Visualizing input and output data to determine black box function

I've got a black box that takes in 11 bits of input, and spits out 7 output bits. While not positive, I believe that the output is a strict function of the input.

I can observe this black box in action, collecting real world data of inputs and the associated outputs. I don't believe that all 2^11 inputs are possible in the real world.... so far across millions of samples, I'm seeing about 500 unique inputs.

How can I determine …

black box data datascience function