Multiplexer select sequencing for parallel-to-serial conversion A 16-input multiplexer (16:1 MUX) is used to perform parallel-to-serial data conversion. Which counter modulus is required to drive the MUX's data-select inputs so that all 16 inputs are scanned sequentially?

Introduction / Context:
This question checks your understanding of how a multiplexer performs parallel-to-serial conversion and how many select states are required to visit each input exactly once per frame. Correctly choosing the driving counter ensures that every parallel bit is sampled in order.

Given Data / Assumptions:

• A single 16:1 multiplexer is used.
• The goal is to serialize 16 parallel lines by time-multiplexing.
• Select inputs are binary encoded (S3 S2 S1 S0).

Concept / Approach:
A 16:1 MUX requires 4 select lines to address inputs 0 through 15. To sweep all inputs cyclically, the select lines must iterate through 16 unique states. Therefore, a 4-bit counter that counts 0..15 (a modulus-16 counter) is required.

Step-by-Step Solution:

Verification / Alternative check:
Any lesser modulus (for example, 8 or 4) would not reach all inputs; any greater modulus would repeat or produce unused states. Thus MOD-16 is both necessary and sufficient.

Why Other Options Are Wrong:

• MOD 8 / MOD 4 / MOD 2: These provide 8, 4, or 2 states respectively, which are insufficient to address 16 inputs.

Common Pitfalls:

• Confusing number of select lines (4) with modulus. Both are linked: 4 lines imply a counter cycling through 2^4 = 16 states.

Final Answer:
MOD 16