Digital Logic: Lookup Table

[ssylee]

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.

 

[Dan Coby]

ssylee wrote:

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.