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Multiplexer sizing — Evaluate: “A four-line multiplexer must have four data inputs and two select inputs.”

Difficulty: Easy

Correct Answer: Correct

Explanation:


Introduction / Context:
A multiplexer (MUX) selects one of N inputs to route to a single output, based on select lines that encode the chosen input. This item checks recognition of the relationship between the number of data inputs and the required number of select inputs.

Given Data / Assumptions:

  • “Four-line” means 4 data inputs (N = 4).
  • Select inputs encode an integer from 0 to N−1.
  • An optional enable input may exist but is not counted among select lines.


Concept / Approach:
The number of select lines k must satisfy 2^k ≥ N. For N = 4, the minimum k is 2 because 2^2 = 4. Thus a 4-to-1 MUX uses two select inputs to choose among the four data inputs, often labeled S1 (MSB) and S0 (LSB).

Step-by-Step Solution:

Set N = 4 inputs.Find smallest k with 2^k ≥ 4 → k = 2.Conclude: a 4-to-1 MUX has 4 data inputs and 2 select inputs (plus optional enable).


Verification / Alternative check:

Standard parts like 74×153 (dual 4:1 MUX) use two select lines per 4:1 channel.


Why Other Options Are Wrong:

Incorrect: Would contradict the 2^k ≥ N requirement.Valid only for tri-state MUXes: Tri-state capability is orthogonal to select count.Depends on enable polarity: Enable polarity does not change the number of select lines.


Common Pitfalls:

Confusing enable pins with select pins.Misreading “four-line” as “four wires total” instead of four data inputs.


Final Answer:

Correct
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