For the question "How many unique functions can a 3-input lookup-table (LUT) implement?", I'm quite puzzled on why is the answer 2^2^8. I'm having trouble finding about the number of functions a hardware look- up table is able to implement on the internet, hence my question.
To specify a truth table for a function with N inputs, you need 2^N entries. To specify a truth table for a function with 3 inputs, you need 8 entries (i.e. 2^3).
Each of the entries in the truth table can be either a 1 or a 0. Thus there can be 2^M possible functions were M is the number of entries in the truth table. Since M = 2^N, this means that there are 2^2^N possible functions of N inputs.
There are 256 (i.e. 2^2^3 or 2^8) possible functions of 3 inputs.
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