Q: Magnitude comparator fundamentals – identify the standard trio of comparison outputs a digital magnitude comparator asserts when comparing two binary numbers A and B.

Introduction / Context: A magnitude comparator is an MSI logic device that compares two numbers and reports their relative ordering. Understanding its outputs is essential for tasks such as sorting networks, range checking, and multiword comparisons. This question asks you to recall the canonical output set that captures less-than, equality, and greater-than relationships. Given Data / Assumptions: Inputs: two unsigned binary numbers A and B of equal width. Goal: produce ordering signals indicating A B. Cascade pins may exist to chain multiple comparator ICs for wider words. Concept / Approach: The complete ordering relationship between two values can be represented by three mutually exclusive signals. A proper magnitude comparator asserts exactly one of these at a time. Many families (for example, 74xx85-type) implement these outputs and include cascade inputs so higher-order results override lower-order ties when expanding to larger bit widths. Step-by-Step Solution: Compare the most significant bit first; if unequal, decide A > B or A B pins to drive control logic. Verification / Alternative check: Review a standard comparator truth table: for any input pair, only one of the three outputs becomes active. Cascading rules ensure that a decision at a higher block suppresses conflicting indications at lower blocks. Why Other Options Are Wrong: “Sum/difference/carry” and “Cin/Cout/Sum” are adder-related. “A=B, A+B, carry” mixes comparison with arithmetic. “Overflow/zero/negative” are ALU status flags, not the basic comparator outputs. Common Pitfalls: Confusing ALU flags with comparator outputs; forgetting signed versus unsigned interpretations (magnitude comparators are typically unsigned). Final Answer: A B

Q: Terminology – another widely used name for a multiplexer, highlighting its function of choosing one of several data inputs, is ________.

Introduction / Context: Multiplexers (MUXes) are MSI devices that select one of many data inputs and forward it to a single output under the control of select lines. Industry literature and textbooks often use an alternative descriptive name that emphasizes this selection behavior. Knowing synonyms helps you recognize the same function across different vendors and families. Given Data / Assumptions: A MUX has N data inputs, log2(N) select inputs, and one output. Exactly one data input is routed at a time, determined by the select code. Enable pins may exist to gate the function. Concept / Approach: Because the essential action of a multiplexer is to select which data input reaches the output, “data selector” is a natural synonym. This distinguishes it from decoders (code → one-of-N outputs), encoders (one-of-N inputs → code), and code converters (map one code set to another). Recognizing the synonym avoids confusion when reading datasheets, where “8-channel data selector” and “8-to-1 multiplexer” refer to the same hardware primitive. Step-by-Step Solution: Map select lines to input index.Route chosen input to output; others are disconnected or ignored.Use enable to force output inactive when needed.Time-multiplex multiple signals by changing selects over time. Verification / Alternative check: Compare datasheets: 74HC151 is called an “8-channel data selector/multiplexer,” illustrating the interchangeable terminology. Why Other Options Are Wrong: An encoder/decoder performs code translation; a code converter maps between code sets; “priority filter” is not a standard digital MSI term. Common Pitfalls: Confusing a MUX’s routing role with decoding; assuming MUXes inherently change codes—they do not, they forward one selected input. Final Answer: data selector

Q: BCD versus pure binary – convert the BCD number 1000 0001 (representing the decimal value 81) into its equivalent straight binary, expressed as an 8-bit group.

Introduction / Context: Binary Coded Decimal (BCD) encodes each decimal digit separately using four bits. Converting a BCD representation to straight binary requires interpreting the two nibbles as decimal digits and then converting the resulting decimal value into ordinary base-2 form. Here, the BCD bits 1000 0001 indicate the decimal number 81; we must produce its binary equivalent as an 8-bit group for clarity and alignment with common register widths. Given Data / Assumptions: BCD 1000 0001 → high nibble 1000 (8), low nibble 0001 (1). Decimal value = 81. Output format requested: straight binary, 8 bits grouped as xxxx xxxx. Concept / Approach: First read the BCD nibbles to determine the decimal value. Then convert that decimal number to ordinary binary. For 81, compute the powers of two that sum to 81: 64 + 16 + 1. This directly yields the 8-bit pattern by setting bits corresponding to 64, 16, and 1, with all others cleared. Formatting with a space after four bits aids readability without changing the value. Step-by-Step Solution: Interpret BCD: 1000 0001 → digits “8” and “1” → decimal 81.Find binary: 81 = 64 + 16 + 1 = 2^6 + 2^4 + 2^0.Write bit pattern (MSB..LSB): 0101 0001.Confirm: 0*128 + 1*64 + 0*32 + 1*16 + 0*8 + 0*4 + 0*2 + 1*1 = 81. Verification / Alternative check: Long division by 2: 81/2 → remainders 1010001; pad to 8 bits → 0101 0001, matching the computed sum-of-powers form. Why Other Options Are Wrong: 0110 0011 = 99; 0100 0001 = 65; 1000 0000 = 128; 0011 0010 = 50. None equal 81. Common Pitfalls: Treating the BCD nibbles as a single 8-bit binary value (which would be 129), forgetting that BCD must be converted via its decimal meaning; dropping leading zeros in 8-bit formatting. Final Answer: 0101 0001

Q: Octal-to-binary encoder output width: An octal-to-binary encoder accepts eight distinct inputs (one active at a time). How many binary output bits are required to encode the active input line unambiguously?

Introduction / Context: Encoders compress one-of-M input selections into a binary word. The number of output bits required is fundamentally tied to the number of unique input lines. Understanding this relationship is essential for sizing address buses, keypad scanners, and interrupt encoders. Given Data / Assumptions: M = 8 input lines (octal domain). Exactly one input is active at a time. Unambiguous encoding is required for all input positions. Concept / Approach: The number of binary bits N needed to represent M unique states follows 2^N ≥ M. For M = 8, we need the smallest N such that 2^N ≥ 8. Since 2^3 = 8, three bits suffice. Two bits yield only four states, which is insufficient, while four bits would be more than necessary. Step-by-Step Solution: Compute: 2^2 = 4 (insufficient).Compute: 2^3 = 8 (exact fit).Thus, N = 3 bits are required.Conclude: an octal-to-binary encoder outputs three bits. Verification / Alternative check: Examine the 74148 priority encoder data: it maps eight inputs to a 3-bit binary code (active-low conventions aside). This confirms the theoretical derivation. Why Other Options Are Wrong: Two cannot represent eight states. Four or five are overprovisioned for eight states and are not minimal. Common Pitfalls: Forgetting the “power of two” relation; ignoring that priority encoders still output only N bits even when multiple inputs are asserted (priority resolves conflicts). Final Answer: three

Q: 1-of-16 decoder input width: A “1-of-16” decoder asserts exactly one of sixteen outputs for each valid binary input code. How many input bits are needed so that all 16 outputs can be uniquely selected?

Introduction / Context: Decoders perform the inverse of encoders: they expand a compact binary code into a one-hot output. Determining the minimum number of input bits is fundamental to address decoding, chip selection, and memory banking. Given Data / Assumptions: There are 16 mutually exclusive outputs. All outputs must be addressable by the input code. Inputs are binary and ideally minimal in number. Concept / Approach: To uniquely select among 16 outputs, the decoder needs N bits where 2^N = 16. Since 2^4 = 16, the minimum is N = 4 input bits. With fewer than four bits, some outputs would be unreachable. With more than four bits, the mapping is not minimal (though sometimes used for hierarchical decoding). Step-by-Step Solution: Check powers: 2^3 = 8 → insufficient.2^4 = 16 → exact match.Therefore, four input bits are required.This aligns with typical 4-to-16 decoder ICs. Verification / Alternative check: Standard parts like the 74xx154 (4-to-16 line decoder) accept 4 inputs and provide 16 active-low outputs, confirming the calculation. Why Other Options Are Wrong: Two and three bits cannot address 16 unique outputs. Six is excessive and non-minimal for selecting among sixteen lines. Common Pitfalls: Confusing demultiplexers with decoders; forgetting enable pins that gate the outputs without changing the required input width. Final Answer: four

Q: Name the device: Which MSI component generates a compact binary code at its outputs corresponding to the index of a single active numeric input line (one-hot input → coded output)?

Introduction / Context: Digital systems frequently need to compress one-of-many signals into a compact binary representation. This occurs in keypad scanners, interrupt controllers, and sensor arrays. Identifying the right MSI device ensures correct design and pin budgeting. Given Data / Assumptions: One input line at a time is active. The device outputs a binary word indicating which line is active. No arithmetic comparison or data selection among many sources to a single sink is implied. Concept / Approach: By definition, an encoder maps a one-hot or one-of-M input to an N-bit binary output. A decoder performs the reverse; a multiplexer selects one data input to drive an output; a comparator evaluates relationships between two binary words. Therefore, the correct device is an encoder. Step-by-Step Solution: Recognize mapping: one-hot input → compact code.Match with MSI definitions → encoder.Exclude other devices (decoder inverse, multiplexer selector, comparator relational logic).Conclude: the device is an encoder. Verification / Alternative check: Parts like 74148 (8-to-3) and 74HC147 implement this behavior directly, sometimes with priority to resolve multiple active inputs. Why Other Options Are Wrong: Decoder expands a code to one-hot. Multiplexer routes data rather than produces a code. Comparator outputs relation flags (less, equal, greater), not a binary index. Common Pitfalls: Assuming any single-output device is a comparator; forgetting the encoder/decoder directionality. Final Answer: an encoder

Question 1

Sizing the control interface for an 8-to-1 multiplexer: An eight-line (8:1) multiplexer requires how many data inputs and how many select inputs to address them uniquely?

Accepted Answer

Introduction / Context: A multiplexer (MUX) selects one of N data inputs based on a binary address applied to its select lines. Determining the required number of select pins is a straightforward application of binary addressing, yet it is a frequent source of simple design errors when scaling channel counts. Given Data / Assumptions: Target device: 8:1 MUX (eight inputs, one output). Binary addressing: k select lines can uniquely address up to 2^k inputs. No additional enable line is assumed in the count of “select lines.” Concept / Approach: To choose among eight inputs uniquely, the address space must cover 8 states. Since 2^3 = 8, exactly three select inputs are needed. The MUX also, by definition, has eight data inputs (D0–D7). Therefore, an 8:1 multiplexer has eight data inputs and three select inputs. This mapping generalizes: an N:1 MUX needs log2(N) select lines, rounded up to the next integer when N is not a power of two. Step-by-Step Solution: Compute number of selects: find k such that 2^k ≥ 8 → k = 3.List interface: data inputs D0…D7 (eight total) plus select inputs S2 S1 S0 (three total).Confirm uniqueness: each 3-bit code selects exactly one of the eight inputs. Verification / Alternative check: Examine common parts like the 74151: it is an 8:1 MUX with three select lines (S2 S1 S0) and one enable. The enable does not change the addressing requirement; it only gates the output, confirming the count of three select inputs for eight data inputs. Why Other Options Are Wrong: Four data inputs: describes a 4:1 MUX, not 8:1.Two select inputs: 2^2 = 4, insufficient to address eight inputs.Four select inputs: 2^4 = 16, more than required for eight inputs.Sixteen data inputs: describes a 16:1 MUX, not 8:1. Common Pitfalls: Confusing enable/strobe pins with select pins, and miscounting required select lines by forgetting the log2(N) relationship. Final Answer: eight data inputs and three select inputs

Question 2

AHDL BCD-to-binary converter design – in hardware description terms, when converting a multi-digit BCD value to its equivalent pure binary, is the multiplication-by-10 step implemented directly using the language’s arithmetic capability, i.e., by us…

Accepted Answer

Introduction / Context: When building a Binary Coded Decimal (BCD) to pure binary converter in a hardware description language such as AHDL, a common subtask is multiplying an accumulated result by 10 as you process each new BCD digit. This question probes whether that “times ten” operation is typically realized using the language’s arithmetic operator, or whether it relies on shifts, special library calls, or type declarations. Given Data / Assumptions: Source format: BCD digits, usually groups of 4 bits per decimal digit. Target format: unsigned binary integer able to hold the full decimal value. Design context: synthesizable AHDL targeting PLDs/CPLDs/FPGAs. Arithmetic is permitted in the HDL and mapped to hardware by synthesis. Concept / Approach: The textbook algorithm for multi-digit conversion iterates through digits and applies result = result * 10 + next_digit. In an HDL, “*” denotes multiplication. Synthesis tools infer the required hardware: either LUT-based multipliers or dedicated DSP blocks. While shifts and adds can also realize *10 via (x << 3) + (x << 1), the direct, intention-revealing way is to use the multiplication operator and allow the tool to optimize the precise implementation. Step-by-Step Solution: Initialize binary_result = 0.For each incoming BCD digit d: binary_result = binary_result * 10 + d.In AHDL, write “* 10” explicitly; the synthesizer generates hardware.Constrain or let the tool choose resources (DSP vs logic) for area/speed. Verification / Alternative check: Implementations using (x << 3) + (x << 1) are mathematically equivalent to *10 and may save resources on very small devices, but they are optional micro-optimizations. The presence of “*” remains the canonical language feature for multiplication. Why Other Options Are Wrong: “Shifting bits” is a technique, not the primary language construct. “A library function” is unnecessary for simple scaling. “A variable type” cannot perform arithmetic. “A clock enable signal” controls timing, not math operations. Common Pitfalls: Forgetting to size the accumulator wide enough; omitting unsigned/signed intent; assuming multiplication cannot be synthesized (modern tools support it well). Final Answer: a multiplication operator

Question 3

Magnitude comparator fundamentals – identify the standard trio of comparison outputs a digital magnitude comparator asserts when comparing two binary numbers A and B.

Accepted Answer

Introduction / Context: A magnitude comparator is an MSI logic device that compares two numbers and reports their relative ordering. Understanding its outputs is essential for tasks such as sorting networks, range checking, and multiword comparisons. This question asks you to recall the canonical output set that captures less-than, equality, and greater-than relationships. Given Data / Assumptions: Inputs: two unsigned binary numbers A and B of equal width. Goal: produce ordering signals indicating A < B, A = B, or A > B. Cascade pins may exist to chain multiple comparator ICs for wider words. Concept / Approach: The complete ordering relationship between two values can be represented by three mutually exclusive signals. A proper magnitude comparator asserts exactly one of these at a time. Many families (for example, 74xx85-type) implement these outputs and include cascade inputs so higher-order results override lower-order ties when expanding to larger bit widths. Step-by-Step Solution: Compare the most significant bit first; if unequal, decide A > B or A < B.If MSBs match, proceed to next bits until a difference is found.If all bits match, assert the equality output.Expose the result on AB pins to drive control logic. Verification / Alternative check: Review a standard comparator truth table: for any input pair, only one of the three outputs becomes active. Cascading rules ensure that a decision at a higher block suppresses conflicting indications at lower blocks. Why Other Options Are Wrong: “Sum/difference/carry” and “Cin/Cout/Sum” are adder-related. “A=B, A+B, carry” mixes comparison with arithmetic. “Overflow/zero/negative” are ALU status flags, not the basic comparator outputs. Common Pitfalls: Confusing ALU flags with comparator outputs; forgetting signed versus unsigned interpretations (magnitude comparators are typically unsigned). Final Answer: A < B, A = B, and A > B

Question 4

Encoder I/O count – for a decimal-to-BCD encoder, how many separate data input lines exist to represent digits 0 through 9 before encoding them into 4-bit BCD?

Accepted Answer

Introduction / Context: An encoder converts one-of-N active inputs into a binary code. The decimal-to-BCD encoder is a classic example found in learning laboratories and MSI catalogs. It accepts decimal digit lines and outputs a 4-bit Binary Coded Decimal representation. This question asks you to recall how many input lines such an encoder must have to cover digits 0–9. Given Data / Assumptions: Decimal digits: 0,1,2,3,4,5,6,7,8,9 (ten distinct symbols). BCD code width: 4 bits (0000 to 1001 used for 0–9). Only one input line is active at a time in the basic (non-priority) encoder. Concept / Approach: Each decimal symbol must have a unique input wire in a simple one-hot interface. Therefore, a decimal-to-BCD encoder requires ten data inputs, each corresponding to a digit. The internal logic maps whichever input is asserted to its 4-bit BCD code on the outputs. Priority encoders extend this idea by resolving conflicts if multiple inputs are asserted simultaneously, typically choosing the highest-priority (largest) digit and producing a valid BCD code plus a “valid” flag. Step-by-Step Solution: List the symbols to be encoded: {0…9} → count = 10.Assign one input line per symbol: I0…I9.Map active input Ik to BCD code of k on outputs Q3..Q0.Confirm width: 4-bit BCD covers up to 9, with 10–15 typically unused or treated as don’t-cares. Verification / Alternative check: Check any standard truth table for a decimal-to-BCD encoder: exactly ten inputs are listed, with corresponding 4-bit outputs and often an “enable” and “valid” pin. Why Other Options Are Wrong: Two, four, five, and sixteen do not match the count of decimal symbols; sixteen would be appropriate for hexadecimal encoders, not decimal. Common Pitfalls: Confusing encoders with decoders (decoders have one code input and many outputs); mixing decimal and hexadecimal contexts. Final Answer: ten

Question 5

Identify the device – which logic circuit accepts an n-bit binary number at its inputs and asserts exactly one output line corresponding to that input value?

Accepted Answer

Introduction / Context: Many MSI building blocks appear similar but perform distinct roles. A decoder translates a compact binary code into a one-hot output where exactly one line is asserted for a valid input value. This is foundational for address decoding, memory selection, and enabling subsystems inside digital designs. Given Data / Assumptions: Inputs: an n-bit binary value. Outputs: 2^n lines where a single line is active at any time for valid input. Enable pins may gate the device on/off without changing the mapping. Concept / Approach: With n input bits, a decoder generates one-of-2^n outputs. For example, a 3-to-8 decoder asserts exactly one of eight outputs based on the 3-bit input. This behavior differs from an encoder (one-of-N inputs to binary code) and a demultiplexer (routes a single input signal to one of many outputs as selected, not based on the numerical value presented across multiple input bits). Understanding these distinctions is crucial when selecting parts for address decoding versus signal routing. Step-by-Step Solution: Recognize: numerical code in → one-hot line out.Count outputs: 2^n for n inputs (e.g., 2^3 = 8 for 3-to-8).Note: enable pin must be active for decoding to occur.Apply to memory maps: address bits drive decoders to select chips or banks. Verification / Alternative check: Device datasheets (e.g., 74HC138/238) show truth tables where only one Y output is low (active) for any input combination when enabled, confirming the one-hot mapping. Why Other Options Are Wrong: An LED is a display element; an encoder performs the inverse function; a demultiplexer routes a single data line to one output rather than decoding a multi-bit numeric input; a “priority latch” is not a standard device for this role. Common Pitfalls: Confusing decoder selection with demultiplexing; overlooking active-low outputs in some families which invert the active level. Final Answer: decoder

Question 6

Octal (1-of-8) decoder basics – a 1-of-8 decoder asserts one of eight outputs and therefore requires how many binary input bit(s) to select among those outputs?

Accepted Answer

Introduction / Context: Decoders translate binary input codes into one-of-N outputs. The “octal” or 1-of-8 decoder is a common MSI element used in address selection and control. Determining the number of input bits required is a direct application of the 2^n relationship between inputs and outputs in decoding logic. Given Data / Assumptions: Outputs: 8 distinct lines, exactly one asserted for any valid input. Mapping: with n bits, you can represent 2^n states. Enable pins may be present but do not add to the selection width. Concept / Approach: You need enough input bits to index all eight outputs uniquely. Since 2^3 = 8, three input bits are sufficient and necessary. This is why devices such as the 74HC138 are described as “3-to-8 decoders.” The enable inputs control whether any decoding occurs but do not increase the selection count; they simply gate the outputs on or off as a group. Step-by-Step Solution: Compute n from 2^n = 8 → n = 3.Assign inputs A2 A1 A0 to select outputs Y0..Y7.Confirm one-hot behavior in truth table when enable is active.Use for address decode of 3-bit fields in larger maps. Verification / Alternative check: Any standard 3-to-8 decoder datasheet confirms the mapping and shows enable-controlled output polarity (often active-low outputs). Why Other Options Are Wrong: Two bits cover only 4 outputs; four bits cover 16 outputs; one bit covers 2 outputs; five bits cover 32 outputs—none match the 8-output case. Common Pitfalls: Counting enable pins as “inputs” for selection; ignoring active-low conventions that might hide the one-hot nature at first glance. Final Answer: three

Question 7

Identify the pictured device and outcome – given a typical digital routing symbol with select lines and labeled outputs D0…D7, determine whether the device is a demultiplexer and, for the shown timing of selects and data, which output (e.g., D3) is …

Accepted Answer

Introduction / Context: Without the original figure, we apply the Recovery-First Policy and infer a standard scenario: a single data input is routed to one of many outputs via select lines, and the waveform timing indicates that output line D3 is selected at the marked instant X. Your task is to identify the device type and predict the logic level at the selected output and at the nonselected outputs. Given Data / Assumptions: The symbol shows one data input, multiple labeled outputs (D0…DN−1), and select inputs S that choose which output is active. At time X, the select code corresponds to line D3. Data input is asserted (logic HIGH) at the same instant. Nonselected outputs remain inactive (logic LOW for active-high style). Concept / Approach: A demultiplexer (DEMUX) performs controlled distribution: it takes a single input and forwards it to one chosen output. If the input is HIGH and D3 is selected, the D3 output becomes HIGH, while all other outputs stay LOW. A decoder, by contrast, asserts one of many outputs based purely on the numeric value of the binary input code rather than routing a separate data input, and a multiplexer does the inverse (many inputs to one output). Step-by-Step Solution: Recognize topology: 1 input → N outputs plus select signals → DEMUX.Read select code at time X: S selects line index 3 → target output D3.Propagate data: with Din = HIGH, the selected output mirrors Din.Conclude: D3 = HIGH; all other outputs = LOW at X. Verification / Alternative check: Cross-check with a truth table of a 1-to-8 DEMUX: when S = 011 (binary 3), Y3 follows Din and Yk≠3 are forced LOW (assuming active-high noninverted outputs and enable asserted). Why Other Options Are Wrong: Multiplexer choice reverses data flow (many-to-one). “LOW, HIGH” polarity contradicts selected-output mirroring. “Decoder, D12” is inconsistent with the labeling and routing role. “Encoder” converts one-of-N to binary, not relevant here. Common Pitfalls: Forgetting output polarity (some families use active-low outputs); neglecting the enable pin, which would force all outputs inactive if deasserted. Final Answer: demultiplexer, D3, HIGH, LOW

Question 8

Priority encoder behavior – if multiple inputs are asserted simultaneously, what does a priority encoder do to resolve the conflict in its encoded output?

Accepted Answer

Introduction / Context: Standard encoders assume only one input is high at a time. Real systems, however, may present multiple active inputs. Priority encoders are designed to handle such conflicts deterministically by assigning precedence to higher-order inputs, guaranteeing a valid output code and a predictable arbitration outcome. Given Data / Assumptions: Inputs: multiple lines, any of which may be asserted concurrently. Priority scheme: higher-numbered (more significant) input has precedence. Outputs: encoded binary index and usually a “valid” indicator. Concept / Approach: A priority encoder scans inputs according to a predefined order and encodes the index of the highest-priority asserted input. In practice, this means lower-priority (less significant) inputs are ignored if a higher-priority line is active. This behavior ensures stable operation in interrupt controllers, bus arbiters, and keyboard encoders where multiple events may coincide. Step-by-Step Solution: Define priority: e.g., I7 highest … I0 lowest.Observe asserted set S; choose the highest index k in S.Output binary code for k; assert “valid” output if any input is active.Ignore all inputs with index < k for the current cycle. Verification / Alternative check: Truth tables for 74xx148-type devices show that when multiple inputs are low (active for active-low inputs), the output corresponds to the highest-priority one and the rest are masked, confirming the ignore behavior for lesser inputs. Why Other Options Are Wrong: Entering fault mode would defeat the purpose of priority handling. “Resampling” does not resolve simultaneous assertion. “Finds some other input” is undefined and non-deterministic. Asserting all outputs simultaneously is nonsensical for an encoder. Common Pitfalls: Forgetting active-low conventions (many priority encoders use active-low inputs/outputs). Misunderstanding that “ignoring least significant” really means “honoring the most significant first.” Final Answer: ignores the least significant input

Question 9

Terminology – another widely used name for a multiplexer, highlighting its function of choosing one of several data inputs, is ________.

Accepted Answer

Introduction / Context: Multiplexers (MUXes) are MSI devices that select one of many data inputs and forward it to a single output under the control of select lines. Industry literature and textbooks often use an alternative descriptive name that emphasizes this selection behavior. Knowing synonyms helps you recognize the same function across different vendors and families. Given Data / Assumptions: A MUX has N data inputs, log2(N) select inputs, and one output. Exactly one data input is routed at a time, determined by the select code. Enable pins may exist to gate the function. Concept / Approach: Because the essential action of a multiplexer is to select which data input reaches the output, “data selector” is a natural synonym. This distinguishes it from decoders (code → one-of-N outputs), encoders (one-of-N inputs → code), and code converters (map one code set to another). Recognizing the synonym avoids confusion when reading datasheets, where “8-channel data selector” and “8-to-1 multiplexer” refer to the same hardware primitive. Step-by-Step Solution: Map select lines to input index.Route chosen input to output; others are disconnected or ignored.Use enable to force output inactive when needed.Time-multiplex multiple signals by changing selects over time. Verification / Alternative check: Compare datasheets: 74HC151 is called an “8-channel data selector/multiplexer,” illustrating the interchangeable terminology. Why Other Options Are Wrong: An encoder/decoder performs code translation; a code converter maps between code sets; “priority filter” is not a standard digital MSI term. Common Pitfalls: Confusing a MUX’s routing role with decoding; assuming MUXes inherently change codes—they do not, they forward one selected input. Final Answer: data selector

Question 10

BCD versus pure binary – convert the BCD number 1000 0001 (representing the decimal value 81) into its equivalent straight binary, expressed as an 8-bit group.

Accepted Answer

Introduction / Context: Binary Coded Decimal (BCD) encodes each decimal digit separately using four bits. Converting a BCD representation to straight binary requires interpreting the two nibbles as decimal digits and then converting the resulting decimal value into ordinary base-2 form. Here, the BCD bits 1000 0001 indicate the decimal number 81; we must produce its binary equivalent as an 8-bit group for clarity and alignment with common register widths. Given Data / Assumptions: BCD 1000 0001 → high nibble 1000 (8), low nibble 0001 (1). Decimal value = 81. Output format requested: straight binary, 8 bits grouped as xxxx xxxx. Concept / Approach: First read the BCD nibbles to determine the decimal value. Then convert that decimal number to ordinary binary. For 81, compute the powers of two that sum to 81: 64 + 16 + 1. This directly yields the 8-bit pattern by setting bits corresponding to 64, 16, and 1, with all others cleared. Formatting with a space after four bits aids readability without changing the value. Step-by-Step Solution: Interpret BCD: 1000 0001 → digits “8” and “1” → decimal 81.Find binary: 81 = 64 + 16 + 1 = 2^6 + 2^4 + 2^0.Write bit pattern (MSB..LSB): 0101 0001.Confirm: 0*128 + 1*64 + 0*32 + 1*16 + 0*8 + 0*4 + 0*2 + 1*1 = 81. Verification / Alternative check: Long division by 2: 81/2 → remainders 1010001; pad to 8 bits → 0101 0001, matching the computed sum-of-powers form. Why Other Options Are Wrong: 0110 0011 = 99; 0100 0001 = 65; 1000 0000 = 128; 0011 0010 = 50. None equal 81. Common Pitfalls: Treating the BCD nibbles as a single 8-bit binary value (which would be 129), forgetting that BCD must be converted via its decimal meaning; dropping leading zeros in 8-bit formatting. Final Answer: 0101 0001

Question 11

Function identification – the logic device that takes a single input data line and routes it to exactly one of several outputs under control of select lines is called a ________.

Accepted Answer

Introduction / Context: In digital systems, you often need to distribute a signal to one of many destinations under programmable control. The primitive that performs this fan-out selection is not a decoder (which maps binary codes to one-hot outputs) nor a multiplexer (many inputs to one output), but the device that effectively performs the inverse of a multiplexer with respect to signal routing. Given Data / Assumptions: There is one data input signal D. There are multiple output lines Y0…YN−1. Select inputs choose which single output should carry D. Only the chosen output follows D; others are forced inactive. Concept / Approach: A demultiplexer (DEMUX) sends the single input to one selected output. If D toggles, the selected output mirrors those toggles while nonselected outputs remain at their inactive level. In some families outputs may be active-low; the routing principle remains unchanged. DEMUXes are used in time-division distribution, addressable control lines, and DAC channel selection when a separate sample-and-hold captures the routed signal downstream. Step-by-Step Solution: Identify the direction: 1 input → N outputs (selection-driven).Tie selects to a binary code to choose the destination output.Ensure enable is active; otherwise outputs are all inactive.Observe that only one output follows D at any instant. Verification / Alternative check: Compare to a multiplexer: a MUX performs N inputs → 1 output, the directional opposite of DEMUX. Decoder: code → one-hot outputs, no routed data line. This confirms naming and functional differences. Why Other Options Are Wrong: Multiplexer is the inverse routing element; comparator evaluates magnitudes; counter produces sequences; priority encoder selects among many inputs to produce an encoded index, not to route a separate data stream. Common Pitfalls: Confusing DEMUX with decoder due to similar select lines; forgetting active-low conventions that might invert apparent logic levels on outputs. Final Answer: demultiplexer

Question 12

MSI fundamentals — identify the component: A digital device has several input lines, exactly one of which is asserted (active) at any given time. Depending on which single input is active, the device produces an N-bit binary code at its outputs that…

Accepted Answer

Introduction / Context: This question targets medium-scale integration (MSI) building blocks used in digital systems. Many textbooks distinguish between devices that select among inputs (multiplexers), distribute one input to many outputs (demultiplexers), translate between codes (encoders/decoders), and compare binary words (comparators). Here, the behavior described is one-hot to binary coding, which is foundational in keyboards, interrupt systems, and priority logic. Given Data / Assumptions: There are multiple input lines; at most one is asserted at a time. The output is an N-bit binary word representing the index (or identity) of the active input. We ignore tie cases (simultaneous inputs) unless a priority version is implied. Outputs are stable for valid, single-active input conditions. Concept / Approach: An encoder converts a one-hot (or one-of-2^N) input pattern into an N-bit binary code. A classic example is an octal-to-binary encoder that maps eight inputs to a 3-bit output. A decoder performs the inverse mapping: an N-bit code word selects one of 2^N outputs. A demultiplexer routes one input line to one of many outputs under control of select lines, not to a binary code. Step-by-Step Solution: Identify mapping direction: many inputs (one active) → compact N-bit code.Match with standard MSI definitions: this is the function of an encoder.Exclude other categories: a decoder is code to one-hot; a demultiplexer is data distribution; a code converter may change code formats but not necessarily one-hot to binary.Therefore, the correct classification is “encoder.” Verification / Alternative check: Part families such as 74148 (8-to-3 priority encoder) and 74HC147 demonstrate exactly this behavior. Their truth tables show a single asserted input producing a binary code on the outputs. Why Other Options Are Wrong: Code converter is too generic and does not imply one-hot to binary with a single active input. Demultiplexer distributes a single input to one of many outputs. Decoder is the inverse of the described behavior. Common Pitfalls: Confusing encoder/decoder directions; overlooking priority encoders where multiple actives are resolved by priority, yet the device is still an encoder. Final Answer: encoder

Question 13

Octal-to-binary encoder output width: An octal-to-binary encoder accepts eight distinct inputs (one active at a time). How many binary output bits are required to encode the active input line unambiguously?

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Introduction / Context: Encoders compress one-of-M input selections into a binary word. The number of output bits required is fundamentally tied to the number of unique input lines. Understanding this relationship is essential for sizing address buses, keypad scanners, and interrupt encoders. Given Data / Assumptions: M = 8 input lines (octal domain). Exactly one input is active at a time. Unambiguous encoding is required for all input positions. Concept / Approach: The number of binary bits N needed to represent M unique states follows 2^N ≥ M. For M = 8, we need the smallest N such that 2^N ≥ 8. Since 2^3 = 8, three bits suffice. Two bits yield only four states, which is insufficient, while four bits would be more than necessary. Step-by-Step Solution: Compute: 2^2 = 4 (insufficient).Compute: 2^3 = 8 (exact fit).Thus, N = 3 bits are required.Conclude: an octal-to-binary encoder outputs three bits. Verification / Alternative check: Examine the 74148 priority encoder data: it maps eight inputs to a 3-bit binary code (active-low conventions aside). This confirms the theoretical derivation. Why Other Options Are Wrong: Two cannot represent eight states. Four or five are overprovisioned for eight states and are not minimal. Common Pitfalls: Forgetting the “power of two” relation; ignoring that priority encoders still output only N bits even when multiple inputs are asserted (priority resolves conflicts). Final Answer: three

Question 14

1-of-16 decoder input width: A “1-of-16” decoder asserts exactly one of sixteen outputs for each valid binary input code. How many input bits are needed so that all 16 outputs can be uniquely selected?

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Introduction / Context: Decoders perform the inverse of encoders: they expand a compact binary code into a one-hot output. Determining the minimum number of input bits is fundamental to address decoding, chip selection, and memory banking. Given Data / Assumptions: There are 16 mutually exclusive outputs. All outputs must be addressable by the input code. Inputs are binary and ideally minimal in number. Concept / Approach: To uniquely select among 16 outputs, the decoder needs N bits where 2^N = 16. Since 2^4 = 16, the minimum is N = 4 input bits. With fewer than four bits, some outputs would be unreachable. With more than four bits, the mapping is not minimal (though sometimes used for hierarchical decoding). Step-by-Step Solution: Check powers: 2^3 = 8 → insufficient.2^4 = 16 → exact match.Therefore, four input bits are required.This aligns with typical 4-to-16 decoder ICs. Verification / Alternative check: Standard parts like the 74xx154 (4-to-16 line decoder) accept 4 inputs and provide 16 active-low outputs, confirming the calculation. Why Other Options Are Wrong: Two and three bits cannot address 16 unique outputs. Six is excessive and non-minimal for selecting among sixteen lines. Common Pitfalls: Confusing demultiplexers with decoders; forgetting enable pins that gate the outputs without changing the required input width. Final Answer: four

Question 15

Name the device: Which MSI component generates a compact binary code at its outputs corresponding to the index of a single active numeric input line (one-hot input → coded output)?

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Introduction / Context: Digital systems frequently need to compress one-of-many signals into a compact binary representation. This occurs in keypad scanners, interrupt controllers, and sensor arrays. Identifying the right MSI device ensures correct design and pin budgeting. Given Data / Assumptions: One input line at a time is active. The device outputs a binary word indicating which line is active. No arithmetic comparison or data selection among many sources to a single sink is implied. Concept / Approach: By definition, an encoder maps a one-hot or one-of-M input to an N-bit binary output. A decoder performs the reverse; a multiplexer selects one data input to drive an output; a comparator evaluates relationships between two binary words. Therefore, the correct device is an encoder. Step-by-Step Solution: Recognize mapping: one-hot input → compact code.Match with MSI definitions → encoder.Exclude other devices (decoder inverse, multiplexer selector, comparator relational logic).Conclude: the device is an encoder. Verification / Alternative check: Parts like 74148 (8-to-3) and 74HC147 implement this behavior directly, sometimes with priority to resolve multiple active inputs. Why Other Options Are Wrong: Decoder expands a code to one-hot. Multiplexer routes data rather than produces a code. Comparator outputs relation flags (less, equal, greater), not a binary index. Common Pitfalls: Assuming any single-output device is a comparator; forgetting the encoder/decoder directionality. Final Answer: an encoder

MSI Logic Circuits Questions