Question 1

Bubble-to-bubble connection intuition (De Morgan view): If a signal leaves a gate through an inverted (bubbled) output and enters the next gate on an inverting (bubbled) input, the two inversions cancel, producing an overall non-inverting transfer r…

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Introduction / Context: Logic symbols often show inversion as a small bubble. Understanding how “bubble-to-bubble” connections behave is crucial for reading schematics quickly and for using De Morgan transformations to simplify or restyle logic without changing function. Given Data / Assumptions: One gate provides an inverted output (bubble on its output). The next gate has an inverting input (bubble on its input pin). We are reasoning functionally, assuming ideal logic levels. Concept / Approach: A bubble denotes inversion. Two inversions in series cancel each other, yielding a non-inverting connection. This is a visual manifestation of De Morgan equivalences and the idea that NOT(NOT(X)) = X. Therefore, bubble-to-bubble effectively passes the signal without net inversion. Step-by-Step Solution: Let the original (internal) signal be S.First inversion at the producer: output = NOT(S).Second inversion at the consumer’s inverting input yields: effective input = NOT(NOT(S)) = S.Net result: no inversion overall (zero inversions remain). Verification / Alternative check: Substitute concrete logic levels: if S = 1, the producing gate output is 0; the inverting input interprets that as NOT(0) = 1 at its internal logic. If S = 0, the chain delivers 0. This confirms cancellation. Why Other Options Are Wrong: “Correct” repeats the original claim that one inversion remains; that is the opposite of the cancellation result. “Only true for CMOS” and “Depends on fan-out” are red herrings; the cancellation is logical, not process-dependent. Common Pitfalls: Mistaking symbol bubbles as delay markers; forgetting that each bubble is a NOT; assuming bubbles affect only thresholds instead of logic sense. Final Answer: Incorrect

Question 2

Two-input NAND timing behavior (conceptual correctness check): A standard two-input NAND gate produces a LOW output only during the time interval when both inputs are simultaneously HIGH; at all other input combinations, the output remains HIGH. Is …

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Introduction / Context: Many textbook and lab questions present timing diagrams for logic gates and ask whether a gate “works correctly.” Even without a specific drawing here, we can state the definitive functional timing rule for a two-input NAND to determine correctness: a NAND outputs LOW only when both inputs are HIGH at the same time. This rule lets you validate any timing diagram qualitatively. Given Data / Assumptions: Two-input NAND gate with ideal logic levels. Functional analysis (truth-based), not accounting for nanosecond-scale hazards unless specifically asked. Inputs are labeled A and B; output is Y. Concept / Approach: Truth table for NAND: A B 00→Y=1, 01→1, 10→1, 11→0. Converting to timing, Y should be HIGH except during those exact intervals when A=1 and B=1 concurrently; during those overlapping windows, Y is LOW. Therefore, a timing diagram is “correct” if it respects this mapping throughout the waveform. Step-by-Step Solution: Identify intervals where both inputs are HIGH together.Mark those intervals on the time axis as spans where Y should be LOW.Everywhere else (any 0 among inputs), Y should be HIGH.Check for spurious pulses only if the problem mentions hazards or unequal delays. Verification / Alternative check: Use the Boolean form: Y = NOT(A · B). During any interval with A · B = 1, Y must be 0; otherwise Y = 1. This cross-checks the timing logic. Why Other Options Are Wrong: “Incorrect” would contradict the established NAND behavior. Options about “Schmitt-trigger” or “rise/fall times” concern analog edges and noise immunity, not the fundamental truth-function. Common Pitfalls: Forgetting that partial overlap matters (both need to be 1 simultaneously); confusing instant transitions with real delays; assuming glitches prove incorrect logic when they may be transient hazards outside the problem’s scope. Final Answer: Correct

Question 3

Structure of a NAND gate (functional view): Evaluate the claim: “A NAND gate is built by connecting an AND gate and an OR gate in series with each other.” Decide whether this structural description is accurate.

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Introduction / Context: In introductory courses, learners sometimes try to infer complex gates as series combinations of simpler ones. It is important to separate functional equivalence from specific internal transistor-level realizations. The statement under test claims that a NAND equals an AND followed by an OR in series, which would imply a specific functional cascade. Given Data / Assumptions: NAND’s Boolean definition is Y = NOT(A · B). “AND then OR in series” suggests a cascade that does not include an inversion stage unless added. Standard gates are considered functionally, not at transistor topology level. Concept / Approach: A NAND is the inversion of an AND: take an AND function and invert its output. An “AND then OR” cascade is neither required nor functionally equivalent to a single NAND. The minimal functional representation is AND followed by NOT (an inverter) or, equivalently, OR with inverted inputs (by De Morgan). None of these is “AND then OR” in series. Step-by-Step Solution: Start from NAND definition: Y = NOT(A · B).Functional build: compute A · B using an AND gate.Invert that result with a NOT gate to obtain Y.Observe no OR gate is necessary in this simple construction. Verification / Alternative check: De Morgan: Y = NOT(A · B) = (NOT A) + (NOT B). This shows an OR combining inverted inputs—not “AND then OR” serial connection. Why Other Options Are Wrong: “Correct” conflicts with Boolean definitions. Wired-logic and RTL/CMOS distinctions do not change the functional truth that NAND is AND plus inversion, not AND then OR. Common Pitfalls: Confusing series/parallel transistor networks with symbolic gate-level blocks; overcomplicating with unnecessary gates. Final Answer: Incorrect

Question 4

Classification of a NAND gate: Determine whether a NAND gate is considered a combinational logic element (i.e., its output depends only on the current inputs and not on past history).

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Introduction / Context: Digital circuits are broadly classified as combinational or sequential. Combinational circuits compute outputs directly from present inputs, while sequential circuits have memory of past states (via feedback, latches, or flip-flops). Knowing where basic gates fit is foundational. Given Data / Assumptions: NAND gate with no internal storage elements is considered. Ideal logic abstraction is used. No external feedback paths are included unless explicitly added by the designer. Concept / Approach: A single NAND gate performs the function Y = NOT(A · B). This is a pure Boolean mapping from the current values of A and B to Y. There is no dependence on previous values of A or B, nor is there an internal state element that stores information across time. Step-by-Step Solution: Identify gate type: two-input NAND.Write its Boolean function: Y = NOT(A · B).Observe lack of feedback or memory: Y is determined instantaneously by A and B (subject to propagation delay).Conclude it is combinational. Verification / Alternative check: Compare with a latch or flip-flop, where outputs depend on past events (clocking, set/reset). A bare NAND lacks such mechanisms, confirming the classification. Why Other Options Are Wrong: “Incorrect” would imply NAND is sequential, which it is not. Claims about frequency or power sequencing conflate practical effects with functional classification. Common Pitfalls: Confusing propagation delay with memory; assuming that because NAND can build latches (when cross-coupled), a single NAND is itself sequential. Only when arranged with feedback does sequential behavior emerge. Final Answer: Correct

Question 5

Recognizing the AND gate symbol (ANSI/IEC): The standard symbol for an AND gate shows a flat input side and a smoothly rounded output side with no inversion bubble at the output, indicating a non-inverting function. Judge this description.

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Introduction / Context: Being fluent with logic symbols accelerates schematic reading and reduces connection mistakes. Recognizing whether an output is inverted (bubble present) or not (no bubble) is especially important when combining gates or translating to HDL. Given Data / Assumptions: Conventional gate symbols (ANSI/IEEE or IEC styles) are in use. AND gate is non-inverting at the output. Inversion is always depicted by a small bubble. Concept / Approach: The canonical AND symbol has a straight (flat) left side where inputs enter and a convex (rounded) right side from which the output leaves. Absence of a bubble at the output denotes no inversion. If a bubble is placed at the output, the symbol becomes a NAND gate, representing logical inversion of the AND function. Step-by-Step Solution: Recall: AND function Y = A · B (non-inverting output).Visual cue: flat left edge for inputs, curved right edge for output.No bubble at output → non-inverting (AND), bubble at output → inverting (NAND).Therefore, the given symbol description matches an AND gate. Verification / Alternative check: Compare with OR symbol: it also has a curved output, but the input edge is curved too, distinguishing it from AND. Compare with NAND: identical to AND but with a bubble on the output. Why Other Options Are Wrong: “Incorrect” contradicts the widely accepted symbol conventions. Claims about region (IEC vs ANSI) or input count do not change the bubble rule and general shape recognition. Common Pitfalls: Confusing OR vs AND outline; overlooking tiny inversion bubbles; assuming stylistic variations change logical meaning. Final Answer: Correct

Question 6

Boolean product evaluation: Confirm the fundamental identity 1 · 0 = 0 in Boolean algebra, where “·” denotes logical AND.

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Introduction / Context: Boolean algebra underpins digital logic. The AND operation corresponds to multiplication-like behavior where the result is true only if all operands are true. Verifying basic identities like 1 · 0 = 0 ensures accurate reasoning about gates and circuits. Given Data / Assumptions: Binary values use 1 for HIGH/true and 0 for LOW/false. AND truth: true only when both inputs are true. We are working at the logical, not analog, level. Concept / Approach: By the AND definition, if any input is 0, the output must be 0. Therefore, 1 AND 0 is 0, and 0 AND 1 is 0, and 0 AND 0 is 0. Only 1 AND 1 yields 1. These form the core truth table reflected in gate behavior and in Boolean equations. Step-by-Step Solution: Define AND: output = 1 only when all inputs = 1.Evaluate 1 · 0: at least one input is 0 → output = 0.Conclude identity: 1 · 0 = 0 holds universally in Boolean algebra.Relate to gate: an AND gate fed by inputs 1 and 0 drives 0. Verification / Alternative check: Truth table check: rows (1,0) and (0,1) both give 0. Algebraic properties (annihilator for AND) also state that 0 is the absorbing element: X · 0 = 0 for any X. Why Other Options Are Wrong: “Incorrect” contradicts the AND definition. “Only true in arithmetic” misunderstands the mapping between Boolean AND and multiplication-like behavior. “Depends on voltage thresholds” addresses implementation details, not the abstract Boolean law. Common Pitfalls: Mixing arithmetic and logic but forgetting the identical outcome for this specific case; considering analog exceptions that are beyond Boolean abstraction. Final Answer: Correct

Question 7

VHDL in historical context: VHDL (VHSIC Hardware Description Language) originated in the 1980s and has been standardized for decades; therefore, in today’s context it is not a “new” language. Evaluate this statement.

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Introduction / Context: VHDL is a cornerstone HDL used for modeling, simulating, and synthesizing digital hardware. When discussing language maturity, “new” typically refers to emerging or recently standardized languages. VHDL’s long history positions it as a mature, not new, choice. Given Data / Assumptions: VHDL emerged from the VHSIC program era in the 1980s. It has multiple IEEE standards and revisions over decades. It remains in wide use alongside Verilog/SystemVerilog. Concept / Approach: A language with decades of standardization, tool support, and a large body of IP and literature is considered mature. Although the language has evolved (with updates and extensions), that does not make it “new.” The statement under test addresses age and maturity, not popularity or capability. Step-by-Step Solution: Identify era of origin: mid-1980s.Recognize IEEE standardization and continued maintenance.Acknowledge ongoing industry adoption in FPGA and ASIC flows.Conclude that calling VHDL “not new” is accurate. Verification / Alternative check: Compare with newer HDLs and methodologies (e.g., SystemVerilog, Chisel). The timeline confirms VHDL’s earlier introduction and long-standing presence. Why Other Options Are Wrong: “Incorrect” denies the historical record. ASIC/FPGA distinctions do not change the age of the language. Referencing SystemVerilog’s timeline is irrelevant to whether VHDL is “new.” Common Pitfalls: Equating “actively used” or “recent revisions” with “newness”; overlooking that language maturity and community size often benefit reliability and tool support. Final Answer: Correct

Question 8

Evaluating a specific NAND input case: For a two-input NAND gate with inputs A = 1 and B = 0 at the same time, determine whether the output equals 0 as claimed.

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Introduction / Context: Being able to quickly evaluate gate outputs for specific input combinations is a fundamental skill in digital logic. NAND is especially important because it is functionally complete (can build any logic) and used to construct latches and sequential elements when cross-coupled. Given Data / Assumptions: Two-input NAND gate. Inputs: A = 1, B = 0 simultaneously. Ideal logic levels considered. Concept / Approach: The Boolean function for a NAND is Y = NOT(A · B). Compute the inner AND first: A · B = 1 · 0 = 0. Then invert: NOT(0) = 1. Therefore, for inputs (1,0) the output must be 1, not 0. Step-by-Step Solution: Write the function: Y = NOT(A · B).Evaluate A · B: 1 · 0 = 0.Invert the result: NOT(0) = 1.Conclude: output is 1, so the claim “output is 0” is incorrect. Verification / Alternative check: Truth table row for NAND: for inputs 10 or 01, Y = 1. Only for 11 does Y = 0. This cross-validates the computation. Why Other Options Are Wrong: “Correct” contradicts the truth table. Environmental or drive-strength claims do not change the logical mapping and are irrelevant in the Boolean abstraction. Common Pitfalls: Confusing NAND with AND; forgetting that only the 11 case produces a LOW; misapplying precedence by trying to invert an incorrect intermediate result. Final Answer: Incorrect

Question 9

Relationship between AND and NAND outputs: Across all possible input combinations, the output of a NAND gate is the logical inversion (complement) of the output of an AND gate driven by the same inputs. Assess this statement.

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Introduction / Context: AND and NAND are tightly linked: a NAND is an AND with an inversion at its output. Recognizing this relationship helps with quick truth-table derivations, hardware substitutions, and De Morgan transformations when optimizing logic. Given Data / Assumptions: We compare a two-input AND gate and a two-input NAND gate with the same inputs. Logic abstraction (no timing hazards) applies. Standard Boolean operations and identities are used. Concept / Approach: Define the functions: AND output is F = A · B. NAND output is G = NOT(A · B). Clearly, G = NOT(F). Therefore, for each input pair, the NAND’s output is the complement of the AND’s output. This holds for all combinations: 00, 01, 10 produce F=0 → G=1; 11 produces F=1 → G=0. Step-by-Step Solution: Write F = A · B (AND).Write G = NOT(A · B) (NAND).Relate G to F: G = NOT(F).Check all four input rows to confirm the complement relationship. Verification / Alternative check: Create a small table: inputs 00,01,10 → F=0 so G=1; input 11 → F=1 so G=0. Every row shows inversion, confirming the statement conclusively. Why Other Options Are Wrong: “Incorrect” contradicts the formal definitions. Claims about rise times or logic families (TTL vs CMOS) concern implementation details and do not alter the Boolean relationship. Common Pitfalls: Forgetting that NAND is simply AND plus an output inversion; mixing up NAND with NOR (which is the inversion of OR). Final Answer: Correct

Question 10

Boolean algebra fundamentals — verify the commutative law statement Evaluate the claim: “The commutative law of Boolean addition states that A + B = A · B.” State whether this statement is correct or incorrect, and recall what the commutative law ac…

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Introduction / Context: Foundational Boolean algebra laws are used every day to simplify logic expressions and design digital circuits. The commutative law is among the most basic. This question asks whether the commutative law of Boolean addition claims A + B = A · B, and invites you to recall the exact statement of the law. Given Data / Assumptions: Binary variables A and B take values 0 or 1. “+” denotes Boolean OR, “·” denotes Boolean AND. We are checking the correctness of the stated identity. Concept / Approach: The commutative law in Boolean algebra states that the order of operands does not affect the result: A + B = B + A for OR, and A · B = B · A for AND. It does not equate OR with AND. Therefore, asserting A + B = A · B is generally false except in special trivial cases (e.g., when A = B = 0 or 1 simultaneously). Step-by-Step Solution: Recall: OR is commutative → A + B = B + A.Recall: AND is commutative → A · B = B · A.Compare with given claim: A + B = A · B. This equates different operators and is not a commutative statement.Test with A=1, B=0: A + B = 1; A · B = 0 → not equal. Verification / Alternative check: Truth-table sampling for any unequal inputs shows a mismatch between OR and AND. Only when A and B are both 0 or both 1 do the two expressions coincide, but commutative law must hold for all inputs. Why Other Options Are Wrong: Correct: Not true; it misstates the law. The choices suggesting conditional correctness still misrepresent the law, which speaks to operand order, not operator equivalence. Common Pitfalls: Confusing commutativity (operand order) with other identities or with DeMorgan’s theorems. Another pitfall is assuming OR and AND can be interchanged without context. Final Answer: Incorrect

Question 11

History check — Boolean algebra in circuit analysis Assess this statement: “Boolean algebra was first applied to the analysis of digital circuits by Claude Shannon at Stanford University.” Indicate whether it is correct or incorrect and recognize th…

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Introduction / Context: Understanding where core ideas originated helps learners connect concepts to their proper contexts. This question checks the historical attribution of the first formal application of Boolean algebra to switching circuit analysis, commonly associated with Claude E. Shannon. Given Data / Assumptions: Subject: Early application of Boolean algebra to circuits. Figure named: Claude Shannon. Institution claimed: Stanford University. Concept / Approach: Claude Shannon famously demonstrated that Boolean algebra could model switching circuits in his master’s thesis and subsequent publication. The institution linked to that breakthrough was not Stanford University. Knowing this disconfirms the statement as written. Step-by-Step Solution: Identify the person: Claude E. Shannon — correct key figure.Identify the work: His pioneering analysis linked relays/switching circuits and Boolean algebra.Identify the place: Not Stanford University; the statement therefore fails. Verification / Alternative check: Historical summaries of Shannon’s early work consistently tie the foundational application to institutions other than the one stated in the prompt. Therefore, the precise claim is incorrect. Why Other Options Are Wrong: “Correct” options affirm the wrong university; adding a different institution within the same answer choice still leaves the original statement incorrect as posed. Common Pitfalls: Remembering the person but misremembering the institution; conflating later career affiliations with the site of the breakthrough. Final Answer: Incorrect

Question 12

Reasoning about circuits without explicit algebra Evaluate the claim: “Output logic levels for certain input conditions of a logic circuit may often be determined without first writing its Boolean expression.” Indicate whether this practical design …

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Introduction / Context: Digital designers frequently predict circuit behavior by inspection using gate intuition, truth tables, and timing diagrams. This can be done even before or without writing a full Boolean expression. The question checks this common practical workflow. Given Data / Assumptions: The circuit may be combinational or simple sequential with known control states. We consider specific input conditions rather than full functional derivation. Concept / Approach: Gate-level reasoning, signal propagation, and known identities (e.g., an input tied LOW on an AND dominates to force LOW) let you infer outputs for chosen inputs. Karnaugh maps and small truth-table fragments also enable partial deductions without full algebraic derivation. Step-by-Step Solution: Pick a concrete input case (e.g., A=0).Apply gate dominance rules: AND with 0 → output 0; OR with 1 → output 1; inverter flips the input.Trace the signal through the gate network to the output.Record the output for that case without needing a symbolic expression. Verification / Alternative check: You can later confirm the inferred outputs by writing the Boolean expression, simplifying it, and comparing isolated truth-table rows for those input cases. Why Other Options Are Wrong: “Incorrect” ignores standard design practice. The restricted options limit validity to symmetry or to combinational-only, but in practice inspection works broadly wherever the behavior for specific inputs is traceable. Common Pitfalls: Overgeneralizing inspection to complex sequential feedback without timing; ignoring hazards and don’t-care conditions when inferring outputs. Final Answer: Correct

Question 13

Identity check — distributive equivalence used in simplification Evaluate whether the Boolean expressions A + (B · C) and (A + B) · (A + C) are equivalent for all binary inputs.

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Introduction / Context: Recognizing standard identities enables fast simplification and structured design using NAND/NOR implementations. One key identity is the distributive relationship connecting sum with product terms. Given Data / Assumptions: Variables A, B, C are Boolean (0 or 1). We compare A + (B · C) with (A + B) · (A + C). Concept / Approach: In Boolean algebra, addition (OR) distributes over multiplication (AND) and vice versa in specific forms. The identity A + (B · C) = (A + B) · (A + C) holds for all input combinations and is frequently used to realize logic using only NAND or only NOR gates. Step-by-Step Solution: If A = 1, left side: 1 + (B · C) = 1; right side: (1 + B)(1 + C) = 1 · 1 = 1.If A = 0, left side: 0 + (B · C) = B · C; right side: (0 + B)(0 + C) = B · C.Therefore equality holds for both A=1 and A=0, which covers all cases. Verification / Alternative check: Construct a short truth-table fragment for A=0 and A=1 and see both sides match for all B, C. Karnaugh-map verification also confirms overlap of minterms. Why Other Options Are Wrong: “Not equivalent” contradicts the identity. Conditional equivalence options limit the identity to special cases, which is incorrect because it holds unconditionally. Common Pitfalls: Confusing this with DeMorgan’s theorems, or misapplying distribution in the reverse form without parentheses, leading to mistakes. Final Answer: Equivalent (Correct)

Question 14

Applying DeMorgan and removing double negations Consider a Boolean expression containing both double inversions and single inversions. After fully applying DeMorgan’s theorems and canceling double inversions, the result should contain only single in…

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Introduction / Context: DeMorgan’s theorems are the primary tools for pushing negations inward through sums and products, essential when mapping logic into NAND-only or NOR-only realizations. Understanding what the fully propagated form looks like prevents common sign errors. Given Data / Assumptions: Negations can exist on groups (parenthesized terms) and on single variables. We apply DeMorgan repeatedly and remove double inversions through the rule that a double inversion restores the original operand. Concept / Approach: DeMorgan’s rules: complement of a sum becomes product of complements, and complement of a product becomes sum of complements. Every time a bar crosses a parenthesis, the operator toggles (+ ↔ ·) and the complement distributes to each literal. Double inversions over any term cancel out. Step-by-Step Solution: Start with a complemented group such as (X + Y)̄ or (X · Y)̄.Apply DeMorgan to push the bar to each literal, switching operators.Wherever a literal is already complemented and receives another bar, remove the pair (double negation).Final form places single inversion marks only on variables (literals), not on multi-term groups. Verification / Alternative check: Construct truth tables before and after the transformation; they match exactly. Logic network drawings with bubbles (signal inversion marks) also show bubble-pushing results in inversions only on inputs of gates. Why Other Options Are Wrong: Limiting validity to two variables or SOP only is unnecessary; the property holds for arbitrary-size expressions and forms as long as DeMorgan and double-negation rules are correctly applied. Common Pitfalls: Forgetting to flip the operator when moving the bar, or missing a double-negation cancellation, leading to incorrect literal polarities. Final Answer: Valid

Question 15

Switch analogy — series vs. parallel behavior Evaluate the claim: “The OR gate performs like two switches wired in series.” Decide whether this statement is correct or incorrect and relate OR to the proper switch wiring.

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Introduction / Context: Physical switch analogies provide intuition for logic gates. Understanding whether an OR gate corresponds to series or parallel wiring prevents conceptual mistakes when sketching quick logic using switches or relays. Given Data / Assumptions: Switches are ideal and control a lamp or output node. Active-HIGH logic is assumed for the basic analogy. Concept / Approach: In the standard active-HIGH analogy, an AND gate behaves like series switches: current flows only when all switches are closed. An OR gate behaves like parallel switches: current flows when any one is closed. Therefore, claiming that an OR gate is like series wiring is incorrect. Step-by-Step Solution: Series wiring requires both switches closed to complete the circuit → AND.Parallel wiring requires at least one switch closed to complete the circuit → OR.Thus the given statement mismatches the correct mapping. Verification / Alternative check: Construct a small truth table mapping switch states to lamp state for both series and parallel cases and compare to the gate truth tables; the parallel case aligns with OR. Why Other Options Are Wrong: The qualifiers about technology families or active-LOW do not change the standard mapping under active-HIGH conventions; inverting logic levels must be explicitly modeled to alter the analogy. Common Pitfalls: Confusing the AND and OR analogies; forgetting to specify active level (HIGH vs. LOW) when using switch metaphors. Final Answer: Incorrect

Question 16

NOR gate truth-table understanding without a figure For a 2-input NOR gate, choose the correct statement describing its truth table and output behavior for all input combinations.

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Introduction / Context: NOR is a fundamental universal gate widely used in logic synthesis. Recognizing its truth-table behavior by description saves time when reading or repairing circuits without printed tables or figures. Given Data / Assumptions: Two inputs: A and B, each 0 or 1. NOR output is the complement of OR: Y = (A + B)̄. Concept / Approach: Compute the OR first; then invert it. OR is 1 if at least one input is 1; otherwise 0. Therefore, NOR is 1 only in the single case when OR is 0, namely when both inputs are 0. Step-by-Step Solution: Case A=0, B=0: OR=0 → NOR=1.Case A=0, B=1: OR=1 → NOR=0.Case A=1, B=0: OR=1 → NOR=0.Case A=1, B=1: OR=1 → NOR=0. Verification / Alternative check: Truth-table reconstruction confirms that only the (0,0) input pair yields output 1. Karnaugh maps also show a single minterm at ĀB̄ for Y. Why Other Options Are Wrong: The statement that output is 1 whenever any input is 1 describes OR, not NOR. Saying output is 0 only when both inputs are 0 flips the correct case. Output toggling independently of inputs has no basis in deterministic combinational logic. Common Pitfalls: Confusing NOR with NAND (which is 0 only when both inputs are 1) or with OR. Omitting the inversion step after computing OR. Final Answer: Output is 1 only when both inputs are 0

Question 17

Distributive law recognition in logic implementations Review the standard Boolean distributive identity: A · (B + C) = A · B + A · C. Decide whether this statement correctly represents the distributive law as implemented in logic.

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Introduction / Context: Distributive properties connect sums and products, guiding how logic networks can be factored or expanded. This identity is used both for algebraic simplification and for mapping to gate-level implementations. Given Data / Assumptions: Boolean variables A, B, C in {0,1}. Operators: “+” for OR and “·” for AND. Concept / Approach: Distribution means a factor can be multiplied across each term inside parentheses. In Boolean algebra, A · (B + C) expands to A · B + A · C for all input combinations. This mirrors arithmetic distribution, albeit with Boolean operators. Step-by-Step Solution: If A=0: Left side 0 · (B + C) = 0; right side 0 · B + 0 · C = 0 + 0 = 0.If A=1: Left side 1 · (B + C) = B + C; right side 1 · B + 1 · C = B + C.Therefore, equality holds regardless of B and C. Verification / Alternative check: Truth-table enumeration confirms row-by-row equality. Karnaugh maps for both sides reduce to the same cover. Why Other Options Are Wrong: Conditional versions unnecessarily limit a universal identity; “Incorrect” contradicts a standard theorem used in all introductory texts. Common Pitfalls: Mixing up with the related identity A + (B · C) = (A + B) · (A + C). Forgetting operator meanings when switching between arithmetic intuition and Boolean logic. Final Answer: Correct

Question 18

Operator symbols — identify Boolean multiplication Evaluate the statement: “Boolean multiplication is symbolized by A + B.” Determine whether this is correct or incorrect and recall the proper notation.

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Introduction / Context: Clear operator notation prevents errors when translating between algebraic forms and gate-level schematics. Confusing AND and OR symbols can lead to incorrect designs and analyses. Given Data / Assumptions: Boolean variables A and B. Standard notation: “+” for OR, “·” (or adjacency) for AND. Concept / Approach: In Boolean algebra, addition corresponds to logical OR, and multiplication corresponds to logical AND. Therefore, A + B represents OR, while A · B (or simply AB) represents AND. The statement given swaps these meanings and is incorrect. Step-by-Step Solution: Map symbols to gates: “+” → OR gate, “·” → AND gate.Interpret the claim: It asserts OR symbol for multiplication, which is wrong.Conclude: The statement is incorrect. Verification / Alternative check: Compare truth-table behaviors: OR and AND are distinct for mixed inputs (e.g., A=1, B=0). Symbol misuse leads to contradictory results. Why Other Options Are Wrong: Context such as positive or active-LOW logic does not change algebraic symbol definitions; only signal polarity or inversion points change. Common Pitfalls: Using arithmetic intuition and transposing symbols; omitting the dot and implying wrong operation by adjacency alone. Final Answer: Incorrect

Question 19

Hardware description languages — comment syntax claim Assess the statement: “The comments in ADHL are enclosed between # characters.” Determine whether this assertion about comment delimiters is correct.

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Introduction / Context: Comment syntax varies across hardware description languages and vendor-specific dialects. Accurate knowledge of delimiters is important for toolchains to parse code correctly. This question checks a specific assertion about using the # character as a comment delimiter. Given Data / Assumptions: “ADHL” is presented as a hardware description language context. We are to judge the correctness of the claim about comment markers. Concept / Approach: Common HDLs such as VHDL and many vendor dialects do not use # as a general comment delimiter. For example, VHDL uses double hyphen for line comments. Therefore, the blanket assertion that comments are enclosed between # characters is not a correct general rule for HDL usage. Step-by-Step Solution: Identify typical HDL comment conventions (e.g., line-based double hyphen in widely used dialects).Compare with the given claim using # … #.The discrepancy indicates the statement is incorrect in the standard HDL context. Verification / Alternative check: Consulting language references or tool documentation will confirm the expected delimiters for comments and that # is not the generic enclosure. Why Other Options Are Wrong: Qualifiers about block comments or simulation-only usage do not convert the base statement into a correct general rule. Common Pitfalls: Transferring comment syntax from scripting languages (which may use #) into HDL code, leading to parsing errors. Final Answer: Incorrect

Question 20

Identify AND–OR–INVERT (AOI) implementation in logic design: outputs of two or more AND gates are combined by an OR gate, and the OR output is then inverted to produce X = (sum of products)'. Decide whether this described structure qualifies as an A…

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Introduction / Context: AND–OR–INVERT (AOI) logic is a standard gate-level realization used in digital electronics and integrated circuit libraries. It constructs a function as a sum of products using an AND stage feeding an OR stage, followed by a final inversion. Recognizing the structural pattern helps in technology mapping, reading schematics, and simplifying expressions efficiently. Given Data / Assumptions: The described network forms product terms using AND gates. Those product terms are combined by a single OR gate. The OR output is passed through one inverter to generate the final output X. No unusual encoding or extra feedback is involved. Concept / Approach: By definition, AOI implements X = (AB + CD + …)' where the inner portion is the OR of multiple ANDed terms and the final apostrophe denotes inversion. This is directly the complement of a sum-of-products, often convenient because many logic families and standard cells provide highly optimized AOI and OAI gates to reduce area and delay. Step-by-Step Solution: Form product terms using AND gates (e.g., AB, CD).Combine product terms with a single OR gate: S = (AB + CD + …).Invert the OR result: X = S'.Match with AOI template: AND → OR → INVERT, which is an AOI. Verification / Alternative check: Use De Morgan alternatives: AOI corresponds to a NAND–NAND structure when implemented with universal gates, reaffirming its classification. Why Other Options Are Wrong: Incorrect: Conflicts with the standard AOI definition.Depends on input encoding only: Encoding does not change the structural gate arrangement.Insufficient information: The description provides the full AOI pattern. Common Pitfalls: Confusing AOI with OAI (OR–AND–INVERT), which inverts the complement order of stages.Assuming AOI requires exactly two product terms; in practice, any number of AND terms can feed the OR. Final Answer: Correct

Describing Logic Circuits Questions