MUX select-line count: for a sixteen-input (16-to-1) multiplexer, how many data-select control lines are required to address all inputs?

Introduction / Context:
Select-line count is a fundamental sizing rule for multiplexers. A 16-to-1 MUX forwards one of sixteen inputs to the output, so the number of address lines must be sufficient to encode sixteen distinct choices. This question reinforces the log2 relationship used throughout digital design.

Given Data / Assumptions:

• The device is a single 16-to-1 multiplexer.
• Binary addressing is used for the select lines.
• Optional enable pins do not replace address bits.

Concept / Approach:
With M inputs, the number of select lines s must satisfy 2^s ≥ M. For M = 16, 2^4 = 16, so s = 4. Fewer than four lines cannot uniquely address all inputs; more than four would be redundant for basic selection, though sometimes extra lines exist for hierarchical selection or banking.

Step-by-Step Solution:

Verification / Alternative check:
Commercial 16:1 MUXes (e.g., 74HC4067 analog MUX) use four address lines S0–S3 to select channels 0–15.

Why Other Options Are Wrong:
Two or three lines: 2^2 = 4 and 2^3 = 8, insufficient.
Five lines: 2^5 = 32, more than needed for 16 inputs.

Common Pitfalls:
Counting enable pins as address lines; mixing up multiplexer and decoder sizing.

Final Answer:
Four select lines