Question 1

Gate identification from behavior: A signal is inhibited by applying a LOW to one input, yet the output remains HIGH. Which logic gate matches this description?

Accepted Answer

Introduction / Context: Recognizing a gate from its qualitative behavior is a key digital logic skill. The description says a LOW on any input inhibits the signal but produces a HIGH output regardless of the other inputs. This strongly hints at the inversion of an AND function, which is the NAND gate. Given Data / Assumptions: At least two-input logic gate. Driving one input LOW forces the output to a known state. Observed output is HIGH when any single input is LOW. Concept / Approach: The NAND truth function is Y = NOT(A * B * …). For NAND, the output is LOW only when all inputs are HIGH. If any input is LOW, the product A * B * … equals 0, so NOT(0) = 1 → output HIGH. Hence a LOW on an input 'inhibits' the low-output condition and produces HIGH, matching the description. Step-by-Step Solution: For NAND: if any input = 0 → product = 0 → output = 1.Therefore a LOW input guarantees a HIGH output (signal inhibited).Only when all inputs are 1 is the output 0. Verification / Alternative check: Compare to AND: any LOW makes output LOW (contradicts the statement). Compare to OR: any HIGH makes HIGH (doesn’t mention LOW causing HIGH). Compare to NOR: any HIGH causes LOW (opposite behavior). Thus only NAND fits. Why Other Options Are Wrong: AND: Any LOW → output LOW, not HIGH. NOR: Any HIGH → output LOW, opposite behavior. OR: Any HIGH → output HIGH; the described trigger is a LOW input. Common Pitfalls: Confusing NAND with NOR; remember NAND inverts AND (only all HIGH gives LOW), while NOR inverts OR (any HIGH gives LOW). Final Answer: NAND

Question 2

74xx logic families: How many independent 2-input NAND gates are contained inside a standard 7400 TTL IC (often called a “quad NAND”)?

Accepted Answer

Introduction / Context: The 7400-series TTL family is a cornerstone of digital electronics. Part numbers encode both function and quantity. The 7400 device is a classic example, widely used in education and industry for simple logic building blocks. Given Data / Assumptions: Device: 7400 TTL logic IC. Function: 2-input NAND gates packaged together. Package: 14-pin DIP in many versions. Concept / Approach: The 7400 is known as a 'quad 2-input NAND'. 'Quad' indicates four independent gates in one package. Pinouts show inputs and outputs mapped to four separate NAND sections, with Vcc and GND on standard pins (e.g., 14 and 7 in DIP packages). Step-by-Step Solution: Identify the family code: 7400.Recall canonical name: quad 2-input NAND.Therefore, the IC contains 4 NAND gates. Verification / Alternative check: Compare to related devices: 7402 is quad 2-input NOR, 7404 is hex inverter (6 NOT gates), 7408 is quad 2-input AND. The pattern corroborates the 7400 having four NANDs. Why Other Options Are Wrong: 1 or 2: Would be 'single' or 'dual,' not 7400. 8: That would be 'octal' and would not match pin constraints of a 14-pin DIP for 2-input gates. Common Pitfalls: Confusing 7400 with 7404 (hex inverters) or with CMOS 4000-series numbering. Always confirm the family and function from the part number. Final Answer: 4

Question 3

Truth table size: For a four-input logic circuit (4 independent binary inputs), how many rows/entries are required in the complete truth table?

Accepted Answer

Introduction / Context: Truth tables enumerate all possible input combinations and the resulting output(s). The size grows exponentially with the number of inputs, a key reason minimization tools (like Karnaugh maps or Boolean algebra) are important for larger systems. Given Data / Assumptions: Number of inputs n = 4. Each input is binary (0 or 1). We seek the number of unique rows in the truth table. Concept / Approach: For n binary variables, the number of distinct combinations is 2^n. Each combination corresponds to one row of the truth table. Thus, for four inputs, the table must have 2^4 entries covering all permutations from 0000 to 1111. Step-by-Step Solution: Let n = 4.Compute 2^n = 2^4.2^4 = 16 unique input combinations → 16 rows. Verification / Alternative check: List a subset to verify: 0000, 0001, 0010, …, 1111. Counting from 0 to 15 in binary gives exactly 16 combinations, confirming the result. Why Other Options Are Wrong: 4 or 8 or 12: Do not equal 2^4; they miss some combinations and would yield an incomplete truth table. Common Pitfalls: Confusing the number of inputs with the number of outputs or forgetting the exponential growth rule 2^n. This error leads to incomplete testing in design and verification. Final Answer: 16

Question 4

Characterizing NAND behavior: Which statement best describes a NAND gate's input–output relationship for the case of LOW inputs?

Accepted Answer

Introduction / Context: NAND is a universal logic gate. Understanding its behavior for edge cases (all inputs LOW vs. all inputs HIGH) helps quickly predict outcomes and design with minimal gates. Here, the focus is on the output when inputs are LOW. Given Data / Assumptions: Two-input NAND gate for simplicity (the conclusion generalizes). Logic levels: LOW = 0, HIGH = 1. Concept / Approach: NAND is the inversion of AND. The AND of two LOWs is 0, and then inverting yields 1. Therefore, with (0, 0) applied to a NAND, the output is HIGH. In general, NAND gives LOW only when all inputs are HIGH; for any other combination (including all LOW), it outputs HIGH. Step-by-Step Solution: For inputs A = 0, B = 0 → AND: 0 * 0 = 0.NAND output Y = NOT(0) = 1.Hence: LOW inputs → HIGH output. Verification / Alternative check: Quick truth table check: (0,0)→1; (0,1)→1; (1,0)→1; (1,1)→0. Only the all-HIGH case creates a LOW output, consistent with the rule of NAND. Why Other Options Are Wrong: LOW inputs and a LOW output: That is the AND behavior, not NAND. HIGH inputs and a HIGH output: NAND of (1,1) is 0, not 1. None of these: One option is correct as shown. Common Pitfalls: Mixing AND and NAND logic; forgetting that NAND inverts the AND result. Also watch ambiguous phrasing—always compute with simple cases to confirm intuition. Final Answer: LOW inputs and a HIGH output

Question 5

Identify the gate that outputs the complement of its single input (i.e., logical inversion): Which basic logic gate performs this operation?

Accepted Answer

Introduction / Context: Digital systems often need the logical complement of a signal for control, timing, and active-low conventions. The device that provides this complement is fundamental and appears in virtually every logic family and integrated function block. Given Data / Assumptions: Single-input, single-output logic function. Output equals NOT(input). Ideal logic levels are assumed. Concept / Approach: The NOT operation maps 0 → 1 and 1 → 0. The simplest gate implementing NOT is called an inverter (sometimes labeled as a NOT gate or 7404 in TTL for a hex inverter). It is distinct from comparators, which are analog-level thresholding devices that produce logic-level outputs but are not simple NOT functions of a single logic input. Step-by-Step Solution: Define the function: Y = NOT(X).Recognize device name: inverter (NOT gate).Select ”INVERTER gate.” Verification / Alternative check: Truth table for an inverter: X=0 → Y=1; X=1 → Y=0. Other gates (AND, OR) require two or more inputs and do not invert a single input by themselves. Why Other Options Are Wrong: OR / AND: Multi-input gates that do not invert a single input. Comparator: Analog threshold device; output depends on analog difference relative to a reference, not merely the logical complement of a logic input. Common Pitfalls: Assuming a comparator is a digital NOT because it outputs logic levels—its function and use cases are different (windowing, thresholding, Schmitt triggering). Final Answer: INVERTER gate

Question 6

Realizing XOR from basic gates: Exclusive-OR (XOR) gates can be implemented using which combination of fundamental logic gates?

Accepted Answer

Introduction / Context: Many digital designs restrict the primitive gate set to AND, OR, and NOT (or to NAND/NOR). Being able to build XOR from these primitives is essential because XOR underlies adders, parity generators, and data comparison logic. Given Data / Assumptions: XOR two-input definition: output HIGH if inputs differ (01 or 10) and LOW if inputs are the same (00 or 11). Available primitives: AND, OR, NOT. Concept / Approach: One canonical realization is: XOR = (A * NOT B) + (NOT A * B). This uses two AND gates and two NOT gates feeding an OR gate. It exactly captures the “one or the other but not both” behavior of XOR. Step-by-Step Solution: Compute term1 = A * NOT B.Compute term2 = NOT A * B.XOR output Y = term1 + term2. Verification / Alternative check: Truth table check: For A,B = 00 → Y=0; 01 → Y=1; 10 → Y=1; 11 → Y=0. This matches XOR. Alternative forms exist using only NAND or only NOR, but they still conceptually reduce to combinations of AND/OR/NOT operations. Why Other Options Are Wrong: OR only: Cannot suppress the 11 case to 0. AND + NOT only or OR + NOT only: Insufficient to generate both terms and combine correctly without all three primitives in the canonical form. Common Pitfalls: Confusing XOR with inclusive OR; XOR excludes the 11 case. Also, forgetting to invert one input per product term yields the wrong function. Final Answer: AND gates, OR gates, and NOT gates

Question 7

Minimal transistor implementation: A single bipolar junction transistor (BJT) stage can be wired to implement which basic digital logic gate?

Accepted Answer

Introduction / Context: At the lowest level, logic gates are built from transistors and resistors. Understanding what a single transistor can realize helps in appreciating how complex logic functions are composed and why certain gates are considered universal only when more devices are used. Given Data / Assumptions: Single active device (one BJT) with resistive biasing. Digital operation (saturation/cutoff for switching or small-signal inversion for logic-level inversion). Standard positive logic conventions. Concept / Approach: A common-emitter BJT stage provides inversion: a HIGH input drives the transistor into conduction and pulls the output LOW; a LOW input turns it off, allowing the pull-up to produce a HIGH output. Thus, a single BJT can act as a NOT gate (inverter). Creating AND, OR, NAND typically requires multiple transistors or diode-resistor networks with transistor inversion. Step-by-Step Solution: Choose topology: common-emitter with collector resistor and input base drive.Input HIGH → base current flows → transistor saturates → collector LOW.Input LOW → transistor off → collector pulled HIGH → inversion achieved. Verification / Alternative check: Many TTL inverters (e.g., one section of a 7404 die) boil down to a single transistor stage performing inversion, often augmented by additional devices for noise margins and current drive. The core function, however, is inversion using one active device. Why Other Options Are Wrong: AND / OR: Require combining multiple inputs; at least two active paths are needed. NAND: Although NAND can be made from series/parallel transistor networks, it still needs more than one active device to handle multiple inputs. Common Pitfalls: Assuming a diode-resistor network alone can implement robust logic levels with good noise margins—it typically needs a transistor stage for restoration and inversion. Final Answer: NOT gates

Question 8

OR gate behavior (any-true condition): Which logic gate outputs a HIGH (logic “1”) when any one of its inputs is HIGH?

Accepted Answer

Introduction / Context: Recognizing the canonical behavior of the OR gate is essential for control logic, enabling conditions, and combining multiple event signals. The key phrase is “any one input HIGH” causes the output to be HIGH, which defines the inclusive OR operation. Given Data / Assumptions: Standard positive logic levels (0 = LOW, 1 = HIGH). Two or more inputs (the rule generalizes to N inputs). Concept / Approach: The inclusive OR function is defined by Y = A + B + … . The output is LOW only when all inputs are LOW. If any single input is HIGH, the sum evaluates to 1 and the output becomes HIGH. This is distinct from XOR, which is HIGH only when an odd number of inputs are HIGH, and from NOR, which outputs the complement of OR. Step-by-Step Solution: Evaluate OR for typical cases: (0,0) → 0; (1,0) → 1; (0,1) → 1; (1,1) → 1.Generalize: if any input = 1 → output = 1.Identify the gate that matches: OR gate. Verification / Alternative check: Truth table or Boolean algebra confirms that only the all-zero input combination yields a zero output. Hardware implementations in TTL/CMOS families (e.g., 7432 for OR) behave accordingly. Why Other Options Are Wrong: AND: Requires all inputs HIGH for a HIGH output. NOR: Produces LOW when any input is HIGH (the inverse of OR). NOT: Single-input inverter; does not implement multi-input any-true logic. Common Pitfalls: Confusing OR with XOR; remember inclusive OR allows multiple HIGH inputs without forcing the output LOW. Final Answer: OR gate

Question 9

AND logic gate behavior In digital electronics, under what input condition(s) will a multi-input AND gate produce a HIGH (logic 1) at its output?

Accepted Answer

Introduction / Context: An AND gate is one of the fundamental combinational logic elements used in digital systems, microcontrollers, and FPGA designs. Knowing precisely when its output goes HIGH is essential for designing control logic, enabling conditions, and safety interlocks. Given Data / Assumptions: Standard positive logic convention is used (HIGH = logic 1, LOW = logic 0). The gate may have two or more inputs. Ideal logic levels with sufficient noise margins. Concept / Approach: The truth table of an AND function is defined by the Boolean expression Y = A * B * C * …, where * denotes the logical AND operation. The product of logic variables equals 1 only if every factor equals 1. Hence, the AND gate outputs a 1 precisely when every input is 1. Step-by-Step Solution: Define the function: Y = A1 * A2 * … * An.Evaluate case when any input is 0: since 0 * X = 0, the output is 0.Evaluate case when all inputs are 1: since 1 * 1 * … * 1 = 1, the output is 1.Therefore, a HIGH output occurs only when all inputs are HIGH. Verification / Alternative check: Construct a truth table for a 3-input AND gate and observe that the sole HIGH output row is A = 1, B = 1, C = 1. Karnaugh mapping also yields a single minterm representing the all-ones input. Why Other Options Are Wrong: At least one input is HIGH: describes OR behavior, not AND.At least one input is LOW: this guarantees a LOW output for AND, not HIGH.All inputs are LOW: AND of zeros is zero. Common Pitfalls: Confusing AND with OR, or mixing negative logic conventions. Also, assuming a floating input acts like a logic 1—floating inputs must be properly biased; otherwise, output can be unpredictable. Final Answer: All inputs are HIGH.

Question 10

Identifying the gate with LOW output when any input is zero In positive-logic digital circuits, which gate outputs a LOW whenever one or more inputs are logic 0?

Accepted Answer

Introduction / Context: Selecting the correct logic gate is a foundational skill in digital design. This question targets recognition of the gate whose output immediately drops LOW if any input is LOW. Given Data / Assumptions: Positive logic (HIGH = 1, LOW = 0). Ideal gate behavior (ignoring propagation delay and noise for the concept). Two or more inputs possible. Concept / Approach: The AND gate is defined by Y = A * B * C * … . In Boolean algebra, the product is 1 only if every factor equals 1. Consequently, if any input is 0, the product becomes 0 and the output is LOW. This directly matches the description. Step-by-Step Solution: Write the Boolean function: Y = A1 * A2 * … * An.Consider any single input Ai = 0: Y = 0 * (rest) = 0.Thus, for any input at 0, the output is forced LOW.Therefore, the described gate behavior belongs to AND. Verification / Alternative check: Truth table for a 2-input AND shows outputs 1 only for (1,1); all other combinations with a 0 produce 0. Extending to more inputs preserves this rule. Why Other Options Are Wrong: OR gate: outputs 1 if any input is 1; contradicts the prompt.NOT gate: single-input inverter; behavior not described by multiple inputs.NAND gate: outputs LOW only when all inputs are 1; not when any input is 0. Common Pitfalls: Confusing NAND with AND because both are related; remember NAND is the complement of AND and is HIGH whenever any input is 0. Final Answer: AND gate

Question 11

AND gate behavior: identify the true statement about a 2-input AND gate and how its output depends on the inputs.

Accepted Answer

Introduction / Context: Logic gates implement Boolean operations used throughout digital electronics. The AND gate outputs a logic HIGH only when all of its inputs are HIGH. Knowing equivalent verbal formulations helps with quick reasoning, troubleshooting, and simplifying logic diagrams. Given Data / Assumptions: We consider a standard 2-input AND gate with one output. Inputs can be either LOW (0) or HIGH (1). Truth table for AND: 0·0=0, 0·1=0, 1·0=0, 1·1=1. Concept / Approach: For a 2-input AND gate, if one input is HIGH (1), the output equals the logical value of the remaining input. If one input is LOW (0), the output is forced LOW regardless of the other input. These properties follow directly from Boolean multiplication rules. Step-by-Step Reasoning: Let inputs be A and B, output X = A·B.If A = 1, then X = 1·B = B, so the output reflects B.If A = 0, then X = 0·B = 0, independent of B.Therefore the statement that a HIGH on one input makes the output follow the other input is correct. Verification / Alternative check: Check the truth table pairs (1,0)→0 and (1,1)→1; the output equals B in both cases when A = 1. Symmetrically, if B = 1, X equals A. Why Other Options Are Wrong: “Two inputs and one output” is common but not universally true—AND gates can have 2 or more inputs; the statement is incomplete as an absolute. “Two or more inputs and two outputs” is incorrect; standard AND gates have a single output. “Eight input possibilities” is false for 2 inputs; there are 2^2 = 4 possible input combinations. Common Pitfalls: Confusing AND with OR, where a single HIGH can produce a HIGH output. Assuming the number of inputs is always 2; practical ICs often provide 3- or 4-input ANDs. Final Answer: If one input to a 2-input AND gate is HIGH, the output reflects the other input.

Question 12

Gate equivalence: A NOR gate’s output is logically equivalent to which basic gate combination?

Accepted Answer

Introduction / Context: Recognizing functional equivalence among logic gate combinations is essential for logic simplification, hardware substitution, and understanding universal gates. NOR and NAND are universal because they can synthesize any Boolean function, but each also corresponds to a simple “gate plus inverter” form. Given Data / Assumptions: Definition: NOR outputs the logical negation of OR. Symbols: “+” denotes OR, an overbar or NOT denotes inversion. Truth tables follow standard Boolean algebra. Concept / Approach: The NOR operation is X = NOT(A + B). This is precisely the output of an OR gate feeding an inverter. No other single “gate plus inverter” pair matches NOR’s truth table directly. Step-by-Step Solution: Start with OR: Y = A + B.Invert: X = NOT(Y) = NOT(A + B).By definition, this equals the NOR function. Verification / Alternative check: Compare truth tables for NOR and the OR-then-inverter combination; they match for all four input pairs (00→1, 01→0, 10→0, 11→0). Why Other Options Are Wrong: NAND followed by inverter equals AND (NOT(NOT(A·B)) = A·B). AND followed by inverter equals NAND (NOT(A·B)). NOR followed by inverter equals OR (double negation cancels). Common Pitfalls: Mixing up De Morgan’s forms: NOR = NOT(OR), NAND = NOT(AND). Assuming the order of operations does not matter—here the OR must precede the inverter. Final Answer: OR gate immediately followed by an inverter

Question 13

Four-input OR evaluation: For inputs A = 1, B = 1, C = 0, and D = 0 to a 4-input OR gate, what is the correct Boolean sum and output value?

Accepted Answer

Introduction / Context: OR gates implement logical addition: the output is HIGH if any input is HIGH. Evaluating multi-input OR expressions reinforces facility with Boolean algebra and prepares learners for sum-of-products simplifications. Given Data / Assumptions: Inputs: A=1, B=1, C=0, D=0. Definition: X = A + B + C + D. Boolean “+” denotes logical OR, not arithmetic addition. Concept / Approach: For OR, the presence of at least one 1 drives the output to 1. Multiple ones do not change the result—it remains 1. No carry or multi-digit result exists in Boolean OR; the output is a single logic level (0 or 1). Step-by-Step Solution: Evaluate A + B = 1 + 1 = 1 (Boolean OR).Then 1 + C = 1 + 0 = 1.Then 1 + D = 1 + 0 = 1.Thus, the expression simplifies to 1, and the output is HIGH. Verification / Alternative check: Truth-table view: any case with A=1 OR B=1 yields X=1 regardless of other inputs. Here both A and B are 1, so X must be 1. Why Other Options Are Wrong: Results such as “01” or “00” imply multi-bit outputs, which do not apply to a single OR gate. “= 0” contradicts the presence of HIGH inputs. Common Pitfalls: Treating Boolean “+” as arithmetic addition; Boolean OR outputs a single logic level. Assuming two ones might “overflow” to something other than 1—this is not applicable in Boolean logic. Final Answer: 1 + 1 + 0 + 0 = 1

Question 14

Core Boolean operations: Identify the choice that is NOT one of the three basic Boolean operations used to build digital logic.

Accepted Answer

Introduction / Context: Digital logic is constructed from a small set of primitive Boolean operations. Mastery of these operations—AND, OR, and NOT—enables the design and analysis of combinational and sequential circuits, as well as simplification with Boolean algebra and Karnaugh maps. Given Data / Assumptions: The three elemental operations are being considered. We are asked to spot the item that is not a Boolean primitive. Terminology follows standard digital electronics convention. Concept / Approach: Boolean algebra is defined over binary variables using AND (·), OR (+), and NOT (inversion). While many other useful operations exist (XOR, NAND, NOR), they are derived from the three basics. The word “FOR” is simply an English preposition, not a Boolean operator. Step-by-Step Reasoning: List standard primitives: AND, OR, NOT.Compare each option to the set: OR ✓, NOT ✓, AND ✓, FOR ✗.Therefore, the non-Boolean item is FOR. Verification / Alternative check: Consider functional completeness: NAND or NOR alone can implement all three basics, further confirming that Boolean logic relies on AND/OR/NOT at its foundation, not an operator named “FOR.” Why Other Options Are Wrong: OR, NOT, AND are indeed basic Boolean operations and appear in every introductory logic text and IC family datasheet. Common Pitfalls: Confusing XOR with a basic primitive. XOR is fundamental in practice but is algebraically derived from AND, OR, and NOT. Assuming natural-language words map to logic terms; only specific defined operators are used. Final Answer: FOR

Question 15

Reading Boolean expressions: When a specification uses the word “NOT” in digital logic, what operation does it indicate?

Accepted Answer

Introduction / Context: Boolean expressions are often written in words, symbols, or a mixture of both. Interpreting the word “NOT” correctly is vital for writing and reading truth tables, understanding gate-level schematics, and converting logic requirements into equations. Given Data / Assumptions: “NOT” is the keyword under examination. We consider standard Boolean algebra and digital circuit conventions. Inputs and outputs take values 0 (LOW) or 1 (HIGH). Concept / Approach: “NOT” denotes logical inversion (complementation). If a variable is A, then NOT A is written as Ā, A̅, A', or simply NOT A, and equals 1 when A = 0, and 0 when A = 1. Physically, this is implemented by an inverter gate. Step-by-Step Reasoning: Define A ∈ {0,1}.Apply inversion: X = NOT A.Truth: if A=0 ⇒ X=1; if A=1 ⇒ X=0.Therefore, “NOT” means inversion (logical complement). Verification / Alternative check: On schematics, an inversion bubble on a gate input or output represents NOT. On timing diagrams, inversion flips HIGH/LOW levels and toggles edge sensitivity where applicable. Why Other Options Are Wrong: “the same as”: opposite of inversion. “high” or “low”: these are signal levels, not operations. NOT may produce either level depending on the input. Common Pitfalls: Confusing active-LOW signals (indicated by a bar or a “/” prefix) with normal signals; active-LOW means the function is asserted when the signal is 0, which is a design choice, not a different operation. Final Answer: inversion

Question 16

Digital IC packaging terminology: The phrase “hex inverter” most commonly refers to which device configuration?

Accepted Answer

Introduction / Context: IC datasheets and catalogs often describe logic packages with counts like “dual,” “quad,” and “hex.” Understanding this shorthand helps engineers pick appropriate parts and pinouts without confusion during schematic capture and PCB layout. Given Data / Assumptions: “Hex” denotes the number six. We are considering inverter (NOT) gates packaged together in one IC. Common logic families (TTL, CMOS) offer standard hex inverter parts (e.g., 7404/74HC04). Concept / Approach: A “hex inverter” is an IC containing six independent inverter gates, each with one input and one output, all sharing power pins. The device provides multiple identical functions in one package to save board area and routing complexity. Step-by-Step Reasoning: Interpret “hex” as six.Associate with inverter function (NOT gate).Conclude: the package contains six separate inverters. Verification / Alternative check: Review a standard part like 74HC04: the pinout shows six inverter sections labeled A–F. Each section operates independently within the same IC. Why Other Options Are Wrong: “An inverter that has six inputs” describes a multi-input gate, not a hex package. “A six-input symbolic logic device” is vague and not standard terminology. “A history of failure” misinterprets “hex” humorously; it is unrelated to reliability. Common Pitfalls: Confusing “hex” (six functions) with “six-input”; they are different concepts. Overlooking that some packages mix functions (e.g., Schmitt-trigger inverters) but still count as hex. Final Answer: six inverters in a single package

Question 17

NOT operation definition: If a NOT gate has input A and output X, write the correct relationship between X and A.

Accepted Answer

Introduction / Context: The NOT gate (inverter) is the simplest logic element that flips a binary value. Accurately expressing the relationship between input and output is central to building and analyzing basic and complex digital systems, from simple oscillators to microprocessor control logic. Given Data / Assumptions: Single input A, single output X. Binary logic levels: 0 (LOW) and 1 (HIGH). Standard Boolean notation where NOT means logical complement. Concept / Approach: By definition, an inverter outputs the complement of its input. This can be denoted several ways: X = NOT A, X = A', or X = Ā. The meaning is identical—X is 1 when A is 0, and X is 0 when A is 1. Step-by-Step Solution: Define X = NOT A.Truth evaluation: A=0 ⇒ X=1; A=1 ⇒ X=0.Thus the correct relationship is X = NOT A. Verification / Alternative check: Observe the inverter symbol on a schematic: an inversion bubble on the output depicts the NOT operation. Measuring with a logic probe will show output transitions opposite to the input transitions. Why Other Options Are Wrong: X = A implies a buffer, not an inverter. X = 0 would mean the output is always LOW, which is not a logic gate function here. “none of the above” is invalid because X = NOT A is a correct and standard statement. Common Pitfalls: Confusing overbar notation with subtraction or arithmetic; it strictly means complement. Overlooking active-LOW signal naming, which sometimes reads as a “NOT” but refers to assertion level, not necessarily an inverter in the path. Final Answer: X = NOT A

Question 18

3-input AND requirement: For a three-input AND gate, what condition on the inputs guarantees a LOW output?

Accepted Answer

Introduction / Context: Understanding how multi-input AND gates behave is critical when designing enable signals, chip selects, and safety interlocks. The AND function outputs HIGH only if all inputs are HIGH, so identifying the condition for a LOW output follows directly from its truth table. Given Data / Assumptions: A 3-input AND gate with inputs A, B, C and output X = A·B·C. Binary logic levels are 0 and 1. No inversion or special active-LOW semantics are present on inputs/outputs. Concept / Approach: For AND, the product is 1 only when every factor is 1. Therefore, the presence of even a single 0 anywhere in the inputs forces the product to 0, guaranteeing a LOW output. Step-by-Step Reasoning: Write the output: X = A·B·C.If A = 0, then X = 0·B·C = 0 regardless of B and C.Similarly for B = 0 or C = 0, the result is 0.Thus, “at least one input LOW” assures X is LOW. Verification / Alternative check: Truth table confirms that only the row A=1, B=1, C=1 yields X=1; all other seven combinations contain at least one 0 and produce X=0. Why Other Options Are Wrong: “All LOW” is sufficient but not necessary; a single LOW already guarantees LOW output. “All HIGH” yields HIGH, not LOW. “At least one HIGH” is insufficient, since two other inputs could be LOW. Common Pitfalls: Confusing AND with OR, where the presence of at least one HIGH is significant. Assuming symmetry with NAND; NAND outputs the complement of AND and changes the required conditions. Final Answer: At least one input must be LOW.

Question 19

Boolean expression recall: Write the standard Boolean equation for the output X of a 3-input AND gate with inputs A, B, and C.

Accepted Answer

Introduction / Context: Boolean equations compactly describe logic behavior and map directly to gate-level implementations. Being able to write the correct expression for common gates like a 3-input AND is essential for circuit analysis, HDL coding, and testbench verification. Given Data / Assumptions: Three inputs: A, B, C. One output: X. Standard notation: juxtaposition or the dot “·” denotes AND; plus “+” denotes OR. Concept / Approach: An AND gate outputs HIGH only when all inputs are HIGH. The Boolean product of all inputs captures this requirement: X equals A AND B AND C, written as X = A·B·C or simply X = ABC (when the AND operator is implied by concatenation). Step-by-Step Solution: Identify operation: AND across three variables.Write product: X = A·B·C.Use concise form: X = ABC (common shorthand).Therefore, the correct expression is X = ABC. Verification / Alternative check: Truth table: only when A=1, B=1, and C=1 does the product evaluate to 1; in all other cases, at least one factor is 0, producing X=0. Why Other Options Are Wrong: X = AB omits C and represents a 2-input AND. X = A + B + C is a 3-input OR, not AND. X = AB + C equals (A AND B) OR C, which differs from pure 3-way AND. Common Pitfalls: Dropping inputs unintentionally when moving from schematic to equation. Confusing additive and multiplicative operators in Boolean algebra. Final Answer: X = ABC

Question 20

Boolean algebra operator symbols In standard Boolean algebra used for digital logic design, which logical operation is represented by the plus sign (+)?

Accepted Answer

Introduction / Context: Boolean algebra provides a compact symbolic way to describe the behavior of logic circuits. Knowing which symbols correspond to which operations is essential when reading datasheets, simplifying expressions, or designing gate-level implementations. Given Data / Assumptions: The question concerns the conventional symbols used in positive logic Boolean algebra. The plus sign (+) appears between Boolean variables (for example, A + B). We assume standard textbook conventions (not arithmetic addition). Concept / Approach: In Boolean algebra: the plus sign (+) denotes the logical OR operation; the dot (·) or adjacency denotes logical AND; and a bar, prime, or overline denotes logical NOT (inversion). Thus, A + B means A OR B; A · B (or AB) means A AND B; and A' (or Ā) means NOT A. Step-by-Step Solution: Identify operator: the symbol in question is +.Recall mapping: + → OR, · → AND, overbar/prime → NOT.Match to option: the only answer naming the OR operation is correct. Verification / Alternative check: Truth tables confirm that A + B equals 1 when either A or B (or both) are 1, exactly the behavior of an OR gate. This aligns with logic symbols used across 74xx/40xx families and HDL textbooks. Why Other Options Are Wrong: Inversion / complementation uses a bar or prime, not +. AND uses a dot or adjacency (AB), not +. XOR is typically written as A ⊕ B, not A + B. Common Pitfalls: Confusing arithmetic addition with Boolean OR. In Boolean algebra, 1 + 1 = 1. Mixing operator precedence; typically NOT applies first, then AND, then OR. Final Answer: OR

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