Explanation:

In the binary number system, which represents digital states, the digit '0' universally signifies the 'off' state, a low voltage level, or a false logical condition. Conversely, the digit '1' represents the 'on' state, a high voltage, or a true logical condition. Option (b) $0$ is correct. Option (a) $1$ represents the 'on' state. Options (c) $3$, (d) $2$, and (e) $5$ are not valid single binary digits; they are decimal representations. Thus, $0$ is the correct binary representation for the 'off' state, a fundamental concept in digital electronics.