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

Introduction / Context:
A multiplexer (MUX) is a data selector. It routes one of many input lines to a single output based on the binary value applied to its select inputs. Correctly determining the number of select lines is essential when sizing control fields in datapaths and designing addressable signal routing.

Given Data / Assumptions:

• MUX size: 8 inputs, 1 output (8:1).
• Each unique input must be selectable with a unique binary code.
• Enable pin, if present, is not counted as a select line.

Concept / Approach:
To select among N inputs, you need enough binary codes to represent the numbers 0 through N − 1. The minimum number of select lines k satisfies 2^k ≥ N. For N = 8, the smallest k with 2^k ≥ 8 is k = 3, because 2^3 = 8 provides exactly eight unique codes (000 to 111).

Step-by-Step Solution:
Set N = 8.Find k such that 2^k ≥ 8.Compute 2^2 = 4 (insufficient), 2^3 = 8 (sufficient).Therefore, k = 3 select lines are required.

Verification / Alternative check:
Examine a standard 8:1 MUX truth table: the 3-bit select S2 S1 S0 uniquely addresses D0..D7. Any vendor datasheet (e.g., 74HC151) confirms 3 select lines for 8 inputs.

Why Other Options Are Wrong:

• 2: 2^2 = 4 addresses only four inputs.
• 4: 2^4 = 16 is more than needed for 8 inputs.
• 8: Misinterprets data inputs as select lines.

Common Pitfalls:
Counting the enable pin as a select line or assuming one select line per input. The mapping is exponential (2^k), not linear.

Final Answer:
3