Explanation:

The binary number system, being a base-$2$ system, fundamentally uses two distinct digits. These digits are $0$ and $1$. These are the foundational symbols for all digital data representation. Option (b) $1$ and $0$ is correct. Options (a) $1$ and $9$, (c) $1$ and $4$, and (d) $1$ and $2$ are incorrect because digits like $9$, $4$, and $2$ are not part of the binary system's allowed symbols. The binary system strictly operates with only $0$ and $1$ to encode information, representing 'off' and 'on' states respectively.