Question:

Minimum number of 2:1 Multiplexers required to design a 16:1 Multiplexer is?

Solution:

A \( 16:1 \) multiplexer has 16 inputs and 1 output. To design it using \( 2:1 \) multiplexers, we can follow a **tree structure**:

• At the first level: 16 inputs are reduced to 8 outputs. → Requires \( 8 \) multiplexers.
• At the second level: 8 outputs are reduced to 4 outputs. → Requires \( 4 \) multiplexers.
• At the third level: 4 outputs are reduced to 2 outputs. → Requires \( 2 \) multiplexers.
• At the final level: 2 outputs are reduced to 1 output. → Requires \( 1 \) multiplexer.

Therefore, total number of \( 2:1 \) MUX required is: \[ 8 + 4 + 2 + 1 = 15 \]

Answer:

Option (C) — 15