Discussion
A decoder converts 'n' inputs to ......... outputs.
Answer: C
A decoder converts \(n\) inputs to \(2^{n}\) outputs.
An \(n\)-bit input can take \(2^{n}\) distinct combinations, and a full binary decoder has one output line for each, with exactly one output active for any input code. A 2-to-4 decoder has 2 inputs and 4 outputs, a 3-to-8 decoder 3 inputs and 8 outputs, and a 4-to-16 decoder 4 inputs and 16 outputs.
\(n\) outputs would mean only one per input, which is not decoding. \(n^{2}\) happens to equal \(2^{n}\) at \(n = 2\) and \(n = 4\) but not in general (for \(n = 3\) it gives 9 rather than 8), and \(n^{n}\) grows far faster than the number of possible input codes.
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