Let ܵ\(S\) denote the set of all functions \(f:\{0,1\}^4 \to \{0,1\}\). Denote…
2014
Let ܵ\(S\) denote the set of all functions \(f:\{0,1\}^4 \to \{0,1\}\). Denote by \(N\) the number of functions from S to the set {0,1}. The value of \(\log_2 \log_2N\) is _______.
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Correct answer: 16
Answer: 16
Explanation:
The set {0,1}^4 has 2^4 = 16 elements.
Each function in S assigns to each of these 16 inputs a value in {0,1}, so |S| = 2^{16}.
N is the number of functions from S to {0,1}, so N = 2^{|S|} = 2^{2^{16}}.
Therefore log2 N = 2^{16}, and log2 log2 N = log2(2^{16}) = 16.
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