Discussion
Number of 2-input multiplexers required to construct a \(2^{10}\) input multiplexer is :
Answer: D
The number of 2-input multiplexers is 1023.
A tree of 2-to-1 multiplexers halves the number of lines at each level. For \(2^{10} = 1024\) inputs the levels hold 512, 256, 128 and so on down to 1 multiplexer:
\[ \begin{aligned} N &= 512 + 256 + \dots + 2 + 1 \\ &= 2^{10} - 1 = 1023 \end{aligned} \]
In general an n-input multiplexer needs n - 1 two-input multiplexers. 9 is the number of select lines short by one (there are 10 levels), and 32 and 128 count only part of the tree.
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