Q: Consider a digital circuit that reads an n-bit input string and writes a 1bit output. Two circuits are considered different if they have a different output for some input string, otherwise they are considered the same (i.e. two circuits are considered the same if they have the same output bit for every possible input string). Count the number of different circuits.

Answer 1

Well, since there are only two outputs possible, I'd say that there are only 2 "different" circuits, regardless of the number of bits read in.

Answer 2

Steve,
will you please elaborate the answer.

Answer 3

huh? I read the problem. It says

two circuits are considered the same if they have the same output bit for every possible input string

There are only two possible output values for a single bit, so ...