To implement an \(n:1\) multiplexer using only \(2:1\) multiplexers, the minimum number required is:
\[ \text{Number of 2:1 MUX} = n - 1 \]
For \(n = 16\):
\[ 16 - 1 = 15 \]
✅ Therefore, the minimum number of \(2:1\) multiplexers required to design a \(16:1\) multiplexer is: \[ \boxed{15} \]
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