Classes of functions closed with respect to a special superposition operation

Functions of the $k$-valued logic with $k=2^m$, $m>1$ are studied in the paper. Such functions are encoded in the binary number system and a special operation of binary superposition is defined. It is shown that the set of classes containing only the functions taking not more than two values and closed under the operations of binary superposition and adding of fictitious variables is countable.