Convert to and from Various Truth Table Formats

Find a pure Boolean function represented by a positional truth table.

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ImageToBooleanFunction[i_Image] := 

 BooleanFunction[Flatten[First[Binarize[i]]]]

In[2]:=

BooleanFunctionToImage[b_BooleanFunction] := 

 Image[Partition[Boole[BooleanTable[b]], 2^(BooleanVariables[b]/2)]]

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