder. Verification / Alternative check: Common ICs: 7447 (BCD-to-7-seg), 7442 (BCD-to-decimal) are canonical decoders that translate coded characters to display/control outputs. Why Other Options Are Wrong: Encoder: opposite operation (many inputs → coded output). Display: a load, not the translator itself. Counter: sequential device that advances states, not a code translator. Common Pitfalls: Assuming “display” performs decoding; often a dedicated decoder/driver IC feeds the display hardware. Final Answer: decoder

Question 11

Demonstrating multiplexer behavior with mechanical switches Which single mechanical device most clearly demonstrates the basic principle of a digital multiplexer (selecting one of many inputs to connect to a single output)?

Accepted Answer

Introduction / Context: A multiplexer (MUX) selects exactly one of multiple inputs and connects it to a single output. Mechanical analogies help students visualize this behavior before moving on to IC-based multiplexers such as the 74HC151 or CMOS analog switches. Given Data / Assumptions: We want a one-of-N selection using a single output contact. The device should offer multiple selectable inputs. The selection mechanism should be unambiguous and exclusive. Concept / Approach: A rotary switch presents many input positions around a dial, with a common wiper that connects exactly one selected position to the common terminal. This is the mechanical equivalent of a k-to-1 digital multiplexer. Other switches either select between only two inputs or provide different functions. Step-by-Step Solution: Identify the need: many-to-one selection.Evaluate candidates: DPDT or SPDT offer only two positions; relays are not inherently multi-position selectors.Rotary switch: multiple positions feeding one common → matches MUX.Therefore the best demonstration device is a rotary switch. Verification / Alternative check: Mapping: rotary switch positions ↔ multiplexer inputs; wiper common ↔ multiplexer output; knob position ↔ select lines. Why Other Options Are Wrong: Single-pole relay: acts like an SPST/SPDT, not many-to-one. DPDT switch: two inputs per pole only. Linear stepper: an actuator, not a selector. Common Pitfalls: Confusing demultiplexing (one-to-many) with multiplexing (many-to-one); the rotary switch models the latter perfectly. Final Answer: rotary switch

Question 12

Why many CMOS logic ICs can serve as both multiplexers and demultiplexers Explain the key device characteristic that allows certain CMOS logic ICs (such as transmission-gate based devices) to be used interchangeably as multiplexers and demultiplexer…

Accepted Answer

Introduction / Context: Analog switch and transmission-gate CMOS ICs (e.g., CD4051/4052/4053 families) can route signals in either direction because their internal pass transistors act as bilateral switches. This enables the same device to function as a multiplexer (many-to-one) or as a demultiplexer (one-to-many). Given Data / Assumptions: CMOS transmission gates are symmetrical bilateral devices. Signal levels remain within the device’s supply rails. Control inputs select which switch paths conduct. Concept / Approach: Because a transmission gate passes signals in both directions with similar impedance, the network does not impose directionality. If you feed the common node and select one branch, you demultiplex; if you feed multiple branches and select which one connects to the common node, you multiplex. The logic of selection does not change, only which side you call “input” or “output.” Step-by-Step Solution: Recognize internal element: bilateral pass gate (NMOS+PMOS in parallel).Note symmetry: conduction path is reversible.Apply selection: same control signals pick the active channel.Hence, device can act as MUX or DEMUX. Verification / Alternative check: Datasheets for CD4051 (8-channel analog multiplexer/demultiplexer) explicitly specify bidirectional operation across channels. Why Other Options Are Wrong: “Cannot be used as both” contradicts standard device behavior. Always tri-stated outputs or TTL compatibility are unrelated to bidirectionality. Common Pitfalls: Ignoring on-resistance and signal range limits; ensure the analog levels stay within VSS–VDD and bandwidth constraints. Final Answer: CMOS uses bidirectional switches.

Question 13

Priority encoder 74148 — determine outputs from given inputs For an SN74148 8-to-3 priority encoder (active-LOW inputs I0–I7, active-LOW outputs A2 A1 A0; EI active-LOW enable), determine the five output leads (GS, A0, A1, A2, EO) when: I0 = 1, I1 =…

Accepted Answer

Introduction / Context: The 74148 is an active-LOW priority encoder: the highest-numbered asserted input (LOW) takes priority and is encoded on active-LOW outputs A2 A1 A0. GS (Group Select) and EO (Enable Output) indicate valid encoding and permit cascading. Interpreting active-LOW conventions correctly is essential. Given Data / Assumptions: Inputs I0–I7 are active-LOW; a logic 0 means “asserted.” Outputs A2 A1 A0 are active-LOW codes of the winning input. EI = 0 enables the device; GS goes LOW and EO goes HIGH when any input is asserted. Concept / Approach: Identify the highest-priority asserted input (lowest logic level among I7..I0). With only I4 = 0 asserted and EI = 0, input 4 wins. Encode decimal 4 (binary 100) onto active-LOW outputs, which means drive A2 LOW, A1 HIGH, A0 HIGH. GS should be LOW (valid), and EO HIGH to indicate a valid output for cascading. Step-by-Step Solution: Find asserted inputs: only I4 = 0.Priority winner: 4 (since I7..I5 are 1).Binary code for 4 = 100; active-LOW outputs → A2 = L, A1 = H, A0 = H.Status: GS = L (valid), EO = H (enable out true). Verification / Alternative check: Check with a 74148 truth table: single LOW on I4 yields A2 L, A1 H, A0 H and GS L, EO H when EI L. Why Other Options Are Wrong: Options a–c contain incorrect bit patterns for the active-LOW code or misplace H/L levels. Common Pitfalls: Forgetting outputs are active-LOW and inverting them mentally; misreading the priority order (I7 highest). Final Answer: GS = L, A0 = H, A1 = H, A2 = L, EO = H

Question 14

BCD to binary using weighting factors — convert two BCD numbers Convert the following BCD groups to pure binary using weighting factors (8–4–2–1 per digit). Treat the first two nibbles as one BCD number and the last three nibbles as a second BCD num…

Accepted Answer

Introduction / Context: BCD (Binary-Coded Decimal) encodes each decimal digit separately using 4 bits (8–4–2–1 weights). To convert full multi-digit BCD numbers into pure binary, first decode each BCD digit to its decimal value, then convert the complete decimal number to binary. The “weighting factors” method emphasizes interpreting each nibble correctly before performing the base-10 to base-2 conversion. Given Data / Assumptions: Nibbles: 0101 0011 represent one number; 0010 0110 1000 represent a second. BCD digits map via 8–4–2–1 weights. We output pure binary (base-2), not BCD. Concept / Approach: Step 1: Translate each 4-bit BCD nibble to its decimal digit. Step 2: Combine the digits into a decimal number. Step 3: Convert that decimal to binary using division-by-2 or place-value decomposition. We present each converted number separated by a space, matching the format of the options. Step-by-Step Solution: Number 1 (0101 0011): 0101 = 5, 0011 = 3 → decimal 53.Convert 53 to binary: 53 = 32 + 16 + 4 + 1 → bits at 5,4,2,0 → 110101.Number 2 (0010 0110 1000): digits 2, 6, 8 → decimal 268.Convert 268 to binary: 268 = 256 + 8 + 4 → bits at 8,3,2 → 100001100.Final paired result: 110101 100001100. Verification / Alternative check: Use repeated division by 2: 53 → 110101, 268 → 100001100. Cross-check with place-value sums to confirm correctness. Why Other Options Are Wrong: (a) Simply echoes the original BCD groups, not pure binary. (b) Incorrect lengths and values; not the proper binary of 53 and 268. (d) Bit pattern errors; digits do not correspond to the correct powers-of-two sums. Common Pitfalls: Confusing BCD with pure binary and concatenating nibbles directly; always convert the decimal value represented by the BCD digits into base-2. Final Answer: 110101 100001100

Question 15

Digital Logic Fundamentals — Decoder Definition and Role In digital electronics, a circuit that recognizes a specific input code or set of input signals and asserts a corresponding output line (or pattern) is called a:

Accepted Answer

Introduction / Context: A decoder is a fundamental combinational logic block used to translate coded inputs into a set of mutually exclusive outputs. Whenever a system needs to identify which code, address, or state is present and activate the corresponding line, a decoder performs this selection. Decoders appear in memory addressing, instruction decoding, seven-segment driving (via BCD-to-7-segment ICs), and chip-select logic. Given Data / Assumptions: The circuit observes a set of input signals (for example, n-bit binary or BCD). For each valid input code, a well-defined output line or pattern is produced (often one-hot). The question asks for the general name of such a circuit. Concept / Approach: In a decoder, inputs represent a code and outputs represent decoded lines. An n-to-2^n decoder activates exactly one of 2^n outputs for each n-bit input combination (ignoring enable and don’t-care cases). In contrast, an encoder converts many input lines into a coded (typically binary) output. A display driver may include decoding but is a more specific functional block, and a “BCD matrix” is not a standard generic name in this context. Step-by-Step Solution: Identify behavior: recognize input code → assert corresponding output line.Map to standard block: this is the canonical definition of a decoder.Exclude alternatives: encoder performs the inverse mapping; display driver is application-specific; “BCD matrix” is nonstandard.Therefore, the circuit is a decoder. Verification / Alternative check: Typical parts such as 74xx138 (3-to-8 decoder) or 74xx154 (4-to-16 decoder) behave exactly as described: for each binary input, one unique output goes active when enabled. Why Other Options Are Wrong: display driver: Usually includes current limiting, multiplexing, and sometimes decoding, but is not the generic name for the decoding function. encoder: Converts many inputs to fewer coded outputs (opposite direction). BCD matrix: Not a standard term for this fundamental function. Common Pitfalls: Confusing “decoder” with “driver/encoder,” or assuming any display-related IC is necessarily a decoder. Always check whether the block maps code→line (decoder) or line→code (encoder). Final Answer: decoder

Question 16

Multiplexers — Determine Select-Line Count For an 8-line-to-1-line multiplexer (8:1 MUX) that chooses one of eight data inputs to pass to a single output, how many select (control) lines are required to uniquely address all inputs?

Accepted Answer

Introduction / Context: A multiplexer (MUX) is a data selector. It routes one of many input lines to a single output based on the binary value applied to its select inputs. Correctly determining the number of select lines is essential when sizing control fields in datapaths and designing addressable signal routing. Given Data / Assumptions: MUX size: 8 inputs, 1 output (8:1). Each unique input must be selectable with a unique binary code. Enable pin, if present, is not counted as a select line. Concept / Approach: To select among N inputs, you need enough binary codes to represent the numbers 0 through N − 1. The minimum number of select lines k satisfies 2^k ≥ N. For N = 8, the smallest k with 2^k ≥ 8 is k = 3, because 2^3 = 8 provides exactly eight unique codes (000 to 111). Step-by-Step Solution: Set N = 8.Find k such that 2^k ≥ 8.Compute 2^2 = 4 (insufficient), 2^3 = 8 (sufficient).Therefore, k = 3 select lines are required. Verification / Alternative check: Examine a standard 8:1 MUX truth table: the 3-bit select S2 S1 S0 uniquely addresses D0..D7. Any vendor datasheet (e.g., 74HC151) confirms 3 select lines for 8 inputs. Why Other Options Are Wrong: 2: 2^2 = 4 addresses only four inputs. 4: 2^4 = 16 is more than needed for 8 inputs. 8: Misinterprets data inputs as select lines. Common Pitfalls: Counting the enable pin as a select line or assuming one select line per input. The mapping is exponential (2^k), not linear. Final Answer: 3

Question 17

Decoders — Required Enable Conditions For reliable operation of a generic 1-line-to-16-line (4-to-16) decoder, what enable condition is typically required before decoding can occur?

Accepted Answer

Introduction / Context: Most decoder ICs include one or more enable (EN) inputs that globally allow or inhibit outputs. This permits chip-select functionality, output gating, and expansion (cascading multiple decoders). Understanding the required enable state ensures that the device actually performs decoding when expected. Given Data / Assumptions: Device: a 4-to-16 decoder (often described as 1-of-16). Enable inputs are present and must be in the active state to pass decoded outputs. Exact polarity of enables varies by family, but the principle remains: enables must be active. Concept / Approach: In many common parts (e.g., 74HC154), enables are active-LOW; in others (e.g., selected programmable logic), they may be active-HIGH. The question is phrased generically, so the correct conceptual answer is that the enable inputs must be in their active (asserted) state. In the provided options, this corresponds to “a HIGH on all gate enable circuits.” Step-by-Step Solution: Identify the role of EN: it globally permits output assertion.Determine the generic condition: EN must be asserted (active).Map to given choices: the only answer expressing “asserted/active” in general terms is “a HIGH on all gate enable circuits.”Therefore, decoding proceeds when enables are active. Verification / Alternative check: Datasheets show that with EN deasserted, all outputs are disabled (often all HIGH or all LOW depending on the device), regardless of the input code. With EN asserted, the one-of-16 output becomes active per the input lines. Why Other Options Are Wrong: a LOW on all gate enable inputs: Only correct for parts with active-LOW EN; the question is generic. input from a hexadecimal counter: A possible source of input data, not an enable condition. flasher circuit control signal: Irrelevant to decoder operation. Common Pitfalls: Forgetting to drive enables, or assuming enables are always active-HIGH. Always check the polarity in the specific part’s datasheet. Final Answer: a HIGH on all gate enable circuits

Question 18

BCD-to-Seven-Segment — Why a Code Converter Is Needed In a BCD-to-seven-segment display system, why must a dedicated code-converter/driver be used between the 4-bit BCD source and the seven display segments (a–g)?

Accepted Answer

Introduction / Context: A seven-segment display requires specific segment patterns for each decimal digit. A 4-bit BCD input encodes digits 0–9 but does not directly drive segments. A BCD-to-seven-segment code converter (often integrated with a driver) translates the 4-bit code into seven control lines to illuminate the correct segments. Given Data / Assumptions: Input: 4-bit BCD representing 0–9. Output: seven control signals for segments a–g. Display type: common anode or common cathode (affects active level but not the need for conversion). Concept / Approach: The mapping from each BCD value to segments is a truth table (e.g., digit 2 lights a, b, g, e, d). A converter implements this logic and may also provide current limiting, blanking, lamp test, and ripple-blanking features. Without conversion, the raw BCD lines cannot produce correct segment combinations. Step-by-Step Solution: Identify inputs: 4 BCD bits → 10 valid combinations.Identify outputs: 7 segment control lines.Define mapping: each digit 0–9 maps to a unique 7-bit pattern.Therefore, a code converter is needed to translate BCD into the required 7-bit segment code. Verification / Alternative check: ICs such as 7447/7448 implement the conversion. Their datasheets provide the BCD-to-segment truth tables confirming the necessity of conversion. Why Other Options Are Wrong: 10-bit code: Seven-segment displays need 7 outputs, not 10. Gray code: Unrelated to segment driving. No conversion: Contradicts the required mapping from digits to segments. Common Pitfalls: Confusing common-anode vs common-cathode drive polarities; the converter may output active-LOW or active-HIGH levels accordingly. Final Answer: to convert the 4-bit BCD into 7-bit code

Question 19

Priority Handling — Multiple Active Inputs When two or more inputs to a system are asserted at the same time, which technique resolves which input should be serviced or encoded first?

Accepted Answer

Introduction / Context: Digital systems often face contention when multiple request or interrupt lines are active simultaneously. An ordered method is needed to decide which request is recognized first or which input gets encoded. The circuit or algorithm that enforces this order is a priority scheme. Given Data / Assumptions: At least two inputs can be active at the same time. The system must select one to service or encode, based on a predefined precedence. We are considering combinational selection, not queuing in time. Concept / Approach: A priority encoder outputs the binary code of the highest-priority active input, ignoring lower-priority active lines. This differs from FIFO (a temporal queue that services requests in arrival order) and ripple blanking (a display feature used to suppress leading zeroes). Priority schemes are common in interrupt controllers and bus arbiters. Step-by-Step Solution: Identify simultaneous-assertion scenario.Apply priority rule: highest-priority input wins.Encode or route only the winning input; others are masked.Thus, the correct process is priority encoding. Verification / Alternative check: Examine a 74xx148 (8-to-3 priority encoder): when multiple inputs are LOW (active), the output code corresponds to the highest-priority position as defined by the device. Why Other Options Are Wrong: first-in, first-out processing: A queue discipline over time, not simultaneous selection. ripple blanking: A seven-segment display feature, not a contention resolver. FIFO or priority (either/or): Mixing unrelated mechanisms; the correct resolution method here is specifically priority encoding. Common Pitfalls: Assuming FIFO solves simultaneous assertion without serialization hardware; FIFO requires sequential arrival, not concurrent signals. Final Answer: priority encoding

Question 20

Microcontroller vs. Microprocessor — Integrated Resources and Typical Use A microcontroller differs from a general-purpose microprocessor because it integrates several ________ ports and ________ on-chip, making it well suited for ________ applicati…

Accepted Answer

Introduction / Context: Microcontrollers (MCUs) are system-on-chip devices built for embedded tasks. Unlike microprocessors (MPUs), which usually require external memory and peripherals, MCUs integrate the essential components for stand-alone operation, making them ideal for control-oriented applications such as appliances, automotive subsystems, and IoT nodes. Given Data / Assumptions: MCUs include GPIO (general-purpose input/output) ports. Nonvolatile and volatile memory (Flash/ROM, SRAM) are typically on-chip. Target domain: deterministic control tasks rather than heavy general-purpose computing. Concept / Approach: By integrating I/O, memory, timers, ADC/DAC, and communication peripherals, MCUs minimize external components. This lowers cost and power while enabling fast, predictable interactions with sensors and actuators—hallmarks of control applications. Step-by-Step Solution: Identify key MCU resources: I/O ports and embedded memory.Match to application domain: control-focused tasks (closed-loop control, scheduling, interfacing).Contrast with MPU: external buses for memory/peripherals; optimized for high-level processing.Therefore, the correct completion is “input/output, memory, control.” Verification / Alternative check: Datasheets for common MCUs (e.g., AVR, PIC, ARM Cortex-M) list multiple GPIO ports, Flash/EEPROM, SRAM, timers, and serial interfaces, all on-chip, confirming suitability for control. Why Other Options Are Wrong: parallel, logic gates, processing: Too vague and misses the integrated memory. communication, PROMs, control: Communication is present but not the defining pair compared to I/O and memory; PROMs alone are insufficient. data, memory, decoding: “Data” and “decoding” are nonspecific in this context. Common Pitfalls: Assuming microprocessors and microcontrollers are interchangeable; system integration level and target applications differ significantly. Final Answer: input/output, memory, control

Code Converters and Multiplexers Questions