Mathematical equation for this if condition Consider a continuous signal u(t) and a binary state b. These two variables are related by the condition: If u(t) = 0 then b = 0, else b = 1. How can I relate b and u(t) in one mathematical equation while having nonzero denominator for u = 0? **Clarification:** The requirement here is to find a tractable expression converting a continuous input to a discrete output. The discrete output should be $0$ if and only if the real input is $0$.

I think the expression $$-\left\lfloor e^{-u(t)^2}-1\right\rfloor$$ will do the trick. Here "$\lfloor\cdot\rfloor$" is the greatest integer function.

To check this, note that if $u(t)=0$, the expression's value is $-\lfloor e^0-1\rfloor = -\lfloor 0\rfloor = 0$.

On the other hand, note that if $u(t)$ is nonzero, then $$0